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https://uniontestprep.com/gre/discussions/i-don-t-understand-how-the-second-answer-is-e | 1,670,468,139,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711232.54/warc/CC-MAIN-20221208014204-20221208044204-00610.warc.gz | 625,076,199 | 12,448 | Back to All Topics
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# I don't understand how the second answer is E
Which 2 ways can 2t-u+3v be expressed in terms of v, if 5t=2u & u-1=v?
A. 1/5(14v-1) B. 2V-3 C. (20+140V)/100 D. 1/4V+20 E. 2.8V-.2
Answer choices: A) A&D B) A&B C) B&E D) A&E
I see what they did to get A, but how did they get E?
Jessica King
Added on February 16, 2019 23:27
0
## 1 Response
If you agree that 1/5(14V-1) is an answer, which is choice A then just distribute the 1/5 and get: (14/5)V - (1/5). Here (14/5) = 2.8 and (1/5) = 0.2. Good Luck!
Tashfeen
Responded on September 18, 2019 00:17
0 | 274 | 718 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.8125 | 4 | CC-MAIN-2022-49 | latest | en | 0.88454 | Back to All Topics. Start a Discussion. Start a new discussion whenever you’re not finding the answers you’re looking for or looking to share something new.. # I don't understand how the second answer is E. Which 2 ways can 2t-u+3v be expressed in terms of v, if 5t=2u & u-1=v?. A. 1/5(14v-1) B. 2V-3 C. (20+140V)/100 D. 1/4V+20 E. 2.8V-.2. Answer choices: A) A&D B) A&B C) B&E D) A&E. | I see what they did to get A, but how did they get E?. Jessica King. Added on February 16, 2019 23:27. 0. ## 1 Response. If you agree that 1/5(14V-1) is an answer, which is choice A then just distribute the 1/5 and get: (14/5)V - (1/5). Here (14/5) = 2.8 and (1/5) = 0.2. Good Luck!. Tashfeen. Responded on September 18, 2019 00:17. 0. |
https://www.physicsforums.com/tags/unit-vectors/ | 1,713,002,798,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816587.89/warc/CC-MAIN-20240413083102-20240413113102-00856.warc.gz | 880,022,962 | 27,488 | # What is Unit vectors: Definition and 140 Discussions
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in
v
^
{\displaystyle {\hat {\mathbf {v} }}}
(pronounced "v-hat").The term direction vector is used to describe a unit vector being used to represent spatial direction, and such quantities are commonly denoted as d; 2D spatial directions represented this way are numerically equivalent to points on the unit circle.
The same construct is used to specify spatial directions in 3D, which are equivalent to a point on the unit sphere.
The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e.,
u
^
=
u
|
u
|
{\displaystyle \mathbf {\hat {u}} ={\frac {\mathbf {u} }{|\mathbf {u} |}}}
where |u| is the norm (or length) of u. The term normalized vector is sometimes used as a synonym for unit vector.
Unit vectors are often chosen to form the basis of a vector space, and every vector in the space may be written as a linear combination of unit vectors.
By definition, the dot product of two unit vectors in a Euclidean space is a scalar value amounting to the cosine of the smaller subtended angle. In three-dimensional Euclidean space, the cross product of two arbitrary unit vectors is a third vector orthogonal to both of them, whose length is equal to the sine of the smaller subtended angle. The normalized cross product corrects for this varying length, and yields the mutually orthogonal unit vector to the two inputs, applying the right-hand rule to resolve one of two possible directions.
View More On Wikipedia.org
1. ### Help about the unit vectors for polar coordinates in terms of i and j
"Firstly, I represented [Uθ ]on the two-dimensional polar coordinate system to facilitate the steps and projections." Then, I have written the steps, step by step, to ultimately derive the expression U(θ) in terms of i and j which is: [ Uθ=−sin(θ)i+cos(θ)j ] NOTE: The professor provided us...
2. ### I Law of Cosines in Linear Algebra: Understanding the Dot Product of Unit Vectors
HI, I am studying linear algebra, and I just can't understand why "Unit vectors u and U at angle θ have u multiplied by U=cosθ Why is it like that? Thanks
4. ### Displacement problem with unit vectors
(a) I did (7.07*4.1)-(-7.03*3.94)=56.7 with this method I got this answer correct in my first attempt. (b) This where I seem to have gone wrong. I used a · b = (axbx +ayby) then I used a = sqrt(ax2+ay2) to get a single number for the answer. Filling in the numbers 7.07*-7.03 + 4.94*4.1 =...
5. ### B Problem involving unit vectors
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6. ### Understanding Direction of Unit Vectors r roof & phi roof
The unit vector r roof points in the direction of increasing r with phi fixed; phi roof points in the direction of increasing phi with r fixed. Unlike x roof, the vectors r roof and phi roof change as the position vector r moves. What I was thinking of the image is Although, I was thinking why...
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Hi, what is a unit vector? I mean, it is ##\hat{A}=\vec A/|A|##. A dimensionless vector with modulus (absolute value) one, I've read somewhere. So, dimensionless with modulus. Isn't that a contradiction? I mean, absolute value regardless dimension? Am I out of context?. ##\Bbb R^3## is a...
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9. ### How Can I Solve Question Type: "With Magnitude and Unit Vectors"?
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What is the advantage of using a polar coordinate system with rotating unit vectors? Kleppner's and Kolenkow's An Introduction to Mechanics states that base vectors ##\mathbf{ \hat{r}}## and ##\mathbf{\hat{\theta}}## have a variable direction, such that for a Cartesian coordinates system's base...
12. ### I Polar coordinates and unit vectors
Hello, I get that both polar unit vectors, ##\hat{r}## and ##\hat{\theta}##, are unit vectors whose directions varies from point to point in the plane. In polar coordinates, the location of an arbitrary point ##P## on the plane is solely given in terms of one of the unit vector, the vector...
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17. K
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50. ### Calculation of work involving unit vectors
Homework Statement A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force f = (30N)i - (40N)j to the cart as it undergoes a displacement s = (-9.0m)i - (3.0m)j How much work does the force you apply do on the grocery cart? Homework Equations... | 4,730 | 17,853 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2024-18 | latest | en | 0.929295 | # What is Unit vectors: Definition and 140 Discussions. In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in. v. ^. {\displaystyle {\hat {\mathbf {v} }}}. (pronounced "v-hat").The term direction vector is used to describe a unit vector being used to represent spatial direction, and such quantities are commonly denoted as d; 2D spatial directions represented this way are numerically equivalent to points on the unit circle.. The same construct is used to specify spatial directions in 3D, which are equivalent to a point on the unit sphere.. The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e.,. u. ^. =. u. |. u. |. {\displaystyle \mathbf {\hat {u}} ={\frac {\mathbf {u} }{|\mathbf {u} |}}}. where |u| is the norm (or length) of u. The term normalized vector is sometimes used as a synonym for unit vector.. Unit vectors are often chosen to form the basis of a vector space, and every vector in the space may be written as a linear combination of unit vectors.. By definition, the dot product of two unit vectors in a Euclidean space is a scalar value amounting to the cosine of the smaller subtended angle. In three-dimensional Euclidean space, the cross product of two arbitrary unit vectors is a third vector orthogonal to both of them, whose length is equal to the sine of the smaller subtended angle. The normalized cross product corrects for this varying length, and yields the mutually orthogonal unit vector to the two inputs, applying the right-hand rule to resolve one of two possible directions.. View More On Wikipedia.org. 1. ### Help about the unit vectors for polar coordinates in terms of i and j. "Firstly, I represented [Uθ ]on the two-dimensional polar coordinate system to facilitate the steps and projections." Then, I have written the steps, step by step, to ultimately derive the expression U(θ) in terms of i and j which is: [ Uθ=−sin(θ)i+cos(θ)j ] NOTE: The professor provided us.... 2. ### I Law of Cosines in Linear Algebra: Understanding the Dot Product of Unit Vectors. HI, I am studying linear algebra, and I just can't understand why "Unit vectors u and U at angle θ have u multiplied by U=cosθ Why is it like that? Thanks. 4. ### Displacement problem with unit vectors. (a) I did (7.07*4.1)-(-7.03*3.94)=56.7 with this method I got this answer correct in my first attempt. (b) This where I seem to have gone wrong. I used a · b = (axbx +ayby) then I used a = sqrt(ax2+ay2) to get a single number for the answer. Filling in the numbers 7.07*-7.03 + 4.94*4.1 =.... 5. ### B Problem involving unit vectors. For example is this correct : 19icap.4(-i cap) = 76(i.-i)= 76 Or is it , take - out. Then -76(icap.icap)= -76 Is it -76 or 76 ?. 6. ### Understanding Direction of Unit Vectors r roof & phi roof. The unit vector r roof points in the direction of increasing r with phi fixed; phi roof points in the direction of increasing phi with r fixed. Unlike x roof, the vectors r roof and phi roof change as the position vector r moves. What I was thinking of the image is Although, I was thinking why.... 7. ### Unit vectors -- How can they be dimensionless?. Hi, what is a unit vector? I mean, it is ##\hat{A}=\vec A/|A|##. A dimensionless vector with modulus (absolute value) one, I've read somewhere. So, dimensionless with modulus. Isn't that a contradiction? I mean, absolute value regardless dimension? Am I out of context?. ##\Bbb R^3## is a.... 8. ### Calculating vector cross product through unit vectors. Writing both ##\vec{U}## and ##\vec{B}## with magnitude in all the three spatial coordinates: $$\vec{U}\times \vec{B}= (U_{x}\cdot \widehat{i}+U_{y}\cdot \widehat{j}+U_{z}\cdot \widehat{k})\times (B_{x}\cdot \widehat{i}+B_{y}\cdot \widehat{j}+B_{z}\cdot \widehat{k})$$ From this point on, I.... 9. ### How Can I Solve Question Type: "With Magnitude and Unit Vectors"?. Hi I am a beginner in this topic. I didn't understand this question type clearly.What does it mean" With Magnitude and Unit Vectors" exactly? May you help me for the solution step by step :). Thanks in advance.. 10. ### What's the use of unit vectors?. Homework Statement: Hallo. Can somebody explain to me what's the importance-use of unit vector in the below (second) equation? Why isn't the first equation just enough to describe r? What's the reason for unit vector to even exist? Homework Equations: in the photos. 11. ### Advantages of Polar Coordinate System & Rotating Unit Vectors. What is the advantage of using a polar coordinate system with rotating unit vectors? Kleppner's and Kolenkow's An Introduction to Mechanics states that base vectors ##\mathbf{ \hat{r}}## and ##\mathbf{\hat{\theta}}## have a variable direction, such that for a Cartesian coordinates system's base.... 12. ### I Polar coordinates and unit vectors. Hello, I get that both polar unit vectors, ##\hat{r}## and ##\hat{\theta}##, are unit vectors whose directions varies from point to point in the plane. In polar coordinates, the location of an arbitrary point ##P## on the plane is solely given in terms of one of the unit vector, the vector.... 13. ### Cylindrical coordinates: unit vectors and time derivatives. Homework Statement Homework EquationsThe Attempt at a Solution I have found expressions for the unit vectors for cylindrical coordinates in terms of unit vectors in rectangular coordinates. I have also found the time derivatives of the unit vectors in cylindrical coordinates. However, I am.... 14. ### Location of charged particle given magnitude of position. Homework Statement A charged particle has an electric field at ##\langle -0.13, 0.14, 0 \rangle## m is ##\langle 6.48\times10^3, -8.64\times10^3, 0 \rangle## N/C. The charged particle is -3nC. Where is the particle located? Homework Equations ##\vec E=\frac 1 {4π\varepsilon_0} \frac q {|\vec.... 15. ### I A Question about Unit Vectors of Cylindrical Coordinates. I wrote the equations of the Nabla, the divergence, the curl, and the Laplacian operators in cylindrical coordinates ##(ρ,φ,z)##. I was wondering how to define the direction of the unit vector ##\hat{φ}##. Can we obtain ##\hat{φ}## by evaluating the cross-product of ##\hat{ρ}## and ##\hat{z}##.... 16. ### Unit Vectors and Momentum Changes in a Block of Ice. Homework Statement A 0.5 kg block of ice is sliding by you on a very slippery floor at 2.5 m/s. As it goes by, you give it a kick perpendicular to its path. Your foot is in contact with the ice block for 0.0035 seconds. The block eventually slides at an angle of 24 degrees from its original.... 17. K. ### Cartesian unit vectors in terms of cylindrical vectors. How do I express ex,ey,ez in terms er,eθ,eZ? r=(x^2+y^2)^1/2,θ=arctan(y/x),Z=z A(r,θ,z) ∂A/∂x=x/(x^2+y^2)^1/2er+(-y)/(x^2+y^2)eθ=cosθer-(sinθ/r)eθ ex=(∂A/∂x)/|∂A/∂x| I should get ex as cosθer-sinθeθ, but I don't get ex correctly. am i doing this wrong?. 18. ### Calculate Change in Speed Using Unit Vectors: Easy Physics Solution. Actually that's very easy question but I have some difficult to understand the logic behind . So-"The initial velocity of an object (m/s) is Vi=1i+5j+2k. And the final velocity is Vf=3i+5j+7k. What was the change in speed of the object?"X Solution - |Vf|-|Vi| = √(32+52+72)-√(12+52+22) = 3.63.... 19. ### I Determining Vector Direction: Finding Unit Vectors. Why is there a need to find unit vector? If we are given a vector we can always find its direction.. 20. ### Statics: Dimensionless Unit Vector. Homework Statement Homework Equations The Attempt at a Solution So I began by subtracting. (205-160)=55 i (495+128)=623 j Both of these vectors are in the positive direction. So if I divide the vector by its magnitude I should get an answer of 1 in the positive direction for both i and.... 21. ### MHB S6.12.3.35 Find the unit vectors. $\tiny{s6.12.3.35}\\$ 35. Find the unit vectors that are parallel to the tangent line to the parabola $y = x^2$ at the point $(2,4)$. \begin{align} \displaystyle y'&=2x \end{align} the book answer to this is $\pm\left(i+4j)/\sqrt{17}\right)$ but don't see how they got this?. 22. ### I Is the Dot Product of Unit Vectors Related to Magnitudes and Angle Between Them?. Okay so I understand that in order to represent a vector which is in cartesian coordinates in spherical coordinates.. we use the transformation which is obtained by dotting the unit vectors. So my question goes like this: when we dot for example the unit vector ar^ with x^ we obtain sin(theta).... 23. ### Unit Vectors as a Function of Time?. | Homework Statement Say I have a vector F something like F = c1(t) x^ + c2(t) y^ were c1 and c2 are some scalar functions of time were you plug in time to into the equation and are given some magnitude. My question seems to be can we define unit vectors/basis vector as a function of time as.... 24. ### Time Derivative of Unit Vectors. Quick question (a little rusty on this): Why don't unit vectors in Cartesian Coordinates not change with time? For example, suppose \mathbf{r} (t) = x(t) \mathbf{x} + y(t) \mathbf{y} + z(t) \mathbf{z} How exactly do we know that the unit vectors don't change with time? Or in other words.... 25. ### Why Use Unit Vectors in Calculations?. I'm confused about what situations you should use unit vectors in... and it seems that when I approach the same problem using unit vectors vs. without unit vectors, I get different answers. Why? To illustrate my confusion, here's an example that I tried solving using unit vectors, and without.... 26. ### Physics: Multiplying Unit vectors. [Moderator note: Post moved from New Member Introductions forum, so no template] I am having trouble understanding how to multiply unit vectors. I know that: (please excuse the notation) i^×j^ = k^ j^×k^ = i^ k^×i^ = j^ The question I am stuck on is: What is (i^×j^)×k^? So far I have (i^×j^).... 27. ### Unit vectors for multiple particles? (Quantum Mechanics). It's been a little bit since I have studied multi-particle quantum mechanics and I am a little rusty on the notation. Let's say I have a wave function, that consists of the tensor product of two spaces, one for each particle moving, ##|\psi_1,\psi_2>##. Each of these particles is moving in a.... 28. ### Perpendicular Unit Vectors in the x-y Plane: Is My Solution Correct?. Homework Statement From Kleppner and Kolenkow Chapter 1 (Just checking to see if I'm right) Given vector A=<3, 4, -4> a) Find a unit vector B that lies in the x-y plane and is perpendicular to A. b) Find a unit vector C that is perpendicular to both A and B. c)Show that A is perpendicular to.... 29. ### Angles between sides of triangle ABC and unit vectors. I was going through this link -.... 30. ### Unit Vectors for Polarization and Wave Vector Directions. Homework Statement I am having difficulty understanding the very first step of the following solved problem (I understand the rest of the solution). How did they obtain the expressions for ##\hat{n}## (the direction of polarization), and ##\hat{k}## (the unit vector pointing in the direction.... 31. ### Find Unit Vectors for f(x,y) w/ D_uf=0. Homework Statement For f(x,y)=x^2-xy+y^2 and the vector u=i+j. ii)Find two unit vectors such D_vf=0 Homework Equations N/A. The Attempt at a Solution Not sure if relevant but the previous questions were asking for the unit vector u - which I got \hat{u}=\frac{1}{\sqrt{2}}(i+j) for the maximum.... 32. ### Cartesian to polar unit vectors + Linear Combination. I've been trying to solve this question all day. If somebody could point me in the right direction I would really appreciate it! (ii) A particle’s motion is described by the following position vector r(t) = 4txˆ + (10t − t)ˆy Determine the polar coordinate unit vectors ˆr and ˆθ for r. [4].... 33. ### Choosing unit vectors for harmonic motion problems. Consider a vertical pendulum affected by gravity (See the pdf file i included). Now i can choose two different opposite directions for my unit vectors which give me different equations. \downarrow : m\ddot x = mg-kx \uparrow : m\ddot x = kx-mg Which of course makes perfect sense, changing.... 34. ### Deriving spherical unit vectors in terms of cartesian unit vectors. I'm trying to find the azimuthal angle unit vector \vec{\phi} in the cartesian basis by taking the cross product of the radial and \vec{z} unit vectors. \vec{z} \times \vec{r} = <0, 0, 1> \times <sin(\theta)cos(\phi), sin(\theta)sin(\phi), cos(\theta)> = <-sin(\theta)sin(\phi).... 35. ### Cartesian unit vectors expressed by Cylindrical unit vectors. please someone explain me the following expression for Cartesian unit vectors expressed by the cylindrical unit vectors: http://web.mit.edu/8.02t/www/materials/modules/ReviewB.pdf at page B-8 line B.2.4 i would like to know which steps led to it. thanks, Chen. 36. ### Deriving sin(a-b) trig identity using Cross Product of Unit Vectors. Homework Statement A and B are two unit vectors in the x-y plane. A = <cos(a), sin(a)> B = <cos(b), sin(b)> I need to derive the trig identity: sin(a-b) = sin(a) cos(b) - sin(b) cos (a) I'm told to do it using the properties of the cross product A x B Homework Equations A x B =.... 37. ### LaTeX Best Unit Vectors in LaTeX for TeX.SE Interaction. During an interaction on TeX.SE, egreg there posted some truly awesome code for doing unit vectors in $\LaTeX$: \usepackage{newtxtext} \usepackage{newtxmath} \usepackage{amsmath} \usepackage{bm} \newcommand{\uveci}{{\bm{\hat{\textnormal{\bfseries\i}}}}}.... 38. ### Example about tangential and normal unit vectors. Here is a example 1.3 from analytical dynamics of Haim Baruh. a particle moves on a path on the xy plane defined by the curve y=3*x^2 , where x varies with the relation x= sin(a). find the radius of curvature of the path and unit vectors in the normal and tangential directions when a=pi/6.... 39. ### Integration including unit vectors. I have an integral of aΘ cos(Θ) dΘ a is the unit vector for Θ. I'm not sure what to do with it in the integration. I know the unit vector equals a/abs(a) but that would give a mess of an integral cause of the abs(a).. 40. ### States are or aren't unit vectors?. I am a little confused by an elementary point. Something must be wrong with the following: On one hand, a Hermitian operator (which is not necessarily unitary) takes one state to another state. Hence a state need not be represented as a unit vector; its norm can be greater (or less than).... 41. ### Unit vectors in different coordinates. Hi everyone, I've some points I want to make sure of. 1- When converting a "POINT" from a coordinate system to another, I'll just use the derived equation to convert (e.g. (1,2,3) from cartestian to cylindrical: \rho=\sqrt{x^{2}+y^{2}}, \phi=tan^{-1}\frac{y}{x}, z=z 2- When converting an.... 42. ### Cross products for unit vectors in other coordinate systems. I am a bit confused often when I have to compute cross products in other coordinate systems (non-Cartesian), I can't seem to find any tables for cross products such as "phi X rho." in spherical I think that these unit vectors are considered to be "perpendicular," so would phi X rho just be "+/-.... 43. ### Understanding Unit Vectors: A Step-by-Step Guide. Hi everyone, Just want to know how does the the unit vector become in that form: \vec{n}=\frac{2x\vec{i}+2y\vec{j}}{\sqrt{(2x)^{2}+(2y)^{2}}}=\frac{x \vec{i}+y \vec{j}}{4}. 44. ### Derivation of Phi-Hat wrt Phi in Spherical Unit Vectors. Homework Statement I just want to know how to get from this: ∂ø^/∂ø = -x^cosø - y^sinø to this: = -(r^sinθ+θ^cosθ) Homework Equations All the equations found here in the Spherical Coordinates section: http://en.wikipedia.org/wiki/Unit_vector The Attempt at a Solution I've.... 45. ### What Is the Dot Product of Two Parallel Unit Vectors?. Homework Statement The dot product for two.parralel pointing.unit.vectors is ? A. 1 B. 0 C. -1 D. Undefined [b]2. Relevant equation The Attempt at a Solutionsince they are unit vectors they have a magnitude of 1,this implies that the dot product is 1,since the angle between.... 46. ### What's the Difference Between Ax and i-Hat in Vector Notation?. Homework Statement So this isn't really a specific homework question, it's more of a general one. What is the difference between ax and i(hat)? I thought they were the same thing. Can someone please explain the difference? Homework Equations The Attempt at a Solution. 47. ### Understanding Vectors vs Unit Vectors: Differences and Uses in Physics. I am a bit confused about what the difference is between the two? To give some specific context where it has thrown me off, say if I were to define a charge with a vector r and compared that to a unit vector r hat, what exactly is the difference between what each of those tells me? I have.... 48. ### MHB Showing relationship between cartesian and spherical unit vectors. I am asked to show that when $$\hat{e_r}$$, $$\hat{e_\theta}$$, and $$\hat{e_\phi}$$ are unit vectors in spherical coordinates, that the cartesian unit vectors $$\hat{i} = \sin{\phi}\cos{\theta}\hat{e_r} + \cos{\phi}\cos{\theta}\hat{e_\phi} - \sin{\theta}\hat{e_\theta}$$ \hat{j} =.... 49. ### MHB If a and b are unit vectors..... If a and b are unit vectors and |a + b| = sqrt(2). What is the value (dot product) of (2a-b).(a+3b)? Is the answer -1 by any chance? If not... I know how to find the dot product and find the magnitude and add vectors, etc. but I have never came across this a question before. I am very unclear.... 50. ### Calculation of work involving unit vectors. Homework Statement A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force f = (30N)i - (40N)j to the cart as it undergoes a displacement s = (-9.0m)i - (3.0m)j How much work does the force you apply do on the grocery cart? Homework Equations... |
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Meaning of Term in Algebra
```Date: 09/16/2007 at 12:22:14
From: Erin
Subject: Terrible Terms
When I was in middle school, I was taught that in algebra we do not
write 2 * x because multiplication is used so much. Instead, we use
2x.
However, as I went through the math course, they explained to me that
something like 2x is considered one term, and that something like
2 + x is considered two terms. Because of this, each are treated
differently. For example, in the problem 3(2x) all you need to do is
multiply to the one term to get 6x. But in a problem like 3(2 + x),
because there are two terms in parentheses, you need to distribute to
get 6 + 3x. This is just one example of how a problem with one term
and a problem with two terms are treated differently.
My question is this: why is it that when you multiply or divide two
numbers or variables they become one term (such as 2*x becoming 2x),
but when you add or subtract two numbers or variables they are still
two terms (such as 2 + x)? This was never really explained to me
because all they told me was that it's easier to not put the
multiplication dot (*) because it's used so much. But I know that's
not the only reason because there are so many different properties
and different ways to treat the terms, that there must be another
reason then just for convenience. Can you help me with my curiosity
on this? Thank you.
Take the problem 2(xy). In 2(xy), since the value in parentheses is
one term, the appropriate thing to simplify it to would be 2xy. This
makes sense. Lets say xy is the area of a box that is x units wide
and y units long. If we combine two of those kind of boxes together,
we would have one rectangle with an an area of 2xy. But if we were
to pretend that xy was two terms, and, using the two-term
distribution rule, multiplied both x and y by 2, this would not make
sense. That would be saying that 2 xy boxes placed together have a
width of 2x and a length of 2y. This is not true because if 4 boxes
were placed together, then the resulting box would be 2x wide and 2y
long. Hence, if we distributed 2(xy) wrongly and got 2x2y, it would
have to be simplified to 4xy. 4 boxes have an area of 4xy, and 2
boxes have an area of 2xy.
x[]
y
x[][]
2y
2x [][]
[][]
2y
Now take the problem 2(x + y). Since x + y is two terms, if we were
to distribute the 2 to both the x and the y, we would get 2x + 2y.
This makes sense. Lets say x + y is the number of units x and the
number of units y in one group. If we get two of these kind of
groups, we would have double the number of units x and well as the
number of units y. But if we were to pretend that x + y was one term,
then we would simply the problem as 2x + y. This does not make sense.
If we were to try to simplify it this way, we would be saying that if
we had two groups, only the number of units x would double. This
doesn't make sense since one group has both units x and units y, and
if we were to double that group we would have double the units x as
well as double the units y.
One group: xxyy
Two groups: xxyy xxyy
Two groups would not be: xx xxyy
My teacher always tells me "terms are terrible". You must treat them
in different ways. In my opinion "terrible terms" are where most
algebraic mistakes come from. I feel knowing more about how terms
work will help me to understand and avoid these mistakes. An example
of a "terrible term" algebraic mistake is that you cannot distribute
an exponent among two terms. (x + y)^2 does not equal x^2 + y^2. But
you can distribute an exponent over one term. (xy)^2 = x^2*y^2.
Another example is that if the same term is added or subtracted in the
numerator and denominator, they cannot be canceled out. (5 + 2)/(10 +
2) does not equal 5/10. But if the same term is multiplied in the
numerator and denominator, they can be canceled out.
(5*2)/(10*2)=5/10.
```
```
Date: 09/16/2007 at 23:34:58
From: Doctor Peterson
Subject: Re: Terrible Terms
Hi, Erin.
You've said a lot of good things; it sounds like you have a pretty
good understanding of the essentials. I'll try saying a little more
that might put things in perspective (which is what I think you want),
and then we can discuss more if there are still gaps.
The reason adding makes two terms is simply that we DEFINE a term as
something that is added to other terms.
In part due to the order of operations, we think of any expression as,
ultimately, a sum: that is the last operation we do, so if there are
any additions (that are not inside parentheses), they break up the
expression into a sum, and the pieces are called terms.
Many of the things you talk about are distributive properties. We can
show that multiplication distributes over addition,
(a+b)*c = ac + bc
and that exponents distribute over multiplication,
(ab)^c = a^c b^c
But exponents do not distribute over addition, and multiplication does
not distribute over another multiplication. So you simply have to
keep in mind the rules that are true, and not do things that LOOK
similar but are not valid.
One help is to relate these properties to the order of operations
(which I believe is a major reason that the order is what it is):
exponentiation
distributes over...
multiplication
distributes over ...
Also, I believe that we leave out the symbol for multiplication not so
much because it is common, but because it is powerful (higher in the
order of operations). By writing ax + by with the a and the x close
together, we make the order of operations look natural; we SEE ax as a
single term, by as another, and the main operation in the expression
as addition, a sum of terms.
Does that help at all?
- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
```
Date: 10/02/2007 at 18:28:23
From: Erin
Subject: Thank you (Terrible Terms)
order of operations really helps - that exponents distribute over
multiplication, which distributes over addition. It helps make sense
of it to me and puts things into better perspective. It seems like it
has a lot to do with how we define math operations.
It was really neat hearing back from a mathematician - I plan
to major in math in college. Thanks again! :)
```
Associated Topics:
High School Basic Algebra
High School Polynomials
Middle School Algebra
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Math Forum Home || Math Library || Quick Reference || Math Forum Search | 1,744 | 6,720 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.40625 | 4 | CC-MAIN-2018-13 | latest | en | 0.975043 | Associated Topics || Dr. Math Home || Search Dr. Math. Meaning of Term in Algebra. ```Date: 09/16/2007 at 12:22:14. From: Erin. Subject: Terrible Terms. When I was in middle school, I was taught that in algebra we do not. write 2 * x because multiplication is used so much. Instead, we use. 2x.. However, as I went through the math course, they explained to me that. something like 2x is considered one term, and that something like. 2 + x is considered two terms. Because of this, each are treated. differently. For example, in the problem 3(2x) all you need to do is. multiply to the one term to get 6x. But in a problem like 3(2 + x),. because there are two terms in parentheses, you need to distribute to. get 6 + 3x. This is just one example of how a problem with one term. and a problem with two terms are treated differently.. My question is this: why is it that when you multiply or divide two. numbers or variables they become one term (such as 2*x becoming 2x),. but when you add or subtract two numbers or variables they are still. two terms (such as 2 + x)? This was never really explained to me. because all they told me was that it's easier to not put the. multiplication dot (*) because it's used so much. But I know that's. not the only reason because there are so many different properties. and different ways to treat the terms, that there must be another. reason then just for convenience. Can you help me with my curiosity. on this? Thank you.. Take the problem 2(xy). In 2(xy), since the value in parentheses is. one term, the appropriate thing to simplify it to would be 2xy. This. makes sense. Lets say xy is the area of a box that is x units wide. and y units long. If we combine two of those kind of boxes together,. we would have one rectangle with an an area of 2xy. But if we were. to pretend that xy was two terms, and, using the two-term. distribution rule, multiplied both x and y by 2, this would not make. sense. That would be saying that 2 xy boxes placed together have a. width of 2x and a length of 2y. This is not true because if 4 boxes. were placed together, then the resulting box would be 2x wide and 2y. long. Hence, if we distributed 2(xy) wrongly and got 2x2y, it would. have to be simplified to 4xy. 4 boxes have an area of 4xy, and 2. boxes have an area of 2xy.. x[]. y. x[][]. 2y. 2x [][]. [][]. 2y. Now take the problem 2(x + y). Since x + y is two terms, if we were. to distribute the 2 to both the x and the y, we would get 2x + 2y.. This makes sense. Lets say x + y is the number of units x and the. number of units y in one group. If we get two of these kind of. groups, we would have double the number of units x and well as the. number of units y. But if we were to pretend that x + y was one term,. then we would simply the problem as 2x + y. This does not make sense.. If we were to try to simplify it this way, we would be saying that if. we had two groups, only the number of units x would double. This. doesn't make sense since one group has both units x and units y, and. if we were to double that group we would have double the units x as. well as double the units y.. One group: xxyy. Two groups: xxyy xxyy. Two groups would not be: xx xxyy. My teacher always tells me "terms are terrible". You must treat them. in different ways. In my opinion "terrible terms" are where most. | algebraic mistakes come from. I feel knowing more about how terms. work will help me to understand and avoid these mistakes. An example. of a "terrible term" algebraic mistake is that you cannot distribute. an exponent among two terms. (x + y)^2 does not equal x^2 + y^2. But. you can distribute an exponent over one term. (xy)^2 = x^2*y^2.. Another example is that if the same term is added or subtracted in the. numerator and denominator, they cannot be canceled out. (5 + 2)/(10 +. 2) does not equal 5/10. But if the same term is multiplied in the. numerator and denominator, they can be canceled out.. (5*2)/(10*2)=5/10.. ```. ```. Date: 09/16/2007 at 23:34:58. From: Doctor Peterson. Subject: Re: Terrible Terms. Hi, Erin.. You've said a lot of good things; it sounds like you have a pretty. good understanding of the essentials. I'll try saying a little more. that might put things in perspective (which is what I think you want),. and then we can discuss more if there are still gaps.. The reason adding makes two terms is simply that we DEFINE a term as. something that is added to other terms.. In part due to the order of operations, we think of any expression as,. ultimately, a sum: that is the last operation we do, so if there are. any additions (that are not inside parentheses), they break up the. expression into a sum, and the pieces are called terms.. Many of the things you talk about are distributive properties. We can. show that multiplication distributes over addition,. (a+b)*c = ac + bc. and that exponents distribute over multiplication,. (ab)^c = a^c b^c. But exponents do not distribute over addition, and multiplication does. not distribute over another multiplication. So you simply have to. keep in mind the rules that are true, and not do things that LOOK. similar but are not valid.. One help is to relate these properties to the order of operations. (which I believe is a major reason that the order is what it is):. exponentiation. distributes over.... multiplication. distributes over .... Also, I believe that we leave out the symbol for multiplication not so. much because it is common, but because it is powerful (higher in the. order of operations). By writing ax + by with the a and the x close. together, we make the order of operations look natural; we SEE ax as a. single term, by as another, and the main operation in the expression. as addition, a sum of terms.. Does that help at all?. - Doctor Peterson, The Math Forum. http://mathforum.org/dr.math/. ```. ```. Date: 10/02/2007 at 18:28:23. From: Erin. Subject: Thank you (Terrible Terms). order of operations really helps - that exponents distribute over. multiplication, which distributes over addition. It helps make sense. of it to me and puts things into better perspective. It seems like it. has a lot to do with how we define math operations.. It was really neat hearing back from a mathematician - I plan. to major in math in college. Thanks again! :). ```. Associated Topics:. High School Basic Algebra. High School Polynomials. Middle School Algebra. Search the Dr. Math Library:. Find items containing (put spaces between keywords): Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words. Submit your own question to Dr. Math. Math Forum Home || Math Library || Quick Reference || Math Forum Search. |
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# help with rates
0
82
1
Bill and Peter can paint a 75 ft wall together in 7 hours. because Bill has more experience he can paint alone in two hours quicker than Peter. how long can it take Peter to paint the wall alone? round to the nearest minute.
Jan 4, 2021
#1
+117573
+2
Let the portion of the wall that Bill can paint in one hour be 1/x = his rate where x is the number of hours that Bill takes to paint the wall by himself
Let the portion of the wall that Peter can paint in one hour = 1/ ( x + 2) = his rate where x + 2 is the number of hours that Peter takes to paint the wall by himself
And
Bill's rate * 7hours + Peter's rate * 7 hours = 1 whole job done.....so...
1/x * 7 + 1/(x + 2) * 7 = 1
7/x + 7/(x + 2) = 1
7 ( x + 2) + 7x
______________ = 1
x ( x + 2)
14x + 14 = x ( x + 2)
14x + 14 = x^2 + 2x rearrange as
x^2 - 12x - 14 = 0 complete the square on x
x^2 -12x + 36 = 14 + 36
(x - 6)^2 = 50 take the positive root
x - 6 = sqrt (50)
x = sqrt (50 ) + 6
x + 2 = sqrt (50 ) + 8 ≈ 15.07 hrs = Peter's time = 15 + .07 *60 ≈ 15 hrs 4 min
Jan 4, 2021
edited by CPhill Jan 5, 2021 | 502 | 1,229 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2021-17 | latest | en | 0.52797 | +0. # help with rates. 0. 82. 1. Bill and Peter can paint a 75 ft wall together in 7 hours. because Bill has more experience he can paint alone in two hours quicker than Peter. how long can it take Peter to paint the wall alone? round to the nearest minute.. Jan 4, 2021. #1. +117573. +2. Let the portion of the wall that Bill can paint in one hour be 1/x = his rate where x is the number of hours that Bill takes to paint the wall by himself. Let the portion of the wall that Peter can paint in one hour = 1/ ( x + 2) = his rate where x + 2 is the number of hours that Peter takes to paint the wall by himself. And. Bill's rate * 7hours + Peter's rate * 7 hours = 1 whole job done.....so... | 1/x * 7 + 1/(x + 2) * 7 = 1. 7/x + 7/(x + 2) = 1. 7 ( x + 2) + 7x. ______________ = 1. x ( x + 2). 14x + 14 = x ( x + 2). 14x + 14 = x^2 + 2x rearrange as. x^2 - 12x - 14 = 0 complete the square on x. x^2 -12x + 36 = 14 + 36. (x - 6)^2 = 50 take the positive root. x - 6 = sqrt (50). x = sqrt (50 ) + 6. x + 2 = sqrt (50 ) + 8 ≈ 15.07 hrs = Peter's time = 15 + .07 *60 ≈ 15 hrs 4 min. Jan 4, 2021. edited by CPhill Jan 5, 2021. |
https://stuffsure.com/what-happens-to-the-expected-value-of-m-as-sample-size-increases/ | 1,723,597,315,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641086966.85/warc/CC-MAIN-20240813235205-20240814025205-00865.warc.gz | 423,439,976 | 15,008 | # The Expected Value of M: What Happens as Sample Size Increases?
As sample size increases, the expected value of M (the mean of the distribution of M values) approaches the population mean. This is due to the law of large numbers, which states that as a sample size gets larger, the sample mean gets closer to the population mean.
Checkout this video:
## Introduction
When we talk about the expected value of M, we are talking about the long-run average value of M. This value can be thought of as the average of all the possible values of M that could be realized. As the sample size increases, the expected value of M will get closer and closer to the population mean.
### What is the Expected Value of M?
In probability theory and statistics, the expected value of a random variable is the weighted average of all possible values that this random variable can take. In other words, if you have a six-sided die and you roll it, what is the average of all the numbers that come up? The answer is 3.5. This average value here is known as the expected value.
### What is the Law of Large Numbers?
The law of large numbers is a formal statement of the intuitive idea that the average of a sequence of random numbers will tend to be close to the expected value as the number of trials becomes large. More precisely, if X1,…,Xn is a sequence of independent and identically distributed random variables with expected value μ, then the sample mean converges in probability to μ as n approaches infinity:
limn→∞P(|X¯n−μ|>ε)=0 for all ε>0.
## Sample Size and the Expected Value of M
If you’re anything like me, you’ve probably wondered how the expected value of M changes as sample size increases. Does it go up? Does it go down? Does it stay the same? To answer these questions, we’ll need to take a quick look at the definition of expected value.
### How Does Sample Size Affect the Expected Value of M?
The Expected Value of M is a statistical tool that measures the center of a data set. It is also known as the mean or average. The Expected Value of M can be affected by two things: the population mean (μ) and the sample size (n).
The population mean is the average of all possible values in a population. For example, if you were to take the average height of all American adults, that would be the population mean. The population mean does not change when new data is added.
The sample size is the number of values you have in your sample. For example, if you were to take the heights of 100 American adults, that would be your sample size. The sample size can change when new data is added.
As the sample size increases, the expected value of M approaches the population mean. This happens because there are more values in the sample and so they better represent the entire population.
### What Happens as Sample Size Increases?
As sample size increases, the expected value of M approaches the population mean. This is because, as the number of samples gets larger, the distribution of M becomes more and more Normal. Recall that the Normal distribution is centered at the population mean. Therefore, as the number of samples gets larger, M will tend to be closer and closer to the population mean.
## Conclusion
As the sample size increased, the value of M tended to approach 3. This was to be expected, since M is the average of a random sample of numbers drawn from a population with a mean of 3. If the sample size is large enough, the value of M will be very close to 3. | 753 | 3,497 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2024-33 | latest | en | 0.938374 | # The Expected Value of M: What Happens as Sample Size Increases?. As sample size increases, the expected value of M (the mean of the distribution of M values) approaches the population mean. This is due to the law of large numbers, which states that as a sample size gets larger, the sample mean gets closer to the population mean.. Checkout this video:. ## Introduction. When we talk about the expected value of M, we are talking about the long-run average value of M. This value can be thought of as the average of all the possible values of M that could be realized. As the sample size increases, the expected value of M will get closer and closer to the population mean.. ### What is the Expected Value of M?. In probability theory and statistics, the expected value of a random variable is the weighted average of all possible values that this random variable can take. In other words, if you have a six-sided die and you roll it, what is the average of all the numbers that come up? The answer is 3.5. This average value here is known as the expected value.. ### What is the Law of Large Numbers?. The law of large numbers is a formal statement of the intuitive idea that the average of a sequence of random numbers will tend to be close to the expected value as the number of trials becomes large. More precisely, if X1,…,Xn is a sequence of independent and identically distributed random variables with expected value μ, then the sample mean converges in probability to μ as n approaches infinity:. limn→∞P(|X¯n−μ|>ε)=0 for all ε>0.. ## Sample Size and the Expected Value of M. If you’re anything like me, you’ve probably wondered how the expected value of M changes as sample size increases. Does it go up? Does it go down? Does it stay the same? To answer these questions, we’ll need to take a quick look at the definition of expected value.. ### How Does Sample Size Affect the Expected Value of M?. The Expected Value of M is a statistical tool that measures the center of a data set. | It is also known as the mean or average. The Expected Value of M can be affected by two things: the population mean (μ) and the sample size (n).. The population mean is the average of all possible values in a population. For example, if you were to take the average height of all American adults, that would be the population mean. The population mean does not change when new data is added.. The sample size is the number of values you have in your sample. For example, if you were to take the heights of 100 American adults, that would be your sample size. The sample size can change when new data is added.. As the sample size increases, the expected value of M approaches the population mean. This happens because there are more values in the sample and so they better represent the entire population.. ### What Happens as Sample Size Increases?. As sample size increases, the expected value of M approaches the population mean. This is because, as the number of samples gets larger, the distribution of M becomes more and more Normal. Recall that the Normal distribution is centered at the population mean. Therefore, as the number of samples gets larger, M will tend to be closer and closer to the population mean.. ## Conclusion. As the sample size increased, the value of M tended to approach 3. This was to be expected, since M is the average of a random sample of numbers drawn from a population with a mean of 3. If the sample size is large enough, the value of M will be very close to 3. |
https://aljenan-kw.com/qa/what-is-the-purpose-of-hypothesis.html | 1,618,648,748,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038118762.49/warc/CC-MAIN-20210417071833-20210417101833-00291.warc.gz | 198,428,307 | 7,372 | # What Is The Purpose Of Hypothesis?
## How do we write a hypothesis?
How to Formulate an Effective Research HypothesisState the problem that you are trying to solve.
Make sure that the hypothesis clearly defines the topic and the focus of the experiment.Try to write the hypothesis as an if-then statement.
Define the variables..
## What does a hypothesis represent?
In science, a hypothesis is an idea or explanation that you then test through study and experimentation. Outside science, a theory or guess can also be called a hypothesis. A hypothesis is something more than a wild guess but less than a well-established theory. … Anyone who uses the word hypothesis is making a guess.
## What are the six steps of hypothesis testing?
Step 1: Specify the Null Hypothesis. … Step 2: Specify the Alternative Hypothesis. … Step 3: Set the Significance Level (a) … Step 4: Calculate the Test Statistic and Corresponding P-Value. … Step 5: Drawing a Conclusion.
## Is a hypothesis a prediction?
The only interpretation of the term hypothesis needed in science is that of a causal hypothesis, defined as a proposed explanation (and for typically a puzzling observation). A hypothesis is not a prediction. Rather, a prediction is derived from a hypothesis.
## What does P value indicate?
In statistics, the p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct. … A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.
## What is the most important step in hypothesis testing?
The most important (and often the most challenging) step in hypothesis testing is selecting the test statistic.
## What is the purpose of hypothesis testing?
The purpose of hypothesis testing is to determine whether there is enough statistical evidence in favor of a certain belief, or hypothesis, about a parameter.
## What are examples of hypothesis?
Examples of Hypothesis:If I replace the battery in my car, then my car will get better gas mileage.If I eat more vegetables, then I will lose weight faster.If I add fertilizer to my garden, then my plants will grow faster.If I brush my teeth every day, then I will not develop cavities.More items…
## What are the two types of hypothesis?
A hypothesis is an approximate explanation that relates to the set of facts that can be tested by certain further investigations. There are basically two types, namely, null hypothesis and alternative hypothesis. A research generally starts with a problem.
## What are the 4 steps of hypothesis testing?
Step 1: Specify the Null Hypothesis. … Step 2: Specify the Alternative Hypothesis. … Step 3: Set the Significance Level (a) … Step 4: Calculate the Test Statistic and Corresponding P-Value. … Step 5: Drawing a Conclusion.
## What is the purpose of a hypothesis quizlet?
What is the purpose of a hypothesis for any study? To provide direction for research by identifying the expected outcome. A hypothesis posed as a declarative statement predicts an expected outcome.
## What is a hypothesis easy definition?
A hypothesis is a suggested solution for an unexplained occurrence that does not fit into current accepted scientific theory. The basic idea of a hypothesis is that there is no pre-determined outcome.
## How do you explain hypothesis testing?
Key TakeawaysHypothesis testing is used to assess the plausibility of a hypothesis by using sample data.The test provides evidence concerning the plausibility of the hypothesis, given the data.Statistical analysts test a hypothesis by measuring and examining a random sample of the population being analyzed.
## What is Z test used for?
A z-test is a statistical test to determine whether two population means are different when the variances are known and the sample size is large. It can be used to test hypotheses in which the z-test follows a normal distribution. A z-statistic, or z-score, is a number representing the result from the z-test. | 822 | 4,055 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2021-17 | latest | en | 0.927781 | # What Is The Purpose Of Hypothesis?. ## How do we write a hypothesis?. How to Formulate an Effective Research HypothesisState the problem that you are trying to solve.. Make sure that the hypothesis clearly defines the topic and the focus of the experiment.Try to write the hypothesis as an if-then statement.. Define the variables... ## What does a hypothesis represent?. In science, a hypothesis is an idea or explanation that you then test through study and experimentation. Outside science, a theory or guess can also be called a hypothesis. A hypothesis is something more than a wild guess but less than a well-established theory. … Anyone who uses the word hypothesis is making a guess.. ## What are the six steps of hypothesis testing?. Step 1: Specify the Null Hypothesis. … Step 2: Specify the Alternative Hypothesis. … Step 3: Set the Significance Level (a) … Step 4: Calculate the Test Statistic and Corresponding P-Value. … Step 5: Drawing a Conclusion.. ## Is a hypothesis a prediction?. The only interpretation of the term hypothesis needed in science is that of a causal hypothesis, defined as a proposed explanation (and for typically a puzzling observation). A hypothesis is not a prediction. Rather, a prediction is derived from a hypothesis.. ## What does P value indicate?. In statistics, the p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct. … A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.. ## What is the most important step in hypothesis testing?. The most important (and often the most challenging) step in hypothesis testing is selecting the test statistic.. ## What is the purpose of hypothesis testing?. The purpose of hypothesis testing is to determine whether there is enough statistical evidence in favor of a certain belief, or hypothesis, about a parameter. | ## What are examples of hypothesis?. Examples of Hypothesis:If I replace the battery in my car, then my car will get better gas mileage.If I eat more vegetables, then I will lose weight faster.If I add fertilizer to my garden, then my plants will grow faster.If I brush my teeth every day, then I will not develop cavities.More items…. ## What are the two types of hypothesis?. A hypothesis is an approximate explanation that relates to the set of facts that can be tested by certain further investigations. There are basically two types, namely, null hypothesis and alternative hypothesis. A research generally starts with a problem.. ## What are the 4 steps of hypothesis testing?. Step 1: Specify the Null Hypothesis. … Step 2: Specify the Alternative Hypothesis. … Step 3: Set the Significance Level (a) … Step 4: Calculate the Test Statistic and Corresponding P-Value. … Step 5: Drawing a Conclusion.. ## What is the purpose of a hypothesis quizlet?. What is the purpose of a hypothesis for any study? To provide direction for research by identifying the expected outcome. A hypothesis posed as a declarative statement predicts an expected outcome.. ## What is a hypothesis easy definition?. A hypothesis is a suggested solution for an unexplained occurrence that does not fit into current accepted scientific theory. The basic idea of a hypothesis is that there is no pre-determined outcome.. ## How do you explain hypothesis testing?. Key TakeawaysHypothesis testing is used to assess the plausibility of a hypothesis by using sample data.The test provides evidence concerning the plausibility of the hypothesis, given the data.Statistical analysts test a hypothesis by measuring and examining a random sample of the population being analyzed.. ## What is Z test used for?. A z-test is a statistical test to determine whether two population means are different when the variances are known and the sample size is large. It can be used to test hypotheses in which the z-test follows a normal distribution. A z-statistic, or z-score, is a number representing the result from the z-test. |
https://people.richland.edu/james/spring05/m113/tech/tech3.html | 1,513,415,480,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948587496.62/warc/CC-MAIN-20171216084601-20171216110601-00525.warc.gz | 616,286,535 | 1,897 | # Math 113 - Technology Project 3
Inferential Statistics
## Group Members
1. __________________________
2. __________________________
3. __________________________
## Project
Follow the Minitab instructions under the technology exercises link on the website for information about how to do the problems.
1. The First Amendment Center in Nashville, TN, conducted a telephone survey of 1002 adults between May 6 and June 6, 2004, and found that 58% of Americans feel the news media is biased in their reporting. http://www.firstamendmentcenter.org/PDF/SOFA2004results.pdf
1. Simulate 200 samples of size n=1002 and a probability of success of p=0.58.
2. Find the 95% confidence interval for each of the 200 samples found in part a. What percent of them contain the claimed proportion of p=0.58?
3. Find the mean of each of the 200 samples from part a. and create a graphical summary of the means. Compare the results of your 200 samples to the three parts of the sampling distribution on page 340.
2. Demonstrate the Central Limit Theorem.
1. Create a discrete probability distribution with at least 5 unique values for x.
2. Find the mean, variance, and standard deviation for your probability distribution using the formulas from chapter 16.
3. Generate 1000 samples of size 4, 25, and 100 from a population with your distribution. Find the mean of each sample and describe it graphically. Compare the results of your 1000 samples to the three parts of the sampling distribution on page 345.
3. Use Minitab to create graphs demonstrating the graph from a hypothesis test.
1. Duplicate the graph to the right that demonstrates a two tail test with α=0.05.
2. Create a graph demonstrating a right tail test with α=0.05.
3. Create a graph demonstrating a left tail test with α=0.05. | 418 | 1,787 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.796875 | 4 | CC-MAIN-2017-51 | latest | en | 0.841458 | # Math 113 - Technology Project 3. Inferential Statistics. ## Group Members. 1. __________________________. 2. __________________________. 3. __________________________. ## Project. Follow the Minitab instructions under the technology exercises link on the website for information about how to do the problems.. 1. The First Amendment Center in Nashville, TN, conducted a telephone survey of 1002 adults between May 6 and June 6, 2004, and found that 58% of Americans feel the news media is biased in their reporting. http://www.firstamendmentcenter.org/PDF/SOFA2004results.pdf. 1. Simulate 200 samples of size n=1002 and a probability of success of p=0.58.. 2. Find the 95% confidence interval for each of the 200 samples found in part a. What percent of them contain the claimed proportion of p=0.58?. 3. Find the mean of each of the 200 samples from part a. | and create a graphical summary of the means. Compare the results of your 200 samples to the three parts of the sampling distribution on page 340.. 2. Demonstrate the Central Limit Theorem.. 1. Create a discrete probability distribution with at least 5 unique values for x.. 2. Find the mean, variance, and standard deviation for your probability distribution using the formulas from chapter 16.. 3. Generate 1000 samples of size 4, 25, and 100 from a population with your distribution. Find the mean of each sample and describe it graphically. Compare the results of your 1000 samples to the three parts of the sampling distribution on page 345.. 3. Use Minitab to create graphs demonstrating the graph from a hypothesis test.. 1. Duplicate the graph to the right that demonstrates a two tail test with α=0.05.. 2. Create a graph demonstrating a right tail test with α=0.05.. 3. Create a graph demonstrating a left tail test with α=0.05. |
https://www.archivemore.com/which-one-is-bigger-cl-or-l/ | 1,713,995,014,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296819971.86/warc/CC-MAIN-20240424205851-20240424235851-00654.warc.gz | 564,972,521 | 8,879 | ## Which one is bigger Cl or L?
Definition: Centilitre A centilitre (cL or cl) a metric unit of volume that is equal to one hundredth of a litre and is equal to a little more than six tenths (0.6102) of acubic inch, or one third (0.338) of a fluid ounce. “Liter” is American spelling and “Litre” is international spelling. 1 L = 1000 mL.
## Is CL bigger than mL?
A centiliter is larger than a milliliter. Simply put, cl is larger than ml. Since a centiliter is 10^1 larger than a milliliter, it means that the conversion factor for cl to ml is 10^1.
## How many moles are in CL?
The answer is 35.453. We assume you are converting between grams Cl and mole. You can view more details on each measurement unit: molecular weight of Cl or mol The SI base unit for amount of substance is the mole. 1 grams Cl is equal to 0.028206357713029 mole.
2 mole
## How do you find moles of Cl in AgCl?
The mass of silver chloride precipitated is used to calculate:
1. (i) moles of AgCl(s) precipitated. moles = mass ÷ molar mass.
2. (ii) moles of chloride ion, Cl-, present. mole ratio AgCl:Cl- is 1:1.
3. (iii) mass of chloride ion, Cl-, present in the seawater. mass = moles × molar mass.
## How many moles are there in 70.9 g of CL?
39.2 g Cl2(1 mole of Cl270.9 g Cl2)(6.022⋅1023molecules Cl21 mole Cl2)=3.33⋅1023 molecules Cl2 . Hence, the answer is 3.33⋅1023 molecules of Cl2. Note that 6.022⋅1023 is also known as Avogadro’s number, and it can be referred to as the number of molecules in one mole of that substance.
## How many moles of CL are in NaCl?
A mole of NaCl contains a mole of sodium ions and a mole of chloride ions. Since a mole of sodium has a mass of 22.990 g and a mole of chlorine has a mass of 35.45 g, the molar mass of NaCl is 58.44 g/mol.
## How many atoms does CL have?
Name Chlorine
Atomic Number 17
Atomic Mass 35.453 atomic mass units
Number of Protons 17
Number of Neutrons 18
12.78g
22.989769 u
24.305 u
## Is sodium a solid?
Sodium is a chemical element with symbol Na and atomic number 11. Classified as an alkali metal, Sodium is a solid at room temperature.
## Where do we find sodium?
Sodium is the sixth most abundant element on Earth. It is never found in its pure form because it is so reactive. It is only found in compounds such as sodium chloride (NaCL) or table salt. Sodium chloride is found in ocean water (salt water), salt lakes, and underground deposits.
## Is Cl A chlorine?
Chlorine (Cl), chemical element, the second lightest member of the halogen elements, or Group 17 (Group VIIa) of the periodic table. Chlorine is a toxic, corrosive, greenish yellow gas that is irritating to the eyes and to the respiratory system.
## How does sodium look like?
Sodium is a very soft silvery-white metal. Sodium is the most common alkali metal and the sixth most abundant element on Earth, comprising 2.8 percent of Earth’s crust.
## How do we use sodium in everyday life?
Sodium is used as a heat exchanger in some nuclear reactors, and as a reagent in the chemicals industry. But sodium salts have more uses than the metal itself. The most common compound of sodium is sodium chloride (common salt). It is added to food and used to de-ice roads in winter.
## How do you purify sodium?
The only purification method is to wait for its natural decay. Sodium hydride and oxide (Na2O, NaH) are crystallising in liquid sodium when cooling, that produces the necessary sodium sur-saturation against hydrogen and oxygen to let the nucleation mechanism happen, and then to allow for crystal growth.
## What makes sodium unique?
It’s a soft metal, reactive and with a low melting point, with a relative density of 0,97 at 20ºC (68ºF). From the commercial point of view, sodium is the most important of all the alkaline metals. Sodium reacts quickly with water, and also with snow and ice, to produce sodium hydroxide and hydrogen. | 1,035 | 3,880 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.71875 | 4 | CC-MAIN-2024-18 | latest | en | 0.88541 | ## Which one is bigger Cl or L?. Definition: Centilitre A centilitre (cL or cl) a metric unit of volume that is equal to one hundredth of a litre and is equal to a little more than six tenths (0.6102) of acubic inch, or one third (0.338) of a fluid ounce. “Liter” is American spelling and “Litre” is international spelling. 1 L = 1000 mL.. ## Is CL bigger than mL?. A centiliter is larger than a milliliter. Simply put, cl is larger than ml. Since a centiliter is 10^1 larger than a milliliter, it means that the conversion factor for cl to ml is 10^1.. ## How many moles are in CL?. The answer is 35.453. We assume you are converting between grams Cl and mole. You can view more details on each measurement unit: molecular weight of Cl or mol The SI base unit for amount of substance is the mole. 1 grams Cl is equal to 0.028206357713029 mole.. 2 mole. ## How do you find moles of Cl in AgCl?. The mass of silver chloride precipitated is used to calculate:. 1. (i) moles of AgCl(s) precipitated. moles = mass ÷ molar mass.. 2. (ii) moles of chloride ion, Cl-, present. mole ratio AgCl:Cl- is 1:1.. 3. (iii) mass of chloride ion, Cl-, present in the seawater. mass = moles × molar mass.. ## How many moles are there in 70.9 g of CL?. 39.2 g Cl2(1 mole of Cl270.9 g Cl2)(6.022⋅1023molecules Cl21 mole Cl2)=3.33⋅1023 molecules Cl2 . Hence, the answer is 3.33⋅1023 molecules of Cl2. Note that 6.022⋅1023 is also known as Avogadro’s number, and it can be referred to as the number of molecules in one mole of that substance.. ## How many moles of CL are in NaCl?. A mole of NaCl contains a mole of sodium ions and a mole of chloride ions. Since a mole of sodium has a mass of 22.990 g and a mole of chlorine has a mass of 35.45 g, the molar mass of NaCl is 58.44 g/mol.. ## How many atoms does CL have?. Name Chlorine. | Atomic Number 17. Atomic Mass 35.453 atomic mass units. Number of Protons 17. Number of Neutrons 18. 12.78g. 22.989769 u. 24.305 u. ## Is sodium a solid?. Sodium is a chemical element with symbol Na and atomic number 11. Classified as an alkali metal, Sodium is a solid at room temperature.. ## Where do we find sodium?. Sodium is the sixth most abundant element on Earth. It is never found in its pure form because it is so reactive. It is only found in compounds such as sodium chloride (NaCL) or table salt. Sodium chloride is found in ocean water (salt water), salt lakes, and underground deposits.. ## Is Cl A chlorine?. Chlorine (Cl), chemical element, the second lightest member of the halogen elements, or Group 17 (Group VIIa) of the periodic table. Chlorine is a toxic, corrosive, greenish yellow gas that is irritating to the eyes and to the respiratory system.. ## How does sodium look like?. Sodium is a very soft silvery-white metal. Sodium is the most common alkali metal and the sixth most abundant element on Earth, comprising 2.8 percent of Earth’s crust.. ## How do we use sodium in everyday life?. Sodium is used as a heat exchanger in some nuclear reactors, and as a reagent in the chemicals industry. But sodium salts have more uses than the metal itself. The most common compound of sodium is sodium chloride (common salt). It is added to food and used to de-ice roads in winter.. ## How do you purify sodium?. The only purification method is to wait for its natural decay. Sodium hydride and oxide (Na2O, NaH) are crystallising in liquid sodium when cooling, that produces the necessary sodium sur-saturation against hydrogen and oxygen to let the nucleation mechanism happen, and then to allow for crystal growth.. ## What makes sodium unique?. It’s a soft metal, reactive and with a low melting point, with a relative density of 0,97 at 20ºC (68ºF). From the commercial point of view, sodium is the most important of all the alkaline metals. Sodium reacts quickly with water, and also with snow and ice, to produce sodium hydroxide and hydrogen. |
https://convertoctopus.com/49-grams-to-pounds | 1,660,272,670,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571538.36/warc/CC-MAIN-20220812014923-20220812044923-00192.warc.gz | 200,447,396 | 7,469 | ## Conversion formula
The conversion factor from grams to pounds is 0.0022046226218488, which means that 1 gram is equal to 0.0022046226218488 pounds:
1 g = 0.0022046226218488 lb
To convert 49 grams into pounds we have to multiply 49 by the conversion factor in order to get the mass amount from grams to pounds. We can also form a simple proportion to calculate the result:
1 g → 0.0022046226218488 lb
49 g → M(lb)
Solve the above proportion to obtain the mass M in pounds:
M(lb) = 49 g × 0.0022046226218488 lb
M(lb) = 0.10802650847059 lb
The final result is:
49 g → 0.10802650847059 lb
We conclude that 49 grams is equivalent to 0.10802650847059 pounds:
49 grams = 0.10802650847059 pounds
## Alternative conversion
We can also convert by utilizing the inverse value of the conversion factor. In this case 1 pound is equal to 9.2569871428571 × 49 grams.
Another way is saying that 49 grams is equal to 1 ÷ 9.2569871428571 pounds.
## Approximate result
For practical purposes we can round our final result to an approximate numerical value. We can say that forty-nine grams is approximately zero point one zero eight pounds:
49 g ≅ 0.108 lb
An alternative is also that one pound is approximately nine point two five seven times forty-nine grams.
## Conversion table
### grams to pounds chart
For quick reference purposes, below is the conversion table you can use to convert from grams to pounds
grams (g) pounds (lb)
50 grams 0.11 pounds
51 grams 0.112 pounds
52 grams 0.115 pounds
53 grams 0.117 pounds
54 grams 0.119 pounds
55 grams 0.121 pounds
56 grams 0.123 pounds
57 grams 0.126 pounds
58 grams 0.128 pounds
59 grams 0.13 pounds | 464 | 1,658 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2022-33 | latest | en | 0.803458 | ## Conversion formula. The conversion factor from grams to pounds is 0.0022046226218488, which means that 1 gram is equal to 0.0022046226218488 pounds:. 1 g = 0.0022046226218488 lb. To convert 49 grams into pounds we have to multiply 49 by the conversion factor in order to get the mass amount from grams to pounds. We can also form a simple proportion to calculate the result:. 1 g → 0.0022046226218488 lb. 49 g → M(lb). Solve the above proportion to obtain the mass M in pounds:. M(lb) = 49 g × 0.0022046226218488 lb. M(lb) = 0.10802650847059 lb. The final result is:. 49 g → 0.10802650847059 lb. We conclude that 49 grams is equivalent to 0.10802650847059 pounds:. 49 grams = 0.10802650847059 pounds. ## Alternative conversion. We can also convert by utilizing the inverse value of the conversion factor. In this case 1 pound is equal to 9.2569871428571 × 49 grams.. Another way is saying that 49 grams is equal to 1 ÷ 9.2569871428571 pounds.. ## Approximate result. | For practical purposes we can round our final result to an approximate numerical value. We can say that forty-nine grams is approximately zero point one zero eight pounds:. 49 g ≅ 0.108 lb. An alternative is also that one pound is approximately nine point two five seven times forty-nine grams.. ## Conversion table. ### grams to pounds chart. For quick reference purposes, below is the conversion table you can use to convert from grams to pounds. grams (g) pounds (lb). 50 grams 0.11 pounds. 51 grams 0.112 pounds. 52 grams 0.115 pounds. 53 grams 0.117 pounds. 54 grams 0.119 pounds. 55 grams 0.121 pounds. 56 grams 0.123 pounds. 57 grams 0.126 pounds. 58 grams 0.128 pounds. 59 grams 0.13 pounds. |
http://www.algebra.com/algebra/homework/equations/Equations.faq.question.127995.html | 1,368,918,464,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368696382920/warc/CC-MAIN-20130516092622-00033-ip-10-60-113-184.ec2.internal.warc.gz | 306,048,802 | 5,049 | # SOLUTION: Tell wether the ordered pair is a solution of the linear system. (1,-1); 2x - y = 3 4x + 2y = 2 Any help with this equation would be <b>Greatly</b> appreciated.
Algebra -> Algebra -> Equations -> SOLUTION: Tell wether the ordered pair is a solution of the linear system. (1,-1); 2x - y = 3 4x + 2y = 2 Any help with this equation would be <b>Greatly</b> appreciated. Log On
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Algebra: Equations Solvers Lessons Answers archive Quiz In Depth
Question 127995: Tell wether the ordered pair is a solution of the linear system. (1,-1); 2x - y = 3 4x + 2y = 2 Any help with this equation would be Greatly appreciated.Answer by JessicaGill(40) (Show Source): You can put this solution on YOUR website!There are two ways you can solve this. By graphing to see if the ordered pair (1, -1) falls on both lines, or by simply substituting the x and y coordinates into both equations and seeing if they prove true. Substitution is shown below To substitute take your first equation and substitute 1 for x and -1 for y would be which simplifies to so the ordered pair is a solution for the first equation. Lets check the second, substituting the values in for the x and y coordinates Simplfy this down to so the ordered pair (1,-1) is a solution for both equations. If you would like me to show you the graphing steps, please let me know. thanks, Ms. G | 406 | 1,545 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2013-20 | latest | en | 0.883373 | # SOLUTION: Tell wether the ordered pair is a solution of the linear system. (1,-1); 2x - y = 3 4x + 2y = 2 Any help with this equation would be <b>Greatly</b> appreciated.. Algebra -> Algebra -> Equations -> SOLUTION: Tell wether the ordered pair is a solution of the linear system. (1,-1); 2x - y = 3 4x + 2y = 2 Any help with this equation would be <b>Greatly</b> appreciated. Log On. Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!. Algebra: Equations Solvers Lessons Answers archive Quiz In Depth. Question 127995: Tell wether the ordered pair is a solution of the linear system. (1,-1); 2x - y = 3 4x + 2y = 2 Any help with this equation would be Greatly appreciated.Answer by JessicaGill(40) (Show Source): You can put this solution on YOUR website!There are two ways you can solve this. | By graphing to see if the ordered pair (1, -1) falls on both lines, or by simply substituting the x and y coordinates into both equations and seeing if they prove true. Substitution is shown below To substitute take your first equation and substitute 1 for x and -1 for y would be which simplifies to so the ordered pair is a solution for the first equation. Lets check the second, substituting the values in for the x and y coordinates Simplfy this down to so the ordered pair (1,-1) is a solution for both equations. If you would like me to show you the graphing steps, please let me know. thanks, Ms. G. |
https://answerlic.com/what-is-the-dimension-of-the-eigenspace/ | 1,686,066,924,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224652959.43/warc/CC-MAIN-20230606150510-20230606180510-00548.warc.gz | 117,964,477 | 20,975 | 11:15 am Science
What Is The Dimension Of The Eigenspace?
This is a slightly more complicated question. We know that the eigenvectors of a matrix are the columns of the matrix. So if we want to find out how many of these columns there are, we have to look at the dimension of each column.
Now, let’s look at our matrix A:
The first column has three elements (1 + i + j), which means that it has three dimensions. The second column has one element (1), so it only has one dimension. The third column has two elements (2 + 3j), so it has two dimensions. In total, our matrix has four dimensions: three for each column and one for the entire row.
The eigenspace for a given pair of numbers generally does not have those exact same dimensions as those numbers do individually; it is only guaranteed to be “close” to them in this way.
(Visited 3 times, 1 visits today) | 204 | 869 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.609375 | 4 | CC-MAIN-2023-23 | latest | en | 0.953314 | 11:15 am Science. What Is The Dimension Of The Eigenspace?. This is a slightly more complicated question. We know that the eigenvectors of a matrix are the columns of the matrix. So if we want to find out how many of these columns there are, we have to look at the dimension of each column.. Now, let’s look at our matrix A:. The first column has three elements (1 + i + j), which means that it has three dimensions. | The second column has one element (1), so it only has one dimension. The third column has two elements (2 + 3j), so it has two dimensions. In total, our matrix has four dimensions: three for each column and one for the entire row.. The eigenspace for a given pair of numbers generally does not have those exact same dimensions as those numbers do individually; it is only guaranteed to be “close” to them in this way.. (Visited 3 times, 1 visits today). |
https://metanumbers.com/12063 | 1,669,541,426,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710218.49/warc/CC-MAIN-20221127073607-20221127103607-00229.warc.gz | 438,607,599 | 7,299 | # 12063 (number)
12,063 (twelve thousand sixty-three) is an odd five-digits composite number following 12062 and preceding 12064. In scientific notation, it is written as 1.2063 × 104. The sum of its digits is 12. It has a total of 2 prime factors and 4 positive divisors. There are 8,040 positive integers (up to 12063) that are relatively prime to 12063.
## Basic properties
• Is Prime? No
• Number parity Odd
• Number length 5
• Sum of Digits 12
• Digital Root 3
## Name
Short name 12 thousand 63 twelve thousand sixty-three
## Notation
Scientific notation 1.2063 × 104 12.063 × 103
## Prime Factorization of 12063
Prime Factorization 3 × 4021
Composite number
Distinct Factors Total Factors Radical ω(n) 2 Total number of distinct prime factors Ω(n) 2 Total number of prime factors rad(n) 12063 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 12,063 is 3 × 4021. Since it has a total of 2 prime factors, 12,063 is a composite number.
## Divisors of 12063
1, 3, 4021, 12063
4 divisors
Even divisors 0 4 2 2
Total Divisors Sum of Divisors Aliquot Sum τ(n) 4 Total number of the positive divisors of n σ(n) 16088 Sum of all the positive divisors of n s(n) 4025 Sum of the proper positive divisors of n A(n) 4022 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 109.832 Returns the nth root of the product of n divisors H(n) 2.99925 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 12,063 can be divided by 4 positive divisors (out of which 0 are even, and 4 are odd). The sum of these divisors (counting 12,063) is 16,088, the average is 4,022.
## Other Arithmetic Functions (n = 12063)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 8040 Total number of positive integers not greater than n that are coprime to n λ(n) 4020 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 1450 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 8,040 positive integers (less than 12,063) that are coprime with 12,063. And there are approximately 1,450 prime numbers less than or equal to 12,063.
## Divisibility of 12063
m n mod m 2 3 4 5 6 7 8 9 1 0 3 3 3 2 7 3
The number 12,063 is divisible by 3.
## Classification of 12063
• Arithmetic
• Semiprime
• Deficient
• Polite
• Square Free
### Other numbers
• LucasCarmichael
## Base conversion (12063)
Base System Value
2 Binary 10111100011111
3 Ternary 121112210
4 Quaternary 2330133
5 Quinary 341223
6 Senary 131503
8 Octal 27437
10 Decimal 12063
12 Duodecimal 6b93
20 Vigesimal 1a33
36 Base36 9b3
## Basic calculations (n = 12063)
### Multiplication
n×y
n×2 24126 36189 48252 60315
### Division
n÷y
n÷2 6031.5 4021 3015.75 2412.6
### Exponentiation
ny
n2 145515969 1755359134047 21174897234008961 255432785333850096543
### Nth Root
y√n
2√n 109.832 22.9343 10.4801 6.55075
## 12063 as geometric shapes
### Circle
Diameter 24126 75794.1 4.57152e+08
### Sphere
Volume 7.35283e+12 1.82861e+09 75794.1
### Square
Length = n
Perimeter 48252 1.45516e+08 17059.7
### Cube
Length = n
Surface area 8.73096e+08 1.75536e+12 20893.7
### Equilateral Triangle
Length = n
Perimeter 36189 6.30103e+07 10446.9
### Triangular Pyramid
Length = n
Surface area 2.52041e+08 2.06871e+11 9849.4
## Cryptographic Hash Functions
md5 887c5a2b0d1bcf5b169ac8d63806bd13 e08e1a4c5e250715736695c3f5f7059dd6ee983d 9aa3cb6ab517a4eac5157d3a2263c1ed4c54b12ab6bfca683cba084ee56b009f ba657ff2d8bbc647d87e8604393d573ecc8564ef4dc9fc2b9c51a6dfcf29b598e5b9445331f64304375a69fa04115fe8557a97bb57f190e12b49f63f08200072 6c0442831911c38b6e2b6ac07836c2fd61725cb7 | 1,452 | 4,082 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.8125 | 4 | CC-MAIN-2022-49 | latest | en | 0.802103 | # 12063 (number). 12,063 (twelve thousand sixty-three) is an odd five-digits composite number following 12062 and preceding 12064. In scientific notation, it is written as 1.2063 × 104. The sum of its digits is 12. It has a total of 2 prime factors and 4 positive divisors. There are 8,040 positive integers (up to 12063) that are relatively prime to 12063.. ## Basic properties. • Is Prime? No. • Number parity Odd. • Number length 5. • Sum of Digits 12. • Digital Root 3. ## Name. Short name 12 thousand 63 twelve thousand sixty-three. ## Notation. Scientific notation 1.2063 × 104 12.063 × 103. ## Prime Factorization of 12063. Prime Factorization 3 × 4021. Composite number. Distinct Factors Total Factors Radical ω(n) 2 Total number of distinct prime factors Ω(n) 2 Total number of prime factors rad(n) 12063 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0. The prime factorization of 12,063 is 3 × 4021. Since it has a total of 2 prime factors, 12,063 is a composite number.. ## Divisors of 12063. 1, 3, 4021, 12063. 4 divisors. Even divisors 0 4 2 2. Total Divisors Sum of Divisors Aliquot Sum τ(n) 4 Total number of the positive divisors of n σ(n) 16088 Sum of all the positive divisors of n s(n) 4025 Sum of the proper positive divisors of n A(n) 4022 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 109.832 Returns the nth root of the product of n divisors H(n) 2.99925 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors. The number 12,063 can be divided by 4 positive divisors (out of which 0 are even, and 4 are odd). The sum of these divisors (counting 12,063) is 16,088, the average is 4,022.. ## Other Arithmetic Functions (n = 12063). 1 φ(n) n. Euler Totient Carmichael Lambda Prime Pi φ(n) 8040 Total number of positive integers not greater than n that are coprime to n λ(n) 4020 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 1450 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares. There are 8,040 positive integers (less than 12,063) that are coprime with 12,063. And there are approximately 1,450 prime numbers less than or equal to 12,063.. ## Divisibility of 12063. m n mod m 2 3 4 5 6 7 8 9 1 0 3 3 3 2 7 3. The number 12,063 is divisible by 3.. ## Classification of 12063. • Arithmetic. • Semiprime. • Deficient. • Polite. • Square Free. ### Other numbers. • LucasCarmichael. ## Base conversion (12063). | Base System Value. 2 Binary 10111100011111. 3 Ternary 121112210. 4 Quaternary 2330133. 5 Quinary 341223. 6 Senary 131503. 8 Octal 27437. 10 Decimal 12063. 12 Duodecimal 6b93. 20 Vigesimal 1a33. 36 Base36 9b3. ## Basic calculations (n = 12063). ### Multiplication. n×y. n×2 24126 36189 48252 60315. ### Division. n÷y. n÷2 6031.5 4021 3015.75 2412.6. ### Exponentiation. ny. n2 145515969 1755359134047 21174897234008961 255432785333850096543. ### Nth Root. y√n. 2√n 109.832 22.9343 10.4801 6.55075. ## 12063 as geometric shapes. ### Circle. Diameter 24126 75794.1 4.57152e+08. ### Sphere. Volume 7.35283e+12 1.82861e+09 75794.1. ### Square. Length = n. Perimeter 48252 1.45516e+08 17059.7. ### Cube. Length = n. Surface area 8.73096e+08 1.75536e+12 20893.7. ### Equilateral Triangle. Length = n. Perimeter 36189 6.30103e+07 10446.9. ### Triangular Pyramid. Length = n. Surface area 2.52041e+08 2.06871e+11 9849.4. ## Cryptographic Hash Functions. md5 887c5a2b0d1bcf5b169ac8d63806bd13 e08e1a4c5e250715736695c3f5f7059dd6ee983d 9aa3cb6ab517a4eac5157d3a2263c1ed4c54b12ab6bfca683cba084ee56b009f ba657ff2d8bbc647d87e8604393d573ecc8564ef4dc9fc2b9c51a6dfcf29b598e5b9445331f64304375a69fa04115fe8557a97bb57f190e12b49f63f08200072 6c0442831911c38b6e2b6ac07836c2fd61725cb7. |
https://aptitude.gateoverflow.in/2034/cat-2003-question-2-89 | 1,675,020,167,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499758.83/warc/CC-MAIN-20230129180008-20230129210008-00013.warc.gz | 128,026,163 | 20,314 | 220 views
If three positive real numbers $x, y, z$ satisfy $y – x = z – y$ and $x y z = 4,$ then what is the minimum possible value of $y?$
1. $2^{\frac{1}{3}}$
2. $2^{\frac{2}{3}}$
3. $2^{\frac{1}{4}}$
4. $2^{\frac{3}{4}}$
y - x = z - y
x + z = 2y$\dots(1)$
xyz =4 $\dots(2)$
We know that, AM >= GM
Hence, $\frac{x+y+z}{3}$ >= $(xyz)^{\frac{1}{3}}$
From (1) and (2)
$\frac{3y}{3}$ >= $4^{\frac{1}{3}}$
y >= $2^{\frac{2}{3}}$
Hence,Option(B)$2^{\frac{2}{3}}$ is the correct choice.
11.1k points
1
381 views | 239 | 521 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.90625 | 4 | CC-MAIN-2023-06 | latest | en | 0.4181 | 220 views. If three positive real numbers $x, y, z$ satisfy $y – x = z – y$ and $x y z = 4,$ then what is the minimum possible value of $y?$. 1. $2^{\frac{1}{3}}$. 2. $2^{\frac{2}{3}}$. 3. $2^{\frac{1}{4}}$. 4. $2^{\frac{3}{4}}$. y - x = z - y. x + z = 2y$\dots(1)$. | xyz =4 $\dots(2)$. We know that, AM >= GM. Hence, $\frac{x+y+z}{3}$ >= $(xyz)^{\frac{1}{3}}$. From (1) and (2). $\frac{3y}{3}$ >= $4^{\frac{1}{3}}$. y >= $2^{\frac{2}{3}}$. Hence,Option(B)$2^{\frac{2}{3}}$ is the correct choice.. 11.1k points. 1. 381 views. |
https://meritbatch.com/cbse-sample-papers-for-class-11-chemistry-set-6/ | 1,680,195,370,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949355.52/warc/CC-MAIN-20230330163823-20230330193823-00761.warc.gz | 445,109,189 | 20,806 | Students must start practicing the questions from CBSE Sample Papers for Class 11 Chemistry with Solutions Set 6 are designed as per the revised syllabus.
## CBSE Sample Papers for Class 11 Chemistry Set 6 with Solutions
Time Allowed: 3 hours
Maximum Marks: 70
General Instructions:
• All questions are compulsory.
• This question paper contains 37 questions.
• Questions 1-20 in Section A are objective type-very short answer type questions carrying 1 mark each.
• Questions 21 – 27 in Section B are short answer type questions carrying 2 marks each.
• Questions 28 – 34 in Section C are long-answer 1 type questions carrying 3 marks each.
• Questions 35 – 37 in Section D are long-answer 11 type questions carrying 5 marks each.
• There is no overall choice. However, an internal choice has been provided in six questions of one mark, two questions of two marks, two questions of three marks and two questions of five marks. You must attempt only one of the choices in such questions.
• Use log tables, if necessary. Use of calculator is not allowed.
Section – A
Question 1.
What is the mass percent of carbon in carbon dioxide? [1]
(A) 0.034%
(B) 27.27%
(C) 3.4%
(D) 28.7%
OR
The empirical formula and molecular mass of a compound are CH2O and 180 g respectively. What will be the molecular formula of the compound?
(A) C9H18O9
(B) CH2O
(C) C6H12O6
(D) C2H4O2
Option (B) is correct.
Explanation:
Molecular mass of CO2 = 12 + 2(16)
= 12 + 32 = 44 g
44 g of CO2 contains 12 g atoms of carbon. Mass percent of carbon
= $$\frac{\text { Mass of carbon in } \mathrm{CO}_2}{\text { Molar mass of } \mathrm{CO}_2}$$ × 100s
= $$\frac{12}{44}$$ × 100
= 27.27%
OR
Option (C) is correct.
Explanation:
Empirical formula mass (CH2O)
= 12 + 2(1) + 16 = 30g
Molecular mass = 180g
n = $$\frac{\text { Molecular mass }}{\text { Empirical formula mass }}$$
= $$\frac{180}{30}$$ = 6
Molecular formula= n × empirical formula
= 6 × CH2O
= C6H12O6
Question 2.
On the basis of thermochemical equations (i), (ii) and (iii), find out which of the algebraic relationship given in options (A) to (D) is correct. [1]
(i) C (graphite) + O2(g) → C02(g); ΔfH = x kj mol-1
(ii) C (graphite) + $$\frac{1}{2}$$O2 (g) → CO(g); ΔrH = y kj mol-1
(iii) CO (g) + $$\frac{1}{2}$$O2 (g) → C02 (g) ;ΔH = z kj mol-1
(A) z = x + y
(B) x = y – z
(C) x = y + z
(D) y = 2z – x
Option (C) is correct.
Explanation: The algebric relationships of the given reaction is Eq.(i) – Eq.(ii) = Eq.(iii)
(i) C(graphite) + O2(g) → CO2(g) ; ΔrH = x kJ mol-1
(ii) C(graphite) + $$\frac{1}{2}$$O2(g) → CO(g) ; ΔrH = V kJ
(iii) CO(g) + $$\frac{1}{2}$$O2(g) → CO2(g) ; ΔrH = z kJ mol-1
Hence, x – y = z or x = y + z
Question 3.
Dipole-dipole forces act between the molecules possessing permanent dipole. Ends of dipoles possess ‘partial charges’. The partial charge is : [1]
(A) more than unit electronic charge.
(B) equal to unit electronic charge.
(C) less than unit electronic charge.
(D) double the unit electronic charge.
Option (C) is correct.
Explanation:
Partial charge is the small charge developed by displacement of electrons.
Question 4.
The first ionisation enthalpies of Na, Mg, Al and Si are in the order : [1]
(A) Na < Mg > Al < Si (B) Na > Mg > Al > Si
(C) Na < Mg < Al < Si (D) Na > Mg > Al < Si OR Which of the following is the correct order of size of the given species: (A) I > I > I+
(B) I+ > I > I
(C) I > I+ > I
(D) I > I > I+
Option (A) is correct.
Explanation:
On moving from left to right in a period first ionisation enthalpy increases normally. But, in Mg, as an electron needs to be removed from fully filled s orbital therefore, first ionisation enthalpy of Mg is more than Al.
OR
Option (D) is correct.
Explanation :
Size of cation is smaller while that of anion is bigger than its parent atom.
Question 5.
What will be correct order of vapour pressure of water, acetone and ether at 30°C. Given that among these compounds, water has maximum boiling point and ether has minimum boiling point? [1]
(A) Water < ether <acetone
(B) Water < acetone < ether
(C) Ether < acetone < water
(D) Acetone < ether < water
Option (B) is correct.
Explanation:
Greater is the boiling point, less is the vapour pressure.
Question 6.
Which of the following carbocation is most stable?
(B) (CH3)3C+
(C) CH3CH2+CH2
(D) CH3+CHCH2CH3
Option (B) is correct.
Explanation:
Tertiary carbocation is most stable.
The variables Pressure, Volume, Concentration and Temperature may change the State of Equilibrium. The change is governed by the Le-Chatelier’s principle. The decomposition of NH3(g) can be made spontaneous by increasing the temperature and lowering pressure. In the reaction, removal of any product from the reaction mixture makes the reversible reaction irreversible and therefore, reaction proceeds to completion.
Answer the questions (7) to (10) given below:
Question 7.
The equilibrium Solid → Liquid → Gas will shift in forward direction when:
(A) temperature is increased
(B) temperature is lowered
(C) pressure is increased
(D) pressure is lowered
Option (A) is correct.
Explanation:
Increase in temperature will favour the forward reaction which is endothermic.
Question 8.
Change in free energy for the equilibrium, gaseous reaction, PCl5 → PCl3 + Cl2 on addition of an inert gas at constant pressure and at constant volume is respectively:
(A) decrease, no change
(B) increase, no change
(C) no change, no change
(D) no change, decrease
Option (A) is correct.
Explanation:
Addition of inert gas at constant volume has no effect on any equilibrium reaction. When inert gas is added at constant pressure in the given reaction, it proceeds in forward direction. DG° remains constant, but DG decreases as the reaction proceeds spontaneously in forward direction to attain equilibrium.
Question 9.
At 25°C, the equilibrium constant K1 and I(z are for the reactions:
Which of the following shows the relation between two equilibrium constants?
(A) K2 = K2
(B) K2 = 1/(K)
(D) K1 = 1/(K)
(D) K1 = 1/K2
Option (C) is correct.
Explanation:
Question 10.
A liquid is in equilibrium with its vapour at its boiling point. On an average, the molecules in the two phases have equal:
(A) Intermolecular forces
(B) Potential energy
(C) Kinetic energy
(D) None of these
Option (C) is correct.
Explanation:
At boiling point, liquid and vapour phases both are present. So, the molecules in the two phases have equal kinetic energy.
Question 11.
The addition of HCl to an alkene proceeds in two steps. The first step is the attack of W ion to >C =C< portion which can be shown as A I
Option (A) is correct.
Explanation:
Since double bond is a source of electrons and the charge flows from source of more electron density, therefore, electrons of the double bond attack the proton.
Question 12.
How will you convert: ethyne to but-2-yne. [1]
Students directly write the products and forget to mention side products and reaction conditions.
Make a list of important conversions and learn them.
Understand each step and conditions involved during conversion reactions.
Question 13.
The structure of triphenylmethyl cation is given here. This is very stable and some of its salts can be stored for months. Explain the cause of high stability of this cation.
Triphenylmethyl cation is a tertiary carbocation which can show nine possible canonical structures and hence is very stable. The three canonical forms for one benzene ring are shown below.
Question 14.
Can we separate two liquids A (b.p. 353 K) and B (b.p. 365 K) present in a mixture by simple distillation? [1]
No, because in simple distillation, vapours of both the liquids will be formed simultaneously and will condense together in receiver as the difference between the boiling points is very less. They can be separated by fractional distillation.
Students sometimes answer in yes or no without giving legit explanation.
The alternate method of separation also must be mentioned.
Question 15.
What do you mean by cracking? [1]
The thermal decomposition of higher hydrocarbons into lower hydrocarbons in the presence or absence of a catalyst is called cracking.
Question 16.
Assign the oxidation number to Cr in K2Cr2O7.
Let the oxidation number of Cr be x
2 × (+1) + 2x + 7 × (- 2) = 0
2 + 2x – 14 = 0
2x – 12 = 0
x = $$\frac{12}{2}$$ = +6
Oxidation number of Cr in K2Cr2O7 = +6
Question 17.
Assertion (A): Toluene on Friedal-Crafts methylation gives o- and p-xylene.
Reason (R): CH3-group bonded to benzene ring increases electron density at o- and p- position.
(A) Both A and R are correct and R is the correct explanation of A.
(B) Both A and R are correct but R is not the correct explanation of A.
(C) Both A and R are not correct.
(D) A is not correct but R is correct.
Option (A) is correct.
Question 18.
Assertion (A): Benzene on heating with cone. H2SO4 gives benzene sulphonic acid which when heated with superheated steam under pressure gives benzene. [1]
Reason (R): Sulphonation is a reversible process.
(A) Both A and R are correct and R is the correct explanation of A.
(B) Both A and R are correct but R is not the correct explanation of A.
(C) Both A and R are not correct.
(D) A is not correct but R is correct.
Option (A) is correct.
Explanation:
Sulphonation of benzene is an electrophilic substitution reaction in which SO3 acts as the electrophile.
Question 19.
Why there is large number of lines in hydrogen spectrum? [1]
Large number of lines are there in hydrogen spec¬trum because different possible transitions can be observed which leads to large number of spectral lines.
Question 20.
Pressure is determined as force per unit area of the surface. The SI unit of pressure, pascal is as shown below:
1 Pa = 1 Nm-2
If mass of air at sea level is 1034 g cm-2, calculate the pressure in pascal. [1]
Mass of air at sea level = 1034 g cm-2
Acceleration due to gravity, g = 9.8 ms-2
Pressure is the force or weight per unit area.
Section – B
Question 21.
What does the following prefixes stand for
(a) pico
(b) nano
(c) micro
(d) deci
OR
Write main points of Dalton’s atomic theory. [2]
Prefixe Stand for (a) pico (p) 10-12 (b) nano (n) 10-9 (c) micro (μ) 10-6 (d) deci (d) 10-1
OR
The main points of Dalton’s atomic theory are:
(i) All matters are made of atoms. Atoms are indivisible and indestructible.
(ii) All atoms of a given element are identical in mass and properties. Atoms of different elements differ in mass.
(iii) Compounds are formed when atoms of different elements combine in a fixed ratio.
(iv) Chemical reactions involve reorganisation of atoms. These are neither created nor destroyed in a chemical reaction.
Question 22.
Chlorophyll present in green leaves of plants absorbs light at 4.620 × 1014Hz. Calculate the wavelength of radiation in nanometer. Which part of the electromagnetic spectrum does it belong to? [2]
Given, v = 4.620 × 1014 Hz
λ = ?
Wavelength λ = $$\frac{c}{v}$$
= 0.6494 × 10-6 m
= 649.4 × 10-9 m
= 649.4 nm
It belongs to visible region.
Question 23.
In both water and diethyl ether, the central atom viz. O-atom has same hybridisation. Why do they have different bond angles? Which one has greater bond angle? [2]
Both water and diethyl ether have the central atom O in sp3 hybrid state with two lone pairs of electrons
But due to the greater repulsion between two ethyl (C2H5) groups in diethyl ether than between two H-atoms in H2O result in greater bond angle (110°) in diethyl ether than 104.5° in that of water (H2O).
Question 24.
(a) Why is an organic compound fused with sodium for testing nitrogen, halogens and sulphur?
(b) Under what conditions can the process of steam distillation used? [2]
(i) On fusing with sodium metal, the elements present in an organic compound are converted from covalent form into the ionic form.
(ii) Steam distillation is used to purify the substances which are steam volatile and water and the liquid are not miscible with each other.
Question 25.
Write the name of the isomerism shown by the following pairs:
(i) Buta-1,3-diene and But-l-yne (C4H6)
(ii) Ethoxy butane and Propoxy propane (C6H14O). [2]
OR
Which bond is more polar in the following pairs of molecules.
(i) H3C-H, H3C-Br
(ii) H3C-NH2, H2C-OH
(i) Functional isomerism
H2C=CH – CH = CH2 and HC = C-CH2CH3
(ii) Metamerism
CH3 – CH2 – CH2 – CH2 – O- CH2CH3 and C3H7OC3H7
Students get confuse and give wrong answers.
Understand different type of isomerism with examples, different functional groups too.
OR
(i) C-Br because Br is more electronegative than H.
(ii) C-O because O is more electronegative than N.
Question 26.
An alkane C8H18 is obtained as the only product on subjecting a primary alkyl halide to Wurtz reaction. On
monobromination this alkane yields a single isomer of a tertiary bromide. Write the structure of alkane and the tertiary bromide. [2]
Question 27.
What are relative stabilities of different conformations of ethane? Is is possible to isolate these at room temperature? [2]
Staggered form of ethane is more stable than the eclipsed form because the force of repulsion between hydrogen atoms on adjacent C atom is minimum. The energy difference between the staggered form and the eclipsed form of ethane is just 12.55 kJ mol- 1. Therefore, it is not possible for these two forms of ethane to isolate at room temperature.
Section – C
Question 28.
What are (a) representative elements (b) transition elements (c) Lanthanoid and actinoids. Give their position in modern periodic table. [3]
(a) Representative Elements : Group 1, 2, 13, 14, 15, 16, 17 and 18 exhibit the main groups of the periodic table and so, the elements of these groups are collectively called representative elements.
These elements belong to s-block and p-block in modern periodic table.
(b) Transition Elements : d-block transition metals form a bridge between the chemically active metals of s-block elements and the less active elements of Groups 13 and 14 are known as transition elements.
(c) Lanthanoids and Actinoids : The elements of 4f series [i.e., from Ce (Z = 58) to Lu (Z = 71)] are called lanthanoids and the elements of 5f series [i.e., from Th (Z = 90) to Lr (Z = 103)] are called actinoids. These elements belong to /-block elements in the modern periodic table which lie at the bottom of the periodic table.
Question 29.
The Mn3+ ion is unstable in solution and undergoes disproportionation to give Mn2+, MnO2 and H+ ion. Write a balanced ionic equation for the reaction. [3]
The skeletal ionic equation is,
Mn3+(aq) → Mn2+(aq) + MnO2(s) + H+(aq)
Reduction half reaction
Mn3+(aq) + e → Mn2+
Oxidation half reaction
Mn3+(aq)→ MnO2 + e
Balance charge by adding 4H+ to right side and then balance O atoms by adding 2H2O to left side in oxidation half reaction
Mn3+(aq) + 2H2O(l) → MnO2(s) + e + 4H+(aq)
By adding both equations, we get
2Mn3+(aq) + 2H2O(l) → Mn2+ + MnO2(s) + 4H+(aq)
This represents the balanced redox reaction (disproportionation reaction).
Question 30.
Calculate the standard enthalpy of formation of CH3OH(l) from the following data :
(i) CH3OH(l) + $$\frac{3}{2}$$02(g) → C02(g)+ 2H2O(l) ΔrH° = – 726 kj/mol
(ii) C(s) + 02(g) → C02(g); ΔcH° = – 393 kj/mol
(iii) H2(g) + ½O2(g) → H2O(l); ΔfH° = – 286 kj/mol. [3]
The required equation is
C(s) + 2H2(g) + $$\frac{1}{2}$$ O2(g) → CH3OHO);
ΔfH° = ± ?
To get the above required equation :
Step 1 : Multiply eq. (iii) by 2 and add to eq. (ii)
C(s) + 2H2(g) + 2O2(g) → CO2(g) + 2H2O(l) ……………(iv)
ΔfH° = (2 x – 286) + (- 393)
= – 572 – 393
= – 965 kJ/mol
Step 2 : Subtract eq. (i) from eq. (iv)
C(s) + 2H2(g) + $$\frac{1}{2}$$O2(g) → CH3OH(l);
ΔH = – 965 – (- 726)
= – 239 kJ/mol
ΔfH° = – 239 kJ/mol
Question 31.
(i) State the formula and name of the conjugate base of each of the following acids :
(a) H3O+
(b) HSO4
(c) NH4+
(d) HF
(e) CH3COOH
(f) CH3NH3+
(g) H3PO4
(h) H2PO4
(ii) The ionic product of water is 0.11 × 10-14 at 273 K, 1 × 10-14 at 298 K and 7.5 × 10-14 at 373K. Deduce from this data whether the ionization of water to hydrogen and hydroxide ion is exothermic or endothermic. [3]
(i) The formula and name of the conjugate base are:
(a) H3O+: Water
(b) SO42- : Sulphate ion
(c) NH3 : Ammonia
(d) F : Fluoride ion
(e) CH3COO : Acetate ion
(f) CH3NH2 : Methylamine
(g) H2PO4 : Dihydrogen phosphate
(h)H2PO42- : Mono hydrogen phosphate
(ii) Kw = [H3O+] [OH]
According to the data, the value of K, is increasing with temperature. Therefore, according to Le- Chateliebs principle, the ionisation of water is endothermic.
Question 32.
Explain:
(i) Tea or coffee is sipped from the saucer, when it is quite hot.
(ii) Liquids possess fluidity. [3]
(i) Tea or coffee is sipped from the saucer, when it is quite hot because it has larger surface area than the cup. In larger surface area, the rate of evaporation is faster due to which tea or coffee cools rapidly.
(ii) Liquids have indefinite shape. They take the shape of the container in which they are placed. This is due to the fact that the molecules of liquids are in a state of constant random motion and therefore they can move freely. So, the liquids possess fluidity.
Question 33.
(a) The effect of uncertainty principle is significant only for motion of microscopic particles and is negligible for the macroscopic particles. Justify the statement with the help of a suitable example.
(b) What is the difference between the terms orbit and orbital ? [3]
If mass of an object = 1 mg = 10-6 kg
Then, according to Heisenberg’s uncertainty principle,
Since, the value of Δx.Δv obtained is very small and is insignificant. So, effect of uncertainty principle is significant only for motion of microscopic particles and is negligible for the macroscopic particles.
(b)
Orbit Orbital 1. An orbit is well defined circular path around the nucleus in which the electrons revolve. 1. An orbital is the threedimensional space around the nucleus within which the probability of finding an electron is maximum (upto 90%). 2. It represents the planar motion of an electron around the nucleus. 2. It represents the three dimensional motion of an electron around the nucleus.
Question 34.
Calculate the number of moles:
(i) 5.0 L of 0.75 M Na2CO3
(ii) 7.85 g of Fe
(iii) 34.2 g of sucrose (C12H22O11) [3]
OR
A compound made up of two elements A and B has A = 70%, B= 30%. Their relative number of moles in the compound is 1.25 and 1.88, calculate:
(i) Atomic masses of the elements A and B.
(ii) Molecular formula of the compound, if its molecular mass is found to be 160.
(i) Number of moles of Na2 CO3 = Molarity × Volume of solution in litre
= 0.75 × 5
= 3.75 mol
(ii) Number of moles of Fe
= $$\frac{\text { Mass }}{\text { Molecular mass }}$$
= $$\frac{34.2}{342}$$
= 0.14
(iii) Number of moles of sucrose
= $$\frac{\text { Mass }}{\text { Molecular mass }}$$
= $$\frac{34.2}{342}$$
= 0.1
OR
(i) Atomic mass of element A
= $$\frac{\% \text { of element } \mathrm{A}}{\text { Relative number of moles }}$$
= $$\frac{70}{1.25}$$
= 56
Atomic mass of element B
= $$\frac{\% \text { of element } \mathrm{B}}{\text { Relative number of moles }}$$
= $$\frac{30}{1.88}$$
= 15.957 ≈ 16
(ii)
Compound Simplest molar ratio Simplest whole-number ratio A $$\frac{1.25}{1.25}$$= 1 2 B $$\frac{1.88}{1.25}$$= 15 3
Empirical formula of compound = A2B3
Molecular mass = 160
Empirical formula mass
= 2(56) + 3(16)
= 112 + 48 = 160
n = $$\frac{\text { Molecular mass }}{\text { Empirical formula mass }}$$
= $$\frac{160}{160}$$ = 1
Molecular formula
= n × Empirical formula
= 1 × A2B3
= A2B3
Sometimes students forget to multiply by n while finding molecular formula and do mistakes.
Understand the problem and check for the necessary data, which are available in the problem. Follow steps and ensure no steps are missed.
Section – D
Question 35.
(i) For each of the following compounds, write a more condensed formula and also their bond-line formulae.
(ii) Write the I.U.RA.C. name of
OR
(a) A sample of 0.50 g of an organic compound was treated according to Kjeldahl’s method. The ammonia evolved was absorbed in 50 ml of 0.5 M H2SO4. The residual acid required 60 mL of 0.5 M solution of NaOH for neutralisation. Find the percentage composition of nitrogen in the compound.
(b) In the estimation of sulphur by Carius method, 0.468 g of an organic sulphur compound afforded 0.668 g of barium sulphate. Find out the percentage of sulphur in the given compound.
(i) Condensed formulae
(a) (CH3)2CHCH2OH
(b) CH3(CH2)5CHBrCH2CHO
(c) HO(CH2)3CH(CH3)CH(CH3)2
(d) HOCH(CN)2
Bond-line formulae-
Sometimes students ignore the triple bond in (ii) question.
While writing bond-line formula, observe carefully. It is similar to structural formula.
OR
Given that, total mass of organic compound = 0.50 g 60 mL of 0.5 M solution of NaOH was required by residual acid for neutralisation.
60 mL of 0.5 M NaOH solution = $$\frac{60}{2}$$mL of 0.5 M
H2SO4 = 30 mL of 0.5 M H2SO4
Acid consumed in absorption of evolved ammonia is (50-30) mL = 20 mL
Again, 20 mL of 0.5 M
H2SO4 = 40 mL of 0.5 M NH3
Also, since 1000 mL of 1 M NH3 contains 14 g of nitrogen,
40 mL of 0.5 M NH3 will contains = $$\frac{14 \times 40}{1000}$$ × 0.5
= 0.28 g of N
Therefore, percentage of nitrogen in 0.50 g of organic compound = $$\frac{0.28}{0.50}$$ × 100
= 5.6%
Students forget steps and end up with mistakes.
Understand the problem and practice steps wise and do calculations carefully.
(b) Given, total mass of organic compound = 0.468 g Mass of barium sulphate formed = 0.668 g
1 mol of BaSO4 = 233 g of BaSO4 = 32 g of sulphur
Thus, 0.668 g of BaSO4 contains $$\frac{32 \times 0.668}{233}$$ g of
sulphur = 0.0917 g of sulphur
Therefore, percentage of sulphur = $$\frac{0.0917}{0.468}$$ × 100
= 19.59 %
Hence, the percentage of sulphur in the given compound is 19.59 %.
Question 36.
Give mechanism of addition of HBr to Propene. [5]
Addition of HBr to propene (unsymmetrical alkene) follows Markovnikov’s rule according to which the negative part of the addendum gets attached to that C atom which possesses lesser number of hydrogen atoms.
Mechanism: Hydrogen bromide provides an electrophile, H+, which attacks the double bond to form carbocation as:
Secondary carbocations are more stable than primary carbocations. Therefore, the former predominates as it will form at a faster rate. Thus, in the next step, Br attacks the carbocation to form 2-bromopropane as the major product.
Addition of HBr to unsymmetrical alkenes like propene in the presence of light or peroxide takes place contrary to the Markovnikov’s rule. This so happens only with HBr but not with HCl and HI. This addition of HBr to propene in the presence of benzoyl peroxide follows anti-Markovnikov’s rule or peroxide effect or Kharasch effect.
Secondary free radicals are more stable than primary radicals. Therefore, the former predominates since it forms at a faster rate. Thus, 1-bromopropane is obtained as the major product.
• Some students write the reaction, but forget to explain the mechanism.
• Some students forget to explain the attack of Br- on carbocation.
Students must explain addition using Markovnikov’s rule as well as anti – Markovnikov’s rule.
Question 37.
Derive the relationship between AH and AU for an ideal gas. Explain each term involved in the equation. [5]
OR
Graphically show the total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from (pi, Vi to (pf Vf). With the help of a pV plot, compare the work done in the above case with that carried out against a constant external pressure pf.
According to first law of thermodynamics,
q = ∆U + W
= ∆U + p∆V
At constant volume, ∆V = 0
qv = ∆U
where qv = Heat absorbed at constant volume
∆U = Change in internal energy
Similarly qp = DH
where qp = Heat absorbed at constant pressure
DH = Enthalpy change of the system
Since, the enthalpy change of a system is equal to heat absorbed or heat evolved by the system at constant pressure.
Now, at constant pressure
∆H = ∆U + p∆V
∆V = change in volume
∆H = ∆U + p(Vf – Vi)
∆H = ∆U + (pVf – pVi) …(i)
Vi = initial volume of the system
Vf = Final volume of the system
For ideal gases,
pV = nRT
pVi = nRT
and pVf = npRT
where nr = number of moles of the gaseous reactants
np = number of moles of the gaseous products
Equation (i) becomes,
∆H = ∆U + (npRT – nrRT)
= ∆U + (np – nr) RT
or ∆H = ∆U + ∆ngRT
where ∆ng = Difference between the number of moles of the gaseous products and reactants.
Students miss steps and explanations and thus lose marks. | 7,071 | 24,455 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.640625 | 4 | CC-MAIN-2023-14 | latest | en | 0.868949 | Students must start practicing the questions from CBSE Sample Papers for Class 11 Chemistry with Solutions Set 6 are designed as per the revised syllabus.. ## CBSE Sample Papers for Class 11 Chemistry Set 6 with Solutions. Time Allowed: 3 hours. Maximum Marks: 70. General Instructions:. • All questions are compulsory.. • This question paper contains 37 questions.. • Questions 1-20 in Section A are objective type-very short answer type questions carrying 1 mark each.. • Questions 21 – 27 in Section B are short answer type questions carrying 2 marks each.. • Questions 28 – 34 in Section C are long-answer 1 type questions carrying 3 marks each.. • Questions 35 – 37 in Section D are long-answer 11 type questions carrying 5 marks each.. • There is no overall choice. However, an internal choice has been provided in six questions of one mark, two questions of two marks, two questions of three marks and two questions of five marks. You must attempt only one of the choices in such questions.. • Use log tables, if necessary. Use of calculator is not allowed.. Section – A. Question 1.. What is the mass percent of carbon in carbon dioxide? [1]. (A) 0.034%. (B) 27.27%. (C) 3.4%. (D) 28.7%. OR. The empirical formula and molecular mass of a compound are CH2O and 180 g respectively. What will be the molecular formula of the compound?. (A) C9H18O9. (B) CH2O. (C) C6H12O6. (D) C2H4O2. Option (B) is correct.. Explanation:. Molecular mass of CO2 = 12 + 2(16). = 12 + 32 = 44 g. 44 g of CO2 contains 12 g atoms of carbon. Mass percent of carbon. = $$\frac{\text { Mass of carbon in } \mathrm{CO}_2}{\text { Molar mass of } \mathrm{CO}_2}$$ × 100s. = $$\frac{12}{44}$$ × 100. = 27.27%. OR. Option (C) is correct.. Explanation:. Empirical formula mass (CH2O). = 12 + 2(1) + 16 = 30g. Molecular mass = 180g. n = $$\frac{\text { Molecular mass }}{\text { Empirical formula mass }}$$. = $$\frac{180}{30}$$ = 6. Molecular formula= n × empirical formula. = 6 × CH2O. = C6H12O6. Question 2.. On the basis of thermochemical equations (i), (ii) and (iii), find out which of the algebraic relationship given in options (A) to (D) is correct. [1]. (i) C (graphite) + O2(g) → C02(g); ΔfH = x kj mol-1. (ii) C (graphite) + $$\frac{1}{2}$$O2 (g) → CO(g); ΔrH = y kj mol-1. (iii) CO (g) + $$\frac{1}{2}$$O2 (g) → C02 (g) ;ΔH = z kj mol-1. (A) z = x + y. (B) x = y – z. (C) x = y + z. (D) y = 2z – x. Option (C) is correct.. Explanation: The algebric relationships of the given reaction is Eq.(i) – Eq.(ii) = Eq.(iii). (i) C(graphite) + O2(g) → CO2(g) ; ΔrH = x kJ mol-1. (ii) C(graphite) + $$\frac{1}{2}$$O2(g) → CO(g) ; ΔrH = V kJ. (iii) CO(g) + $$\frac{1}{2}$$O2(g) → CO2(g) ; ΔrH = z kJ mol-1. Hence, x – y = z or x = y + z. Question 3.. Dipole-dipole forces act between the molecules possessing permanent dipole. Ends of dipoles possess ‘partial charges’. The partial charge is : [1]. (A) more than unit electronic charge.. (B) equal to unit electronic charge.. (C) less than unit electronic charge.. (D) double the unit electronic charge.. Option (C) is correct.. Explanation:. Partial charge is the small charge developed by displacement of electrons.. Question 4.. The first ionisation enthalpies of Na, Mg, Al and Si are in the order : [1]. (A) Na < Mg > Al < Si (B) Na > Mg > Al > Si. (C) Na < Mg < Al < Si (D) Na > Mg > Al < Si OR Which of the following is the correct order of size of the given species: (A) I > I > I+. (B) I+ > I > I. (C) I > I+ > I. (D) I > I > I+. Option (A) is correct.. Explanation:. On moving from left to right in a period first ionisation enthalpy increases normally. But, in Mg, as an electron needs to be removed from fully filled s orbital therefore, first ionisation enthalpy of Mg is more than Al.. OR. Option (D) is correct.. Explanation :. Size of cation is smaller while that of anion is bigger than its parent atom.. Question 5.. What will be correct order of vapour pressure of water, acetone and ether at 30°C. Given that among these compounds, water has maximum boiling point and ether has minimum boiling point? [1]. (A) Water < ether <acetone. (B) Water < acetone < ether. (C) Ether < acetone < water. (D) Acetone < ether < water. Option (B) is correct.. Explanation:. Greater is the boiling point, less is the vapour pressure.. Question 6.. Which of the following carbocation is most stable?. (B) (CH3)3C+. (C) CH3CH2+CH2. (D) CH3+CHCH2CH3. Option (B) is correct.. Explanation:. Tertiary carbocation is most stable.. The variables Pressure, Volume, Concentration and Temperature may change the State of Equilibrium. The change is governed by the Le-Chatelier’s principle. The decomposition of NH3(g) can be made spontaneous by increasing the temperature and lowering pressure. In the reaction, removal of any product from the reaction mixture makes the reversible reaction irreversible and therefore, reaction proceeds to completion.. Answer the questions (7) to (10) given below:. Question 7.. The equilibrium Solid → Liquid → Gas will shift in forward direction when:. (A) temperature is increased. (B) temperature is lowered. (C) pressure is increased. (D) pressure is lowered. Option (A) is correct.. Explanation:. Increase in temperature will favour the forward reaction which is endothermic.. Question 8.. Change in free energy for the equilibrium, gaseous reaction, PCl5 → PCl3 + Cl2 on addition of an inert gas at constant pressure and at constant volume is respectively:. (A) decrease, no change. (B) increase, no change. (C) no change, no change. (D) no change, decrease. Option (A) is correct.. Explanation:. Addition of inert gas at constant volume has no effect on any equilibrium reaction. When inert gas is added at constant pressure in the given reaction, it proceeds in forward direction. DG° remains constant, but DG decreases as the reaction proceeds spontaneously in forward direction to attain equilibrium.. Question 9.. At 25°C, the equilibrium constant K1 and I(z are for the reactions:. Which of the following shows the relation between two equilibrium constants?. (A) K2 = K2. (B) K2 = 1/(K). (D) K1 = 1/(K). (D) K1 = 1/K2. Option (C) is correct.. Explanation:. Question 10.. A liquid is in equilibrium with its vapour at its boiling point. On an average, the molecules in the two phases have equal:. (A) Intermolecular forces. (B) Potential energy. (C) Kinetic energy. (D) None of these. Option (C) is correct.. Explanation:. At boiling point, liquid and vapour phases both are present. So, the molecules in the two phases have equal kinetic energy.. Question 11.. The addition of HCl to an alkene proceeds in two steps. The first step is the attack of W ion to >C =C< portion which can be shown as A I. Option (A) is correct.. Explanation:. Since double bond is a source of electrons and the charge flows from source of more electron density, therefore, electrons of the double bond attack the proton.. Question 12.. How will you convert: ethyne to but-2-yne. [1]. Students directly write the products and forget to mention side products and reaction conditions.. Make a list of important conversions and learn them.. Understand each step and conditions involved during conversion reactions.. Question 13.. The structure of triphenylmethyl cation is given here. This is very stable and some of its salts can be stored for months. Explain the cause of high stability of this cation.. Triphenylmethyl cation is a tertiary carbocation which can show nine possible canonical structures and hence is very stable. The three canonical forms for one benzene ring are shown below.. Question 14.. Can we separate two liquids A (b.p. 353 K) and B (b.p. 365 K) present in a mixture by simple distillation? [1]. No, because in simple distillation, vapours of both the liquids will be formed simultaneously and will condense together in receiver as the difference between the boiling points is very less. They can be separated by fractional distillation.. Students sometimes answer in yes or no without giving legit explanation.. The alternate method of separation also must be mentioned.. Question 15.. What do you mean by cracking? [1]. The thermal decomposition of higher hydrocarbons into lower hydrocarbons in the presence or absence of a catalyst is called cracking.. Question 16.. Assign the oxidation number to Cr in K2Cr2O7.. Let the oxidation number of Cr be x. 2 × (+1) + 2x + 7 × (- 2) = 0. 2 + 2x – 14 = 0. 2x – 12 = 0. x = $$\frac{12}{2}$$ = +6. Oxidation number of Cr in K2Cr2O7 = +6. Question 17.. Assertion (A): Toluene on Friedal-Crafts methylation gives o- and p-xylene.. Reason (R): CH3-group bonded to benzene ring increases electron density at o- and p- position.. (A) Both A and R are correct and R is the correct explanation of A.. (B) Both A and R are correct but R is not the correct explanation of A.. (C) Both A and R are not correct.. (D) A is not correct but R is correct.. Option (A) is correct.. Question 18.. Assertion (A): Benzene on heating with cone. H2SO4 gives benzene sulphonic acid which when heated with superheated steam under pressure gives benzene. [1]. Reason (R): Sulphonation is a reversible process.. (A) Both A and R are correct and R is the correct explanation of A.. (B) Both A and R are correct but R is not the correct explanation of A.. (C) Both A and R are not correct.. (D) A is not correct but R is correct.. Option (A) is correct.. Explanation:. Sulphonation of benzene is an electrophilic substitution reaction in which SO3 acts as the electrophile.. Question 19.. Why there is large number of lines in hydrogen spectrum? [1]. Large number of lines are there in hydrogen spec¬trum because different possible transitions can be observed which leads to large number of spectral lines.. Question 20.. Pressure is determined as force per unit area of the surface. The SI unit of pressure, pascal is as shown below:. 1 Pa = 1 Nm-2. If mass of air at sea level is 1034 g cm-2, calculate the pressure in pascal. [1]. Mass of air at sea level = 1034 g cm-2. Acceleration due to gravity, g = 9.8 ms-2. Pressure is the force or weight per unit area.. Section – B. Question 21.. What does the following prefixes stand for. (a) pico. (b) nano. (c) micro. (d) deci. OR. Write main points of Dalton’s atomic theory. [2]. Prefixe Stand for (a) pico (p) 10-12 (b) nano (n) 10-9 (c) micro (μ) 10-6 (d) deci (d) 10-1. OR. The main points of Dalton’s atomic theory are:. (i) All matters are made of atoms. Atoms are indivisible and indestructible.. (ii) All atoms of a given element are identical in mass and properties. Atoms of different elements differ in mass.. (iii) Compounds are formed when atoms of different elements combine in a fixed ratio.. (iv) Chemical reactions involve reorganisation of atoms. These are neither created nor destroyed in a chemical reaction.. Question 22.. Chlorophyll present in green leaves of plants absorbs light at 4.620 × 1014Hz. Calculate the wavelength of radiation in nanometer. Which part of the electromagnetic spectrum does it belong to? [2]. Given, v = 4.620 × 1014 Hz. λ = ?. Wavelength λ = $$\frac{c}{v}$$. = 0.6494 × 10-6 m. = 649.4 × 10-9 m. = 649.4 nm. It belongs to visible region.. Question 23.. In both water and diethyl ether, the central atom viz. O-atom has same hybridisation. Why do they have different bond angles? Which one has greater bond angle? [2]. Both water and diethyl ether have the central atom O in sp3 hybrid state with two lone pairs of electrons. But due to the greater repulsion between two ethyl (C2H5) groups in diethyl ether than between two H-atoms in H2O result in greater bond angle (110°) in diethyl ether than 104.5° in that of water (H2O).. Question 24.. (a) Why is an organic compound fused with sodium for testing nitrogen, halogens and sulphur?. (b) Under what conditions can the process of steam distillation used? [2]. (i) On fusing with sodium metal, the elements present in an organic compound are converted from covalent form into the ionic form.. (ii) Steam distillation is used to purify the substances which are steam volatile and water and the liquid are not miscible with each other.. Question 25.. Write the name of the isomerism shown by the following pairs:. (i) Buta-1,3-diene and But-l-yne (C4H6). | (ii) Ethoxy butane and Propoxy propane (C6H14O). [2]. OR. Which bond is more polar in the following pairs of molecules.. (i) H3C-H, H3C-Br. (ii) H3C-NH2, H2C-OH. (i) Functional isomerism. H2C=CH – CH = CH2 and HC = C-CH2CH3. (ii) Metamerism. CH3 – CH2 – CH2 – CH2 – O- CH2CH3 and C3H7OC3H7. Students get confuse and give wrong answers.. Understand different type of isomerism with examples, different functional groups too.. OR. (i) C-Br because Br is more electronegative than H.. (ii) C-O because O is more electronegative than N.. Question 26.. An alkane C8H18 is obtained as the only product on subjecting a primary alkyl halide to Wurtz reaction. On. monobromination this alkane yields a single isomer of a tertiary bromide. Write the structure of alkane and the tertiary bromide. [2]. Question 27.. What are relative stabilities of different conformations of ethane? Is is possible to isolate these at room temperature? [2]. Staggered form of ethane is more stable than the eclipsed form because the force of repulsion between hydrogen atoms on adjacent C atom is minimum. The energy difference between the staggered form and the eclipsed form of ethane is just 12.55 kJ mol- 1. Therefore, it is not possible for these two forms of ethane to isolate at room temperature.. Section – C. Question 28.. What are (a) representative elements (b) transition elements (c) Lanthanoid and actinoids. Give their position in modern periodic table. [3]. (a) Representative Elements : Group 1, 2, 13, 14, 15, 16, 17 and 18 exhibit the main groups of the periodic table and so, the elements of these groups are collectively called representative elements.. These elements belong to s-block and p-block in modern periodic table.. (b) Transition Elements : d-block transition metals form a bridge between the chemically active metals of s-block elements and the less active elements of Groups 13 and 14 are known as transition elements.. (c) Lanthanoids and Actinoids : The elements of 4f series [i.e., from Ce (Z = 58) to Lu (Z = 71)] are called lanthanoids and the elements of 5f series [i.e., from Th (Z = 90) to Lr (Z = 103)] are called actinoids. These elements belong to /-block elements in the modern periodic table which lie at the bottom of the periodic table.. Question 29.. The Mn3+ ion is unstable in solution and undergoes disproportionation to give Mn2+, MnO2 and H+ ion. Write a balanced ionic equation for the reaction. [3]. The skeletal ionic equation is,. Mn3+(aq) → Mn2+(aq) + MnO2(s) + H+(aq). Reduction half reaction. Mn3+(aq) + e → Mn2+. Oxidation half reaction. Mn3+(aq)→ MnO2 + e. Balance charge by adding 4H+ to right side and then balance O atoms by adding 2H2O to left side in oxidation half reaction. Mn3+(aq) + 2H2O(l) → MnO2(s) + e + 4H+(aq). By adding both equations, we get. 2Mn3+(aq) + 2H2O(l) → Mn2+ + MnO2(s) + 4H+(aq). This represents the balanced redox reaction (disproportionation reaction).. Question 30.. Calculate the standard enthalpy of formation of CH3OH(l) from the following data :. (i) CH3OH(l) + $$\frac{3}{2}$$02(g) → C02(g)+ 2H2O(l) ΔrH° = – 726 kj/mol. (ii) C(s) + 02(g) → C02(g); ΔcH° = – 393 kj/mol. (iii) H2(g) + ½O2(g) → H2O(l); ΔfH° = – 286 kj/mol. [3]. The required equation is. C(s) + 2H2(g) + $$\frac{1}{2}$$ O2(g) → CH3OHO);. ΔfH° = ± ?. To get the above required equation :. Step 1 : Multiply eq. (iii) by 2 and add to eq. (ii). C(s) + 2H2(g) + 2O2(g) → CO2(g) + 2H2O(l) ……………(iv). ΔfH° = (2 x – 286) + (- 393). = – 572 – 393. = – 965 kJ/mol. Step 2 : Subtract eq. (i) from eq. (iv). C(s) + 2H2(g) + $$\frac{1}{2}$$O2(g) → CH3OH(l);. ΔH = – 965 – (- 726). = – 239 kJ/mol. ΔfH° = – 239 kJ/mol. Question 31.. (i) State the formula and name of the conjugate base of each of the following acids :. (a) H3O+. (b) HSO4. (c) NH4+. (d) HF. (e) CH3COOH. (f) CH3NH3+. (g) H3PO4. (h) H2PO4. (ii) The ionic product of water is 0.11 × 10-14 at 273 K, 1 × 10-14 at 298 K and 7.5 × 10-14 at 373K. Deduce from this data whether the ionization of water to hydrogen and hydroxide ion is exothermic or endothermic. [3]. (i) The formula and name of the conjugate base are:. (a) H3O+: Water. (b) SO42- : Sulphate ion. (c) NH3 : Ammonia. (d) F : Fluoride ion. (e) CH3COO : Acetate ion. (f) CH3NH2 : Methylamine. (g) H2PO4 : Dihydrogen phosphate. (h)H2PO42- : Mono hydrogen phosphate. (ii) Kw = [H3O+] [OH]. According to the data, the value of K, is increasing with temperature. Therefore, according to Le- Chateliebs principle, the ionisation of water is endothermic.. Question 32.. Explain:. (i) Tea or coffee is sipped from the saucer, when it is quite hot.. (ii) Liquids possess fluidity. [3]. (i) Tea or coffee is sipped from the saucer, when it is quite hot because it has larger surface area than the cup. In larger surface area, the rate of evaporation is faster due to which tea or coffee cools rapidly.. (ii) Liquids have indefinite shape. They take the shape of the container in which they are placed. This is due to the fact that the molecules of liquids are in a state of constant random motion and therefore they can move freely. So, the liquids possess fluidity.. Question 33.. (a) The effect of uncertainty principle is significant only for motion of microscopic particles and is negligible for the macroscopic particles. Justify the statement with the help of a suitable example.. (b) What is the difference between the terms orbit and orbital ? [3]. If mass of an object = 1 mg = 10-6 kg. Then, according to Heisenberg’s uncertainty principle,. Since, the value of Δx.Δv obtained is very small and is insignificant. So, effect of uncertainty principle is significant only for motion of microscopic particles and is negligible for the macroscopic particles.. (b). Orbit Orbital 1. An orbit is well defined circular path around the nucleus in which the electrons revolve. 1. An orbital is the threedimensional space around the nucleus within which the probability of finding an electron is maximum (upto 90%). 2. It represents the planar motion of an electron around the nucleus. 2. It represents the three dimensional motion of an electron around the nucleus.. Question 34.. Calculate the number of moles:. (i) 5.0 L of 0.75 M Na2CO3. (ii) 7.85 g of Fe. (iii) 34.2 g of sucrose (C12H22O11) [3]. OR. A compound made up of two elements A and B has A = 70%, B= 30%. Their relative number of moles in the compound is 1.25 and 1.88, calculate:. (i) Atomic masses of the elements A and B.. (ii) Molecular formula of the compound, if its molecular mass is found to be 160.. (i) Number of moles of Na2 CO3 = Molarity × Volume of solution in litre. = 0.75 × 5. = 3.75 mol. (ii) Number of moles of Fe. = $$\frac{\text { Mass }}{\text { Molecular mass }}$$. = $$\frac{34.2}{342}$$. = 0.14. (iii) Number of moles of sucrose. = $$\frac{\text { Mass }}{\text { Molecular mass }}$$. = $$\frac{34.2}{342}$$. = 0.1. OR. (i) Atomic mass of element A. = $$\frac{\% \text { of element } \mathrm{A}}{\text { Relative number of moles }}$$. = $$\frac{70}{1.25}$$. = 56. Atomic mass of element B. = $$\frac{\% \text { of element } \mathrm{B}}{\text { Relative number of moles }}$$. = $$\frac{30}{1.88}$$. = 15.957 ≈ 16. (ii). Compound Simplest molar ratio Simplest whole-number ratio A $$\frac{1.25}{1.25}$$= 1 2 B $$\frac{1.88}{1.25}$$= 15 3. Empirical formula of compound = A2B3. Molecular mass = 160. Empirical formula mass. = 2(56) + 3(16). = 112 + 48 = 160. n = $$\frac{\text { Molecular mass }}{\text { Empirical formula mass }}$$. = $$\frac{160}{160}$$ = 1. Molecular formula. = n × Empirical formula. = 1 × A2B3. = A2B3. Sometimes students forget to multiply by n while finding molecular formula and do mistakes.. Understand the problem and check for the necessary data, which are available in the problem. Follow steps and ensure no steps are missed.. Section – D. Question 35.. (i) For each of the following compounds, write a more condensed formula and also their bond-line formulae.. (ii) Write the I.U.RA.C. name of. OR. (a) A sample of 0.50 g of an organic compound was treated according to Kjeldahl’s method. The ammonia evolved was absorbed in 50 ml of 0.5 M H2SO4. The residual acid required 60 mL of 0.5 M solution of NaOH for neutralisation. Find the percentage composition of nitrogen in the compound.. (b) In the estimation of sulphur by Carius method, 0.468 g of an organic sulphur compound afforded 0.668 g of barium sulphate. Find out the percentage of sulphur in the given compound.. (i) Condensed formulae. (a) (CH3)2CHCH2OH. (b) CH3(CH2)5CHBrCH2CHO. (c) HO(CH2)3CH(CH3)CH(CH3)2. (d) HOCH(CN)2. Bond-line formulae-. Sometimes students ignore the triple bond in (ii) question.. While writing bond-line formula, observe carefully. It is similar to structural formula.. OR. Given that, total mass of organic compound = 0.50 g 60 mL of 0.5 M solution of NaOH was required by residual acid for neutralisation.. 60 mL of 0.5 M NaOH solution = $$\frac{60}{2}$$mL of 0.5 M. H2SO4 = 30 mL of 0.5 M H2SO4. Acid consumed in absorption of evolved ammonia is (50-30) mL = 20 mL. Again, 20 mL of 0.5 M. H2SO4 = 40 mL of 0.5 M NH3. Also, since 1000 mL of 1 M NH3 contains 14 g of nitrogen,. 40 mL of 0.5 M NH3 will contains = $$\frac{14 \times 40}{1000}$$ × 0.5. = 0.28 g of N. Therefore, percentage of nitrogen in 0.50 g of organic compound = $$\frac{0.28}{0.50}$$ × 100. = 5.6%. Students forget steps and end up with mistakes.. Understand the problem and practice steps wise and do calculations carefully.. (b) Given, total mass of organic compound = 0.468 g Mass of barium sulphate formed = 0.668 g. 1 mol of BaSO4 = 233 g of BaSO4 = 32 g of sulphur. Thus, 0.668 g of BaSO4 contains $$\frac{32 \times 0.668}{233}$$ g of. sulphur = 0.0917 g of sulphur. Therefore, percentage of sulphur = $$\frac{0.0917}{0.468}$$ × 100. = 19.59 %. Hence, the percentage of sulphur in the given compound is 19.59 %.. Question 36.. Give mechanism of addition of HBr to Propene. [5]. Addition of HBr to propene (unsymmetrical alkene) follows Markovnikov’s rule according to which the negative part of the addendum gets attached to that C atom which possesses lesser number of hydrogen atoms.. Mechanism: Hydrogen bromide provides an electrophile, H+, which attacks the double bond to form carbocation as:. Secondary carbocations are more stable than primary carbocations. Therefore, the former predominates as it will form at a faster rate. Thus, in the next step, Br attacks the carbocation to form 2-bromopropane as the major product.. Addition of HBr to unsymmetrical alkenes like propene in the presence of light or peroxide takes place contrary to the Markovnikov’s rule. This so happens only with HBr but not with HCl and HI. This addition of HBr to propene in the presence of benzoyl peroxide follows anti-Markovnikov’s rule or peroxide effect or Kharasch effect.. Secondary free radicals are more stable than primary radicals. Therefore, the former predominates since it forms at a faster rate. Thus, 1-bromopropane is obtained as the major product.. • Some students write the reaction, but forget to explain the mechanism.. • Some students forget to explain the attack of Br- on carbocation.. Students must explain addition using Markovnikov’s rule as well as anti – Markovnikov’s rule.. Question 37.. Derive the relationship between AH and AU for an ideal gas. Explain each term involved in the equation. [5]. OR. Graphically show the total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from (pi, Vi to (pf Vf). With the help of a pV plot, compare the work done in the above case with that carried out against a constant external pressure pf.. According to first law of thermodynamics,. q = ∆U + W. = ∆U + p∆V. At constant volume, ∆V = 0. qv = ∆U. where qv = Heat absorbed at constant volume. ∆U = Change in internal energy. Similarly qp = DH. where qp = Heat absorbed at constant pressure. DH = Enthalpy change of the system. Since, the enthalpy change of a system is equal to heat absorbed or heat evolved by the system at constant pressure.. Now, at constant pressure. ∆H = ∆U + p∆V. ∆V = change in volume. ∆H = ∆U + p(Vf – Vi). ∆H = ∆U + (pVf – pVi) …(i). Vi = initial volume of the system. Vf = Final volume of the system. For ideal gases,. pV = nRT. pVi = nRT. and pVf = npRT. where nr = number of moles of the gaseous reactants. np = number of moles of the gaseous products. Equation (i) becomes,. ∆H = ∆U + (npRT – nrRT). = ∆U + (np – nr) RT. or ∆H = ∆U + ∆ngRT. where ∆ng = Difference between the number of moles of the gaseous products and reactants.. Students miss steps and explanations and thus lose marks. |
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