6.13B: Damage to Proteins and Nucleic Acids
- Explain how microbes are controlled through DNA and protein damage
A bacteriostatic agent or bacteriostat, abbreviated Bstatic, is a biological or chemical agent that stops bacteria from reproducing, while not necessarily harming them. Depending on their application, bacteriostatic antibiotics, disinfectants, antiseptics, and preservatives can be distinguished. Upon removal of the bacteriostat, the bacteria usually start to grow again. This is in contrast to bactericides, which kill bacteria.
Bacteriostats are often used in plastics to prevent growth of bacteria on surfaces. Bacteriostats commonly used in laboratory work include sodium azide (which is acutely toxic) and thiomersal (which is a mutagen in mammalian cells).
Bacteriostatic antibiotics limit the growth of bacteria by interfering with bacterial protein production, DNA replication, or other aspects of bacterial cellular metabolism. They must work together with the immune system to remove the microorganisms from the body. However, there is not always a precise distinction between them and bactericidal antibiotics. High concentrations of some bacteriostatic agents are also bactericidal, whereas low concentrations of some bacteriocidal agents are bacteriostatic.
This group of drugs include: Tetracyclines, sulfonamides, Spectinomycin, Trimethoprim, Chloramphenicol, Macrolides, and Lincosamides.
Tetracycline is a broad-spectrum polyketide antibiotic produced by the Streptomyces genus of Actinobacteria, indicated for use against many bacterial infections. It is a protein synthesis inhibitor. It is commonly used to treat acne today, and, more recently, rosacea, and is historically important in reducing the number of deaths from cholera. Tetracycline is marketed under the brand names Sumycin, Tetracyn, and Panmycin, among others. Actisite is a thread-like fiber formulation used in dental applications. It is also used to produce several semisynthetic derivatives, which together are known as the tetracycline antibiotics. The term “tetracycline” is also used to denote the four-ring system of this compound. “Tetracyclines” are related substances that contain the same four-ring system.
LICENSES AND ATTRIBUTIONS
CC LICENSED CONTENT, SPECIFIC ATTRIBUTION
- Gramicidin. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Gramicidin. License : CC BY-SA: Attribution-ShareAlike
- Bacterial cell structure. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Bacterial_cell_structure. License : CC BY-SA: Attribution-ShareAlike
- Polymyxin. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Polymyxin. License : CC BY-SA: Attribution-ShareAlike
- permeable. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/permeable. License : CC BY-SA: Attribution-ShareAlike
- membrane. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/membrane. License : CC BY-SA: Attribution-ShareAlike
- antimicrobial. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/antimicrobial. License : CC BY-SA: Attribution-ShareAlike
- Polymyxin. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Polymyxin. License : Public Domain: No Known Copyright
- Tetracycline. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Tetracycline. License : CC BY-SA: Attribution-ShareAlike
- Bacteriostatic. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Bacteriostatic. License : CC BY-SA: Attribution-ShareAlike
- replication. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/replication. License : CC BY-SA: Attribution-ShareAlike
- bacteriostatic. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/bacteriostatic. License : CC BY-SA: Attribution-ShareAlike
- bacteria. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/bacteria. License : CC BY-SA: Attribution-ShareAlike
- Polymyxin. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Polymyxin. License : Public Domain: No Known Copyright
- Tetracycline. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Tetracycline. License : Public Domain: No Known Copyright
Key Points
- Bacteriostatic antibiotics limit the growth of bacteria by interfering with bacterial protein production, DNA replication, or other aspects of bacterial cellular metabolism.
- Upon removal of the bacteriostat, the bacteria usually start to grow again.
- Bacteriostatic antibiotics must work together with the immune system to remove the microorganisms from the body.
Key Terms
- bacteriostatic : A drug that prevents bacterial growth and reproduction but does not necessarily kill them. When it is removed from the environment the bacteria start growing again.
- bacteria : A type, species, or strain of bacterium.
- replication : Process by which an object, person, place or idea may be copied mimicked or reproduced.


23.2: Multinomial Coefficients
The expansion of the trinomial \((x + y + z)^n\) is the sum of all possible products
\begin{equation*} \dfrac{n!}{i! \, j!\, k!}\,x^i y^j z^k, \end{equation*}
where \(0 \le i,j,k \le n\) such that \(i + j + k = n\text{.}\)
- Proof Idea.
-
Similarly to the proof of the Binomial Theorem , write
\begin{gather} (x + y + z)^n = (x + y + z) (x + y + z) \cdots (x + y + z) \text{,}\label{equation-multinomial-trinomial}\tag{\(\star\)} \end{gather}
with \(n\) factors. To expand this out, we generalize the FOIL method: from each factor, choose either \(x\text{,}\) \(y\text{,}\) or \(z\text{,}\) then multiply all your choices together. For any such product, the powers on \(x\text{,}\) \(y\text{,}\) and \(z\) must sum to \(n\text{.}\) To get the final expansion, add the results of all possible such products.But we can collect terms that have the same exponent on each of \(x\text{,}\) \(y\text{,}\) and \(z\text{.}\) How many ways can we form a specific term \(x^i y^j z^k\text{,}\) for \(0 \le i,j,k \le n\) such that \(i + j + k = n\text{?}\) We have \(C^n_i\) ways to choose \(i\) factors from the right-hand side of (\(\star\)) from which to take \(x\text{,}\) then \(C^{n-i}_j\) ways to choose \(j\) factors from which to take \(y\text{.}\) But now from all remaining factors we must choose \(z\text{,}\) and there is only \(1\) way to do this. So the coefficient on \(x^i y^j z^k\) is
\begin{equation*} \binom{n}{i} \binom{n-i}{j} = \left(\dfrac{n!}{i! (n-i)!}\right) \:\: \left(\dfrac{(n-i)!}{j! (n-i-j)!}\right) = \dfrac{n!}{i! \, j! \, k!}\text{.} \end{equation*}
- Alternative proof idea.
-
Use the Binomial Theorem on \((x + (y + z))^n\text{,}\) then again on \((y + z)^k\) for each term \(C^n_k x^{n - k} (y + z)^k\text{.}\) (This would be very tedious!)
Determine the terms in the expansion of \((2 x + y - 3 z)^3\text{.}\)
Solution
First, rewrite
\begin{equation*} (2 x + y - 3 z)^3 = ((2 x) + y + (-3 z))^3 \text{.} \end{equation*}
So the terms in the expansion involve products
\begin{equation*} (2 x)^i y^j (-3 z)^k \text{.} \end{equation*}
We need to account for all triples of exponents \(i, j, k\) that sum to \(3\text{.}\)
| \(i\) | \(j\) | \(k\) | \(n! \over i! \, j! \, k! \) | term | simplified |
| \(3\) | \(0\) | \(0\) | \(1\) | \((2 x)^3 \) | \(8 x^3 \) |
| \(0\) | \(3\) | \(0\) | \(1\) | \(y^3 \) | \(y^3 \) |
| \(0\) | \(0\) | \(3\) | \(1\) | \((-3 x)^3 \) | \(-27 z^3 \) |
| \(2\) | \(1\) | \(0\) | \(3\) | \(3 (2 x)^2 y \) | \(12 x^2y \) |
| \(2\) | \(0\) | \(1\) | \(3\) | \(3 (2 x)^2 (-3 z) \) | \(-36 x^2 z \) |
| \(1\) | \(2\) | \(0\) | \(3\) | \(3 (2 x) y^2 \) | \(6 x y^2 \) |
| \(0\) | \(2\) | \(1\) | \(3\) | \(3 y^2 (-3 z) \) | \(-9 y^2 z \) |
| \(1\) | \(0\) | \(2\) | \(3\) | \(3 (2 x) (-3 z)^2 \) | \(-54 x z^2 \) |
| \(0\) | \(1\) | \(2\) | \(3\) | \(3 y (-3 z)^2 \) | \(-9 y z^2 \) |
| \(1\) | \(1\) | \(1\) | \(3!\) | \(6 (2 x) y (-3 z) \) | \(-36 x y z \) |
Collecting this together, we have
\begin{align*} & (2 x + y - 3 z)^3 \\ & = 8 x^3 + y^3 - 27 z^3 + 12 x^2y - 36 x^2 z \\ & + 6 x y^2 - 9 y^2 z - 54 x z^2 - 36 x y z \text{.} \end{align*}
Determine the coefficient on \(x^5 y^2 z^7\) in the expansion of \((x + y + z)^{14}\text{.}\)
Solution
Here we don't have any extra contributions to the coefficient from constants inside the trinomial, so using \(n=14\text{,}\) \(i = 5\text{,}\) \(j = 2\text{,}\) \(k = 7\text{,}\) the coefficient is simply
\begin{equation*} \dfrac{14!}{5! \, 2! \, 7!} = \dfrac{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8} {5 \cdot 4 \cdot 3 \cdot 2 \cdot 2} = 14 \cdot 13 \cdot 11 \cdot 9 \cdot 4 = 72,072\text{.} \end{equation*}
The pattern of the Binomial Theorem and Trinomial Theorem continues.
The expansion of \((x_1 + x_2 + \cdots + x_m)^n\) is the sum of all possible products
\begin{equation*} \dfrac{n!}{i_1! \, i_2! \, \cdots \, i_m!} \, x_1^{i_1} x_2^{i_2} \cdots x_m^{i_m} \text{,} \end{equation*}
where the exponents \(i_1, i_2, \ldots, i_n\) sum to \(n\text{.}\)
- Proof Idea.
-
Use the same generalized FOIL method argument as in the Binomial and Trinomial Theorem proofs, and simplify the product of combination formulas obtained.
Determine the coefficient on \(x^2 y z^6\) in the expansion of \((3 x + 2 y + z^2 + 6)^8\text{.}\)
Solution
Rewriting
\begin{equation*} (3 x + 2 y + z^2 + 6)^8 = ((3 x) + (2 y) + (z^2) + 6)^8 \text{,} \end{equation*}
we see that the four terms in this multinomial are
\begin{equation*} 3 x, \quad 2 y, \quad z^2, \quad 6 \text{.} \end{equation*}
So what we really want to know is the total coefficient on the term involving
\begin{equation*} (3 x)^2 (2 y)^1 (z^2)^3 6^2 \text{.} \end{equation*}
The
Multinomial Theorem
tells us that there will be
\begin{equation*} \dfrac{8!}{2! \, 1! \, 3! \, 2!} = 1,680 \end{equation*}
such terms in the expansion of the multinomial. Therefore, we obtain the term
\begin{equation*} (1,680) (3 x)^2 (2 y)^1 (z^2)^3 6^2 = (1,088,640) x^2 y z^6 \end{equation*}
with a total coefficient of \(1,088,640\text{.}\)
a number appearing as a coefficient in the expansion of \((x_1 + x_2 + \cdots + x_m)^n\)
the coefficient on the term \(x_1^{i_1} x_2^{i_2} \cdots x_m^{i_m}\) in the expansion of \((x_1 + x_2 + \cdots + x_m)^n\text{,}\) where the exponents \(i_1, i_2, \ldots, i_m\) must sum to \(n\)
- The Multinomial Theorem tells us \(\displaystyle \binom{n}{i_1,i_2,\ldots,i_m} = \dfrac{n!}{i_1! \, i_2! \, \cdots \, i_m!} \text{.}\)
- In the case of a binomial expansion \((x_1 + x_2)^n\text{,}\) the term \(x_1^{i_1} x_2^{i_2}\) must have \(i_1 + i_2 = n\text{,}\) or \(i_2 = n - i_1\text{.}\) The Multinomial Theorem tells us that the coefficient on this term is
\begin{equation*} \binom{n}{i_1,i_2} = \dfrac{n!}{i_1!i_2!} = \dfrac{n!}{ i_1! (n - i_1)!} = \binom{n}{i_1}. \end{equation*}
Therefore, in the case \(m=2\text{,}\) the
Multinomial Theorem
reduces to the
Binomial Theorem
.


<IP_ADDRESS>: The Corpse
Remember, my Beloved, what thing we met
By the roadside on that sweet summer day;
There on a grassy couch with pebbles set,
A loathsome body lay.
The wanton limbs stiff-stretched into the air,
Steaming with exhalations vile and dank,
In ruthless cynic fashion had laid bare
The swollen side and flank.
On this decay the sun shone hot from heaven
As though with chemic heat to broil and burn,
And unto Nature all that she had given
A hundredfold return.
The sky smiled down upon the horror there
As on a flower that opens to the day;
So awful an infection smote the air,
Almost you swooned away.
The swarming flies hummed on the putrid side,
Whence poured the maggots in a darkling stream,
That ran along these tatters of life's pride
With a liquescent gleam.
And like a wave the maggots rose and fell,
The murmuring flies swirled round in busy strife:
It seemed as though a vague breath came to swell
And multiply with life
The hideous corpse. From all this living world
A music as of wind and water ran,
Or as of grain in rhythmic motion swirled
By the swift winnower's fan.
And then the vague forms like a dream died out,
Or like some distant scene that slowly falls
Upon the artist's canvas, that with doubt
He only half recalls.
A homeless dog behind the boulders lay
And watched us both with angry eyes forlorn,
Waiting a chance to come and take away
The morsel she had torn.
 Sun that lights my spring!
O passionate and pure!
Yes, such will you be, Queen of every grace!
When the last sacramental words are said;
And beneath grass and flowers that lovely face
Moulders among the dead.
Then, O Beloved, whisper to the worm
That crawls up to devour you with a kiss,
That I still guard in memory the dear form
Of love that comes to this!


Page 1.6: Factoring Polynomials
Suppose we were asked to simplify \( 7x^2yz(2y^2 + 3xz^2) \). How would we do this? Quite simply, we would distribute to obtain \( 14x^2 y^3 z + 21x^3 yz^3 \).
The question we will now consider is essentially the reverse. That is, starting with \( 14x^2 y^3 z + 21x^3 yz^3 \) how can we go back to \( 7x^2yz(2y^2 + 3xz^2) \)?
The answer is that we simply check the greatest common factor/divisor of each corresponding part. Notice that:
1) \( gcd(14, 21) = 7 \)
2) \( gcd( x^2, x^3) = x^2 \)
3) \( gcd( y^2, y) = y \)
4) \( gcd( z, z^3) = z \)
So each term in \( 14x^2 y^3 z + 21x^3 yz^3 \) shares a factor of \( 7x^2yz \). Hence
\[ \frac{14x^2 y^3 z + 21x^3 yz^3 }{ 7x^2yz} = \frac{14x^2 y^3 z }{7x^2yz} + \frac{21x^3 yz^3}{7x^2yz} = 2y^2 + 3xz^2 \nonumber\ \]
That is, \[ \frac{14x^2 y^3 z + 21x^3 yz^3 }{ 7x^2yz} = 2y^2 + 3xz^2 \nonumber\ \]
Cross multiplying yields \( 14x^2 y^3 z + 21x^3 yz^3 = 7x^2yz(2y^2 + 3xz^2) \). With enough practice, we will be able to do this in one line.
Factor \( 8x^2y^3 + 16xy^4 - 32x^5y \).
- Answer
-
\(8xy( xy^2 + 2y^3 - 4x^4 ) \)
Factor \( 48ab^2 - 64 a^3b^5\).
- Answer
-
\( 16ab^2(3-4a^2b^3) \)
When factoring, we should keep an eye out for special cases. For example, one such case we should look out for is when we are asked to factor the difference of two squares.
More concretely, consider the expression \( 100x^2 - 25 \) which is a difference of two squares. Observe that \( 100x^2 - 25 = (100x + 5)(100x - 5) \).
More generally, \(a^2 - b^2) = (a-b)(a+b) \) where \(a\) and \(b\) may represent real numbers or algebraic expressions. A list of some special cases are provided below.
Theorem: Let \(a\) and \(b\) denote real numbers or algebraic expressions. Then
1) \(a^2 - b^2) = (a+b)(a-b) \)
2) \(a^2 + 2ab + b^2 = (a+b)^2 \)
3) \(a^2 - 2ab + b^2 = (a-b)^2 \)
Factor the following:
1) \( 49x^2 - 81 \)
2) \( 4x^2-36 \)
Answer
-
1) \( 49x^2 - 81 = (7x+9)(7x-9) \)
2) \( 4x^2-36 = (2x+6)(2x-6) = 2(x+3)2(x-3) = 4(x+3)(x-3) \)
We will often have to factor a polynomial, especially quadratics. Recall from the last section that a quadratic is a polynomial of the form \( a_2 x^2 + a_1 x + a_0 \). However, we will commonly denote a quadratic as \(ax^2 + bx + c \). Allow us to now discuss some techniques on how to factor a quadratic.
To factor \(ax^2 + bx + c \), we perform the following steps:
1) First multiply \(a\) by \(c\).
2) Search for two factors of \(ac\) whose sum is \(b\).
3) Rewrite \(b\) as a sum in the quadratic and then factor by grouping.
Factor \( x^2 - 5x + 6 \)
- Answer
-
1) We first multiply the \(a\) term with the \(c\) term. Doing so yields 6.
2) We now must find factors of \(6\) which sums to \(-5\). We see that \(-2\) and \(-3\) does the trick.
3) \begin{align*} x^2 - 5x + 6 &= x^2 -2x - 3x + 6 \\ &= (x^2 - 2x) + (-3x + 6) \\ &= x(x-2) - 3(x-2) \\ &= (x-2)(x-3) \end{align*}
In your previous studies, you may have seen a more "simple" way to factor quadratics when \(a = 1\).
To factor \(x^2 + bx + c \) the AC Method can be simplified to the following:
1) Search for two factors of \(c\) whose sum is \(b\). Let us call these factors \(r_1\) and \(r_2\).
2) Then \(x^2 + bx + c = (x + r_1) (x + r_2) \).
Factor \( x^2 - 5x + 6 \)
- Answer
-
1) Since \(a = 1\) our first step should be finding factors of \(6\) which sums to \(-5\). We see that \(-2\) and \(-3\) does the trick. So \(r_1 = -2 \) and \( r_2 = -3 \).
2) Then \( x^2 - 5x + 6 = (x -2) (x-3) \)
Again, this latter technique only works when \(a= 1\).
Factor \( 2x^2 - 5x -3 \)
- Answer
-
1) We first multiply the \(a\) term with the \(c\) term. Doing so yields \(-6 \).
2) We now must find factors of \(-6\) which sums to \(-5\). We see that \(-6\) and \(1\) does the trick.
3) \begin{align*} 2x^2 - 5x -3 &= 2x^2 - 6x + x -3 \\ &= (2x^2 - 6x) + (x -3) \\ &= 2x (x-3) + 1(x-3) \\ &= (x-3)(2x+1) \end{align*}
Factor:
1) \(3x^2 + x - 4 \)
2) \(4x^2 + 5x - 6 \)
3) \(2x^2 - 7x + 6 \)
4) \(5x^2 - 9x -2 \)
5) \( x^2 +2x - 24 \)
6) \(x^2 + 8x + 15 \)
- Answer
-
1) \(3x^2 + x - 4 = (3x+4)(x-1) \)
2) \(4x^2 + 5x - 6 = (x+2)(4x-3) \)
3)\(2x^2 - 7x + 6 = (2x-3)(x-2) \)
4) \(5x^2 - 9x -2 = (5x+1)(x-2) \)
5) \( x^2 +2x - 24 = (x+6)(x-4) \)
6) \(x^2 + 8x + 15 (x+3)(x+5) \)
Solving Quadratic Equations
We will now turn our attention to solving quadratic equations. We first note the following theorem.
Theorem: Suppose \(a\) and \(b\) are real numbers or algebraic expressions. If \(ab=0\) then either \(a = 0\) or \(b = 0 \).
With The Zero Product Property, we can begin to solve equations such as quadratics. When we say solve an equation we mean we can find all values for the variable which will make the equation true.
To solve \(ax^2 + bx + c = 0 \) we first attempt to factor the quadratic. Then we set each factor equal to zero and solve.
Solve the equation \( 2x^2 - 5x -3 = 0 \)
- Answer
-
1) We first multiply the \(a\) term with the \(c\) term. Doing so yields \(-6 \).
2) We now must find factors of \(-6\) which sums to \(-5\). We see that \(-6\) and \(1\) does the trick.
3) \begin{align*} 2x^2 - 5x -3 &= 2x^2 - 6x + x -3 \\ &= (2x^2 - 6x) + (x -3) \\ &= 2x (x-3) + 1(x-3) \\ &= (x-3)(2x+1) \end{align*}
4) \begin{align*} 2x^2 - 5x -3 &= 0 \\ (x-3)(2x+1) &= 0 \\ x-3 = 0 ~ &\text{or} ~ 2x+1=0 \\ x=3 ~ &\text{or} x = - \frac{1}{2} \end{align*}
Solve the equation \( x^2 - 7x = 0 \)
- Answer
-
1) We first factor this as \(x(x-7) = 0 \).
2) We now set each factor to 0 and solve. Hence either \(x=0\) or \(x=7\).
Solve the equation \( x^2 + 2x - 24 = 0 \)
- Answer
-
1) We first factor \(x^2 + 2x - 24 \) as \( (x+6)(x-4) \).
2) We now set each factor to 0 and solve. Hence either \(x=-6\) or \(x=4\).
Let us now modify the above problem ever so slightly. Suppose we were asked to solve the equation \( x^2 + 2x - 25 = 0 \). Take a few moments and try our AC technique!
The above request shows that not every quadratic equation can be solved via the AC Method. Allow us to play around with the above equation and let us see what we can do. For now, do not worry as to why we are performing the following steps. Instead, just follow along:
\begin{align*} x^2 + 2x - 25 &= 0 && \text{adding 25 to both sides yields} \\ x^2 + 2x &= 25 && \text{adding 1 to both sides yields} \\ x^2 + 2x + 1 &= 26 && \text{factoring the left hand side yields} \\ (x+1)^2 &= 26 && \text{taking the square roots of both sides yields} \\ \sqrt{(x+1)^2} &= \sqrt{26} && \text{recall that} \sqrt{a^2} = |a| \\ |x+1| &= \sqrt{26} && \text{so either}~ x+1 = \sqrt{26} ~ \text{or} ~ x+1 = - \sqrt{26} \end{align*}
If \( x+1 = \sqrt{26} \) then \(x = 1 - \sqrt{26} \) and if \( x+1 = - \sqrt{26} \) then \(x = -1 - \sqrt{26} \).
Allow us to now reflect on the above process. We initially had an equation of the form \(ax^2 + bx +c = 0 \) which we could not factor. We then subtracted \(c\) from both sides to obtain \(ax^2 + bx = -c \). Then, we added in a "magical" number, \(m\) to both sides and obtained \(ax^2 + bx +m = -c + m\). The reason this number was "magical" is because the left hand side then turned into a perfect square!
The process outlined above is called completing the square . Completing the square is a method which can be used to solve all quadratics - factorable and non-factorable!
One question you may have is how do we determine this magical number \(m\)? Allow us to state the process of completing the square which answers this question.
1) Given an equation of the form \( ax^2 + bx + c = 0 \) subtract \(c\) from both sides.
2) Divide both sides by \(a\).
3) Add \(m\) to both sides where \(m = \bigg(dfrac{\text{coefficient on x}}{2}\bigg)^2 \).
4) The left hand side is now a perfect square and so we may solve the equation.
Solve \(x^2 - 4x + 2 = 0\).
- Answer
-
1) Subtracting 2 from both sides yields \(x^2 - 4x = -2\).
2) Dividing both sides by 1 does not affect the equation.
3) \( m = \bigg( \frac{-4}{2} \bigg)^2 = 4 \) and so we add 4 to both sides of the equation.
4) Adding 4 to both sides of the equation yields \(x^2 - 4x +4 = 2\). The left hand side is precisely \( (x-2)^2 \) and so we have to solve \( (x-2)^2 = 2\). Taking the square root of both sides yields \( |x-2| = \sqrt{2} \) and so either \( x-2 = sqrt{2} \) or \( x-2 = - \sqrt{2} \). Hence \(x = 2 \pm \sqrt{2} \).
Solve \(5x^2 - 9x - 2 = 0\).
- Answer
-
1) Adding 2 to both sides yields \(5x^2 - 9x = 2 \).
2) Dividing both sides by 5 yields \( x^2 - \frac{9}{5} x = \frac{2}{5} \).
3) \( m = \bigg( \frac{ \frac{9}{5} }{2} \bigg)^2 = \frac{81}{100} \) and so we add \( \frac{81}{100} \) to both sides of the equation.
4) Adding \( \frac{81}{100} \) to both sides of the equation yields \( x^2 - \frac{9}{5} x + \frac{81}{100} = \frac{2}{5} + \frac{81}{100} \). The left hand side is precisely \( (x- \frac{9}{10})^2 \) and so we have to solve \( (x- \frac{9}{10})^2 = \frac{121}{100} \). Taking the square root of both sides yields \( |x- \frac{9}{10}| = \sqrt{ \frac{121}{100}} \) and so either \( x- \frac{9}{10} = \sqrt{ \frac{121}{100}} \) or \( x- \frac{9}{10} = - \sqrt{ \frac{121}{100}}\). Hence \(x = \frac{9}{10} \pm \frac{121}{100}\) which yields \(x = 2 \) or \( x = - \frac{1}{5} \).
Solve \(2x^2 - 10x - 3 = 0\).
- Answer
-
\( x = \frac{5}{2} \pm \sqrt{\frac{31}{4}} \).
Solve \(ax^2 + bx + c = 0\). You may assume that \(a \neq 0 \).
- Answer
-
1) Subtracting \(c\) from both sides yields \(ax^2 + bx = -c \).
2) Dividing both sides by \(a\) yields \( x^2 + \frac{b}{a}x = - \frac{c}{a} \).
3) \( m = \bigg( \frac{ \frac{b}{a} }{2} \bigg)^2 = \frac{b^2}{4a^2} \) and so we add \( \frac{b^2}{4a^2} \) to both sides of the equation.
4) Adding \( \frac{b^2}{4a^2} \) to both sides of the equation yields \( x^2 + \frac{b}{a} x + \frac{b^2}{4a^2} = \frac{b^2}{4a^2} - \frac{c}{a} \). Simplifying the right hand side via a common denominator yields \( x^2 + \frac{b}{a} x + \frac{b^2}{4a^2} = \frac{b^2}{4a^2} - \frac{4ac}{4a^2} \) or equivalently \( x^2 + \frac{b}{a} x + \frac{b^2}{4a^2} = \frac{b^2 - 4ac}{4a^2} \).
Now we will simplify the left hand side and solve. Doing so yields \( (x+ \frac{b}{2a} )^2 = \frac{b^2 - 4ac}{4a^2} \).
Taking the square root of both sides yields \[\sqrt{(x+ \frac{b}{2a} )^2} = \sqrt{\frac{b^2 - 4ac}{4a^2}} \nonumber\ \]. Recalling that \( \sqrt{a^2} = |a| \) the above line becomes
\[ |x+ \frac{b}{2a}| = \sqrt{\frac{b^2 - 4ac}{4a^2}} \nonumber\ \]
Hence \[ x+ \frac{b}{2a}= \pm \sqrt{\frac{b^2 - 4ac}{4a^2}} \nonumber\ \] and so \[ x= - \frac{b}{2a} \pm \sqrt{\frac{b^2 - 4ac}{4a^2}} \nonumber\ \] Simplifying the right hand side yields \[ x= - \frac{b}{2a} \pm \frac{\sqrt{b^2-4ac}}{2a} \nonumber\ \] and adding the two fractions yields \[ x = \frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \]
which is precisely the quadratic formula.
The Quadratic Formula
Theorem: The solution(s) to \(ax^2 + bx + c = 0 \) where \(a \neq 0 \) are given by \[ x = \frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \nonumber \]
Using the quadratic formula, solve \(5x^2 - 9x - 2 = 0\).
- Answer
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\[ x = \frac{-b\pm\sqrt[]{b^2-4ac}}{2a} = \frac{9\pm\sqrt[]{(-9)^2-4(5)(-2)}}{2(5)} = \frac{9\pm\sqrt{121}}{10} = frac{9\pm 11}{10} \nonumber \] Hence \(x = 2 \) or \( x = - \frac{1}{5} \).
Using the quadratic formula, solve \(3x^2 - 4x - 2 = 0\).
- Answer
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\[ x = \frac{2 \pm \sqrt{10}}{3} \nonumber\ \].
Note that in the quadratic formula, we refer to \( b^2 - 4ac \) as the discriminant . Whenever the discriminant is negative, the quadratic will have no real solutions. For instance, one may check that the solutions to \( 3x^2 - 4x + 2 = 0 \) do not exist among the real numbers.


11.9: Ethical and Social Responsibilities
Learning OUTCOME
- Summarize the ethical and social responsibilities that come with buying decisions.
Ethical and Social responsibility is the idea that businesses should balance profit-making activities with activities that benefit society. It involves developing businesses with a positive relationship to the society in which they operate.
Social responsibility takes on different meanings within industries and companies. For example, Starbucks Corporation and Ben & Jerry’s Homemade Holdings Inc. have blended social responsibility into the core of their operations. Both companies purchase Fair Trade Certified ingredients to manufacture their products and actively support sustainable farming in the regions where they source ingredients. Conversely, big-box retailer Target Corporation, also well- known for its social responsibility programs, has donated money to communities in which the stores operate, including education grants. [1]
The Fair Trade concept is a world-wide movement where goods are produced and sourced in a sustainable and environmentally-friendly way. For retailers who procure products from less-developed countries, sustainable sources of supply cannot be maintained without workers and farmers receiving a living wage.
“When people have the capacity to invest in better futures, the result is a healthier workforce and ultimately higher quality goods. Our model is fueled by committees of farmers, workers, and fishermen who decide how to invest the Fair Trade Premium based on their community’s greatest needs: often clean water, education, and healthcare.” [2]
So-called “green” companies enjoy enhanced reputations and receive positive support from customers that often results in increased revenues.
Practice Questions
Contributors and Attributions
- Ethical and Social Responsibilities. Authored by : Robert Danielson. Provided by : Lumen Learning. License : CC BY: Attribution


1.3: The Mechanics of the Accounting Process
1.3.1 The Journal
Financial statements are key goals of the accounting process. In order to prepare them at the end of an accounting period, individual financial transactions must be analyzed, classified, and recorded all throughout the period. This initially takes place in a record book called the journal , where financial events called transactions are recorded as they happen, in chronological order.
When a transaction occurs, two or more accounts are affected. There is also a dollar amount associated with each of the accounts. Determining which accounts are impacted, and by how much, is the first step in making a journal entry.
This is a sample of a few rows in a journal. It has five columns: Date, Account, Post. Ref., Debit, Credit.
| Date | Account | Debit | Credit | |
In the journal, the column heading Debit means “left” and Credit means “right.” There are other familiar interpretations of these words, so don’t be confused: the terms here only have to do with whether a dollar amount is entered in the left or the right number column.
These words may also be used as verbs: To “debit an account” means to enter its amount in the left column. To “credit an account” means to enter its amount in the right column.
1.3.2 Rules of Debit and Credit
Whether a particular account should be debited or credited is based on (1) the type of account it is and (2) whether the account is increasing or decreasing.
for Cash and Revenue and Expense accounts
| Debit CASH when you receive it | Cash increases |
| Credit CASH when you pay it out | Cash decreases |
| Debit EXPENSES when you incur them | Expenses increase |
| Credit REVENUE when you earn it | Revenue increases |
1.3.3 Journalizing Transactions
We now will come to one of the most important procedures in the recordkeeping process : journal entries . It involves analyzing and writing down financial transactions in a record book called a journal . Financial events are evaluated and translated into the language of accounting using the process of journalizing .
Select two accounts and, according to the rules of debit and credit for cash, revenue, and expense accounts, decide which account to debit (left column) and which to credit (right column). The debit entry is always listed first. No dollar signs are required in the journal.
Journalizing involves the following steps:
- Select two (or more) accounts impacted by a transaction.
- Determine how much, in dollars, each account is affected. Often times the amounts are given; other times the amounts must be calculated based on the information provided.
- Based on the rules of debit and credit, decide which account(s) is debited and which is credited.
- Enter the date on the first line of the transaction only.
- Enter the account that will be debited on the first line of the transaction. Enter its amount in the Debit column on the same line.
- Enter the account that will be credited on the second line of the transaction. Enter its amount in the Credit column on the same line. NOTE: Indent the credit account name three spaces.
On 6/1, a company paid rent of $2,000 for the month of June.
| Date | Account | Debit | Credit | PARTIAL TRANSACTION | |
| 6/1 | Rent Expense | 2,000 | ▲ Rent Expense is an expense account that is increasing . Therefore, it is debited . The account with the debit amount is entered first. | ||
| Date | Account | Debit | Credit | COMPLETE TRANSACTION | |
| Credit | Rent Expense | 2,000 | ▼ Cash is an asset account that is decreasing . Therefore, it is credited . The account with the credit amount is entered next. | ||
| Cash | 2,000 | ||||
On 6/5, a customer paid $800 cash for services the company provided.
| Date | Account | Debit | Credit | PARTIAL TRANSACTION | |
| 6/5 | Cash | 800 | ▲ Cash is an asset account that is increasing . Therefore, it is debited . The account with the debit amount is entered first. | ||
| Date | Account | Debit | Credit | COMPLETE TRANSACTION | |
| 6/5 | Cash | 800 | ▼ Fees Earned is a revenue account that is increasing . Therefore, it is credited . The account with the credit amount is entered next. | ||
| Fees Earned | 800 | ||||
In practice, each transaction follows immediately after the previous one, as shown here.
| Date | Account | Debit | Credit | |
| 6/1 | Rent Expense | 2,000 | ||
| Cash | 2,000 | |||
| 6/5 | Cash | 800 | ||
| Fees Earned | 800 | |||
| 6/8 | Wages Expense | 500 | ||
| Cash | 500 | |||
| 6/10 | Cash | 600 | ||
| Fees Earned | 600 |
The same journal continues on from period to period. You do not start a new journal for a new accounting period (month or year).
1.3.4 Ledger
The ledger is the second accounting record book that is a list of a company’s individual accounts list in order of account category. While the journal lists all types of transactions chronologically, the ledgers separate this same information out by account and keep a running balance of each of these accounts.
Each account has its own ledger page. The account name appears across the top. The ledger form has six columns: Date, Item, Debit, Credit, Debit, Credit. The first set of Debit and Credit columns are where amounts from the journal transactions are copied . The second set of Debit and Credit columns are where the account’s running total is maintained. An account’s running balance typically appears in either the Debit or the Credit column, not both.
The following is a sample ledger for the Cash account.
| Cash | |||||
| Date | Item | Debit | Credit | Debit | Credit |
| 6/1 | 12,000 | 12,000 | |||
| 6/2 | 2,000 | 14,000 | |||
| 6/3 | 3,000 | 11,000 | |||
| Copy amounts from journal (use either column) | BALANCE columns (use one of the two) |
IMPORTANT: Information entered in the ledger is always copied from what is already in the journal.
1.3.5 Posting
The process of copying from the journal to the ledger is called posting . It is done one line at a time from the journal. Here are step-by-step instructions for doing so.
- Take note of the account name in the first line of the journal. Find that ledger account.
- Copy the date from the journal to the first blank row in that ledger.
- Leave the Item column blank in the ledger at this point.
- Take note of the amount on the first line of the journal and the column it is in.
- Copy that amount to the same column in the ledger on the same line where you entered the date.
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Update the account’s running balance. Take note of the previous balance in the last two columns of the ledger, if there is one. Do one of the following, based on the situation.
- If there is no previous balance and the entry is a Debit, enter the same amount in the Debit balance column.
- If there is no previous balance and the entry is a Credit, enter the same amount in the Credit balance column.
- If the previous balance is in the Debit column and the entry is a Debit, add the two amounts and enter the total in the Debit balance column.
- If the previous balance is in the Debit column and the entry is a Credit, subtract the credit amount from the balance and enter the difference in the Debit balance column. *
- If the previous balance is in the Credit column and the entry is a Credit, add the two amounts and enter the total in the Credit balance column.
- If the previous balance is in the Credit column and the entry is a Debit, subtract the debit amount from the balance and enter the difference in the Credit balance column. *
* Note: The only exception to the above is the rare occasion when one of the calculations above results in a negative number. No negative amounts should appear in the ledgers. Instead, the balance will appear in the opposite balance column.
- Go back to the journal and enter an “x” or checkmark in the PR column to indicate that you have posted that line item.
- Repeat the process for the next line in the journal.
Every time an account appears on a line in the journal, its amount is copied to the proper column in that account’s ledger. A running total is maintained for each account and is updated every time an amount is posted.
The example that follows shows a journal with five transactions that involve Cash . On each row where Cash appears in the journal, the amount on the same line is copied to the same column in the Cash ledger, in either the first Debit or the first Credit column. Superscripts are used here to match each Cash amount in the journal to its posting in the ledger. For example, the first debit to Cash in the journal for $6,000 is copied to the debit column in the ledger (#1). The next time Cash appears in the journal is a credit for $2,000, so that is copied to the first credit column in the ledger (#2).
| Date | Account | Debit | Credit | |
| 6/1 | Cash | x | 6,000 1 | |
| Fees Earned | 6,000 | |||
| 6/2 | Rent Expense | 2,000 | ||
| Cash | x | 2,000 2 | ||
| 6/3 | Wages Expense | 1,000 | ||
| Cash | x | 1,000 3 | ||
| 6/4 | Cash | x | 5,000 4 | |
| Fees Earned | 5,000 | |||
| 6/5 | Wages Expense | 1,000 | ||
| Cash | x | 1,000 5 | ||
| Date | Item | Debit | Credit | Debit | Credit |
| 6/1 | 6,000 1 | 6,000 | |||
| 6/2 | 2,000 2 | 4,000 | |||
| 6/3 | 1,000 3 | 3,000 | |||
| 6/4 | 5,000 4 | 8,000 | |||
| 6/5 | 1,000 5 | 7,000 | |||
As shown in the previous example, the first entry in the ledger indicates which of the two final columns will normally be used to maintain the accounts running balance. For the Cash account, the first entry is in the first Debit column, so the running balance begins accumulating in the second Debit column. On the first row, the amounts in the two Debit columns will be the same. In this case, the amount is $6,000 in both. After the first entry in the ledger, subsequent debit entries are added to the previous debit balance, and subsequent credit entries are deducted from the previous debit balance.
You can go to an ATM to withdraw cash from your checking account. The first steps are to insert your debit card into the ATM machine and select the amount you would like to receive. If that is all you do, no money will come out no matter how long you stand there. In order to get the job done, you also need to enter your PIN. The goal is to withdraw cash, and if you do not complete that step, it is not going to happen.
Similarly, there is a goal to preparing the journal and ledgers – to maintain a running balance of each account your business has. If you enter a transaction in the journal, you are off to a good start, but if you don’t complete the step of posting the journal entry to the ledgers, the correct balances are not going to happen.
1.3.6 Normal Balance
The last two Debit and Credit columns in the ledger are where a running total (balance) is maintained for each account. An account’s running balance will accumulate in EITHER the Debit balance column OR Credit balance column (two far right columns), but rarely both. The normal balance is also whatever it takes to increase that type of account, either Debit or Credit. The normal balance for an account is the column in which its running total is maintained.
An example of a journal and ledgers follows. Try to follow how the numbers from the journal on the left appear in the ledgers on the right and how the running balances in the ledgers are determined.
| Date | Account | Debit | Credit | |
| 6/1 | Cash | x | 2,000 | |
| Fees Earned | x | 2,000 | ||
| 6/2 | Supplies Expense | x | 300 | |
| Cash | x | 300 | ||
| 6/3 | Cash | x | 500 | |
| Fees Earned | x | 500 | ||
| 6/4 | Supplies Expense | x | 200 | |
| Cash | ||||
| 6/5 | Cash | x | 800 | |
| Fees Earned | x | 800 | ||
| 6/6 | Supplies Expense | x | 400 | |
| Cash | x | 400 | ||
| 6/7 | Cash | x | 600 | |
| Fees Earned | x | 600 | ||
| Cash | |||||
| Date | Item | Debit | Credit | Debit | Credit |
| 6/1 | 2,000 | 2,000 | |||
| 6/2 | 300 | 1,700 | |||
| 6/3 | 500 | 2,200 | |||
| 6/4 | 200 | 2,000 | |||
| 6/5 | 800 | 2,800 | |||
| 6/6 | 400 | 2,400 | |||
| 6/7 | 600 | 3,000 | |||
| Fees Earned | |||||
| Date | Item | Debit | Credit | Debit | Credit |
| 6/1 | 2,000 | 2,000 | |||
| 6/3 | 500 | 2,500 | |||
| 6/5 | 800 | 3,300 | |||
| 6/7 | 600 | 3,900 | |||
| Supplies Expense | |||||
| Date | Item | Debit | Credit | Debit | Credit |
| 6/2 | 300 | 300 | |||
| 6/4 | 200 | 500 | |||
| 6/6 | 400 | 900 | |||
The first entry in each ledger, either Debit or Credit, dictates whether the running balance will appear in the Debit or the Credit balance column. If the first entry is a Debit, the running balance accumulates in the Debit balance column. A debit is the “positive” for this type of account; any subsequent debit entries are added and credit entries are subtracted from the running balance. Conversely, if the first entry is a Credit, the running balance accumulates in the Credit balance column. A credit is the “positive” for this type of account; any subsequent credit entries are added and debit entries are subtracted from the running balance.
The grayed column above in each ledger represents the balance column that will normally remain blank.
The total of all the Debit balances in the ledgers MUST EQUAL the total of all the Credit balances in the ledgers. If this is not the case, there is a recording error that must be located and corrected. In the example above, the ledgers balance: 3,000 + 900 (debit balances) = 3,900 (credit balance).
The same ledgers continue on from period to period. You do not start new ledgers for a new accounting period (month or year).
To summarize the two record books, the journal first records all types of transactions chronologically, in time sequence order. The ledgers separate the same information out by account and keep a balance for each of these accounts.
IMPORTANT: If you are making entries in the ledgers, you must be COPYING from the journal.
I have a great recipe for chocolate chip cookies. Here are the ingredients
At this point you must be confused, or think I am crazy. The cookies could not possibly be the result of those ingredients—the input does not match the output. Anyone who knows anything about cookies can see that.
It is the same with the accounting process. It is not possible to have a correct ledger and/or financial statement balances if the input in the journal has errors. Yet some students “know,” or copy from others, what the correct results should be in spite of incorrect journal entries. This violates the process of posting to the ledgers, which is carrying over what is in the journal.
It is more correct for an error to carry through to all parts than for one part to be incorrect and subsequent parts to be correct. To your accounting instructor, a correct balance based on a faulty journal is as unlikely an outcome as is chocolate chip cookies from taco ingredients. It just can’t happen!
If there is an error in the journal, procedurally the mistake should carry through to the ledgers and the financial statements.
1.3.7 Trial Balance
The total of all the debit balances in a company’s ledger accounts must always equal the total of all the credit balances. A trial balance is a list of all a business’s accounts and its current ledger balances (copied over from the ledger accounts). A trial balance may be generated at any time to test whether total debits equals total credits. It is simply a worksheet to check for accuracy before preparing financial statements. If both of the Total columns do not equal, there is an error that must be found and corrected.
The example that follows is for a company with only four accounts. The trial balance on the left lists these accounts and their corresponding balances at the end of the month, which are copied over from the ledgers on the right.
| Account | Debit | Credit |
| Cash | 3,000 | |
| Common Stock | 2,000 | |
| Fees Earned | 1,900 | |
| Supplies Expense | 900 | |
| TOTAL | 3,900 | 3,900 |
LEDGERS
| Date | Item | Debit | Credit | Debit | Credit |
| 6/1 | 2,000 | 2,000 | |||
| 6/2 | 300 | 1,700 | |||
| 6/3 | 500 | 2,200 | |||
| 6/4 | 200 | 2,000 | |||
| 6/5 | 800 | 2,800 | |||
| 6/6 | 400 | 2,400 | |||
| 6/7 | 600 | 3,000 | |||
| Date | Item | Debit | Credit | Debit | Credit |
| 6/1 | 2,000 | 2,000 | |||
| Date | Item | Debit | Credit | Debit | Credit |
| 6/3 | 500 | 500 | |||
| 6/5 | 800 | 1,300 | |||
| 6/7 | 600 | 1,900 | |||
| Date | Item | Debit | Credit | Debit | Credit |
| 6/2 | 300 | 300 | |||
| 6/4 | 200 | 500 | |||
| 6/6 | 400 | 900 | |||


12.1: Introduction
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- Berke, Bleil, & Cofer
- Middle Georgia State University, College of Coastal Georgia, & Abraham Baldwin Agricultural College via University of North Georgia Press
Emily Dickinson and Walt Whitman, the authors whose works appear in this chapter, are unlikely protagonists or leading characters for a literary movement. Each was an outsider: Dickinson, an unmarried woman who lived a life of quiet seclusion in western Massachusetts, and Whitman, a vagabond who lived a life in search of community. Dickinson and Whitman promoted a spirit of exploration and inventiveness that matched the geographical, industrial, political, and social growth of the United States. From their works, we gain not so much a literary renaissance as we do a sense of artistic innovation that developed alongside these other areas of American life and commerce.
As literary historians like William Charvat have noted, the development of an American literary tradition owes as much to the development of the American publishing industry in the middle decades of the nineteenth century as it does to the prominence of individual authors like Catharine Maria Sedgwick, Washington Irving, Nathaniel Hawthorne, Edgar Allan Poe, Herman Melville, Ralph Waldo Emerson, Henry David Thoreau, and Harriet Beecher Stowe. Sales of these authors’ works were dwarfed by the sales of pirated editions of novels by British authors like Walter Scott and Charles Dickens. Nonetheless, the success of these British imports convinced American publishers that the American market was sufficiently robust to demand new works; this demand created an opportunity for American writers to expand their audience, and a flourishing literary culture began to prosper.
American authors still faced steep odds in seeing their works into print, and American literary publishing did not flourish until the completion of the First Transcontinental Railroad in 1869 allowed the reliably consistent shipment of individuals and goods across the country. Additional technological improvements, including the widespread adoption of steam-powered machinery and gas-fueled lights, also provide the necessary conditions for the rapid production of printed materials and the means by which these materials could be enjoyed at the conclusion of a day of laboring. Thus, only when the Industrial Age expands the definition of leisure do Americans begin to embrace the culture of print and expand the boundaries of American literature.
The first attempts to define the literary culture of the mid-nineteenth century began in the 1930s and early 1940s as the United States took on a larger role in global politics, and the need for definition gained sharper focus with the publication of F. O. Matthiessen’s The American Renaissance in 1941. Matthiessen argued that writers like Hawthorne, Melville, Emerson, and Thoreau represented the expansion of a uniquely American style of writing that interacted with, and embraced, the North American landscape in new ways. What Matthiessen called a renaissance, however, was less of a cultural flourishing than the limited success of a few male authors from New England. Despite the real impact of Matthiessen’s work in recognizing the presence of significant male American writers, his cataloguestill neglected writing of women, African-Americans, and Native Americans whose works would not be widely recognized until the 1970s.
In order to describe the work of these authors, Matthiessen and others turned to literary labels popularized in reference to British authors of the late eighteenth and early nineteenth centuries. Romanticism , a literary movement emphasizing the freedom and originality of self-expression that began in Europe at the end of the eighteenth century, also seemed to capture the spirit of nineteenth-century America and was frequently applied to authors of both prose and poetry. In the hands of these authors, the meadows of western Massachusetts replaced the Lake District as the source of inspiration, and the rejection of Puritan morality continued the American emphasis on freedom of expression. When Whitman and Dickinson began writing poetry in the 1850s, the thriving Abolitionist movement added urgency to the need for new voices and rapid change.
When we refer to Whitman and Dickinson as late Romantics, we place them at the end of a period that begins in the 1820s, and we suggest that their works are merely derivative from those that preceded them chronologically. Yet Whitman’s and Dickinson’s poetry is contemporary with these other works, and it seems more fruitful to consider the differences in genre than the differences in chronology. Whitman and Dickinson achieved their fame by changing American poetry from patriotic and historical ballads to free verse poetry that lacks both rhyme and regular meter and musically inspired celebrations of the individual in the American landscape.
Whitman and Dickinson are the most famous of the Late Romantics, and their work inspired successive generations of American authors. From these poets, Mark Twain, Stephen Crane, and Charles Chesnutt found the freedom to use a variety of American dialects in their work, the realists of the late nineteenth and early twentieth centuries discovered the richness of the American landscape, and the Modernist poets located a source of new poetical forms to meet the needs of the adolescent Republic that came of age in the decades immediately following the Civil War .
That national coming of age, in the years of Reconstruction, Western Expansion, Manifest Destiny, industrial might, and rapid immigration, also marks the traditional beginning of courses like this one. The Civil War, while not a precise dividing line, is regarded as the most reliable current method for marking the split between the first and second half of the literary history of the United States. Teachers and critics quickly realized, however, that the continued growth of the literary and cultural productions of the United States required more precise divisions than the chronological division into pre-bellum and post-bellum periods can provide. This collection of readings follows those new divisions, with chapters on Late Romanticism, Realism, Naturalism, Pre-Modernism, Modernism, and post-1945 American Literature, but the boundaries between these divisions remain fluid.
The readings that follow are arranged loosely by chronology, and the author editors of this collection have tried to provide useful headnotes to the sections and the individual authors, but do not be afraid to draw connections beyond the loose boundaries and invent new terms that better describe these works. As American literature continues to grow, we create new categories that better describe our shared experience.


14.5: State Legislative Term Limit
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Learning Objectives
By the end of this section, you will be able to:
- Describe the history of state legislative term limits
- Compare the costs and benefits of term limits
Term limits restrict the length of time a member can serve in the state legislature by capping either lifetime service or the number of consecutive terms. The term limits movement gained momentum in the 1990s, spreading across a wide array of state legislative institutions. Today, fifteen states have imposed term limits on their state house and state senate members. On the other hand, six states, one as recently as 2004, have repealed the term limits imposed on them by the electorate, through either judicial action in the state Supreme Courts or through legislative action in the state legislature. 71
The Basics of Term Limits
The first term limits were enacted in 1990 in California, Colorado, and Oklahoma. In 1992, eight more states followed suit in one large wave. The last state to enact term limits on legislative members was Nebraska in 2000. 73 However, term limits did not stay in effect in all these states; many state supreme courts repealed them and declared them unconstitutional for a variety of reasons (Figure 14.18). For instance, in Massachusetts and Washington, term limits were deemed unconstitutional because they affected candidate qualifications to compete for a given office. The courts ruled that changes to those qualifications could be made only by amending the state constitution, not by voters changing the state law. 74
Advantages of Term Limits
In many cases, the movement to institute term limits was initiated by voters and passed through citizen initiatives, which allow citizens to place a proposed law or constitutional amendment on the ballot for a popular vote. 75 Proponents of term limits felt new blood was needed in state legislatures to bring fresh ideas and perspectives to lawmaking. In addition, they hoped term limits would compel turnover among members by shortening the time anyone could serve and by reducing the tendency for elected officials to make legislative service their career. In conjunction with this thinking, some supporters hoped term limits would increase the motivation to make good public policy. If members were less focused on reelection and knew they could not serve more than a certain number of years, perhaps they would get right down to the business of making laws and produce innovative policy within a narrow window of time. 76
For other proponents, the hope was that term limits would increase diversity within the chamber by encouraging more women, members of racial and ethnic minority groups, members of the minority party, and people with unconventional occupations to run for office because seats would be open more frequently. In addition, supporters speculated that increased turnover might prompt higher rates of electoral competition and voter interest. Finally, they believed the loss of long-term legislators due to term limits would allow new members and younger legislators to assume leadership positions within the chamber and committees, creating another way to bring fresh approaches to the lawmaking process. 77
Get Connected!
Working to Expand Term Limits
One pro–term limits advocacy group, U.S. Term Limits, is dedicated to the expansion of term limits across the United States. Its members work to prevent states from repealing limits that are already in place. They also support efforts by citizens to institute term limits in states where they are not currently in place, and in Congress, where the Supreme Court declared them unconstitutional. 78
If you support their cause, you can follow the link below to learn more about these efforts or to participate directly. Write a letter to the editor encouraging the adoption of term limits in a given state, or encourage your member of Congress to sign a pledge agreeing to cosponsor and vote for an amendment to the Constitution to adopt term limits. You can also sign an online petition to support the adoption of term limits at the federal level or make a donation to a term-limit advocacy group.
What is your state’s policy on term limits? If limits are in place, how have they changed your representation in the state capitol? If they are not in place, what effect would adopting them have on your representation? There is no comparable national movement against term limits, why do you think that is the case? Based on your answers, do you favor term limits or not, and why?
Link to Learning
For more information about supporting term limits, visit U.S. Terms an advocacy group for term limits.
Disadvantages of Term Limits
Although proponents have many reasons for supporting term limits, opponents also have compelling reasons for not supporting their implementation in the state legislature. In addition, research by political scientists has uncovered a number of negative consequences since term limits took effect.
Although proponents argued that term limits would increase legislative diversity, research comparing the rate of female and minority representation in term-limited and non-term-limited states does not bear out this expectation. There is no statistically significant difference in diversity between the two groups of states. 79 Although term limits may have produced more open seats, additional barriers to holding office can still exist and affect the willingness of women and minorities to run for office. In addition, women and minorities are subject to the same term limits as men, and given their low numbers among candidates for office, on balance a legislature can lose more women or minorities than it gains.
Term limits also affect the power structure between the legislative and executive branches and the key sources from whom legislators draw information about bills before the chamber. Research demonstrates that, post-term limits, legislators became more likely to consult with lobbyists to gain information about legislation under consideration than had been the case before term limits. 80 This is likely the result of legislators having less policy expertise and political experience as a function of having fewer years in office, being younger when they first enter legislative service, reducing institutional memory and expertise within the chamber as a whole due to member turnover, or all the above. Interest groups may thus enjoy greater ability to set the agenda and push for policy that favors their organization. This same research also found that under term limits state legislators feel they have lost power relative to the governor and to various bureaucratic agency officials. 81 This presumed loss of power could damage the state legislature’s ability to adequately check the actions of the executive branch and to perform legislative functions, such as oversight.
Finally, term limits could affect voter enthusiasm and turnout if voters are disappointed they cannot retain legislators they like or have developed a positive relationship with. Once term limits take effect, all legislators are at the voters’ mercy, regardless of the skill or talent they may bring to the office.


SECTION 10.4 PROBLEM SET: ABSORBING MARKOV CHAINS
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Given the following absorbing Markov chain.
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Identify the absorbing states.
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Write the solution matrix.
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Starting from state 4, what is the probability of eventual absorption in state 1?
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Starting from state 2, what is the probability of eventual absorption in state 3?
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Two tennis players, Andre and Vijay each with two dollars in their pocket, decide to bet each other $1, for every game they play. They continue playing until one of them is broke.
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Write the transition matrix for Andre.
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Identify the absorbing states.
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Write the solution matrix.
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At a given stage if Andre has $1, what is the chance that he will eventually lose it all?
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Repeat the previous problem, if the chance of winning for Andre is .4 and for Vijay .6.
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Write the transition matrix for Andre.
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Identify the absorbing states.
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If Andre has $3, what is the probability that he will eventually be ruined?
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If Vijay has $1, what is the probability that he will eventually triumph?
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Repeat problem 2, if initially Andre has $3 and Vijay has $2.
-
Write the transition matrix.
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Identify the absorbing states.
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Write the solution matrix
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If Andre has $4, what is the probability that he will eventually be ruined?
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The non-tenured professors at a community college are regularly evaluated. After an evaluation they are classified as good, bad, or improvable. The "improvable" are given a set of recommendations and are re-evaluated the following semester. At the next evaluation, 60% of the improvable turn out to be good, 20% bad, and 20% improvable. These percentages never change and the process continues.
-
Write the transition matrix.
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Identify the absorbing states.
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Write the solution matrix
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What is the probability that a professor who is improvable will eventually become good?
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Questions 6 refer to the following:
In a professional certification program students take classes and then participate in an internships.
There are 4 states: taking classes (C), internship (I), drop out (D), and graduate (G).
If a student drops out they are never readmitted to the program.
Of those students currently taking classes, 70% have an internship the next year, 20% are still taking classes the next year, and 10% have dropped out by the next year. Of the students who are currently doing an internship, 65% graduate by the next year; 20% drop out by the next year, and 15% are still completing their internship the next year.
-
Write the transition matrix and indicate which are the absorbing states.
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If a student is taking classes now:
-
find the probability that the student will graduate in 2 years
-
find the probability that the student will be in the internship in 2 years.
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find the probability that the student will have dropped out by 2 years from now.
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Find the probability that a student currently doing an internship will eventually drop out.
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Find the probability that a student taking classes now will eventually graduate.
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If 40% of students are currently taking classes and 60% of current students are doing internships, what is the eventual long term distribution of students for graduating versus dropping out?
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If 70% of students are currently taking classes and 30% of current students are doing internships, what is the eventual long term distribution of students for graduating versus dropping out?
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A mouse is placed in the maze shown below, and it moves from room to room randomly. From any room, the mouse will choose a door to the next room with equal probabilities. Once the mouse reaches room 1, it finds food and never leaves that room. And when it reaches room 5, it is trapped and cannot leave that room. What is the probability the mouse will end up in room 5 if it was initially placed in room 3?
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In problem 12, what is the probability the mouse will end up in room 1 if initially placed in room 2?


Partial Pressures
Skills to Develop
- Define partial pressure using math equations
What if we have a mixture of different gases? We might want to know how much of each there is. We can define the mole fraction of a particular gas A as the number of moles of A divided by the total number of moles of gas:
\[x_{A} = \frac{n_{A}}{n_{total}}\]
Then we can define the partial pressure of A as:
\[p_{A} = x_{A}P\]
This works for real or ideal gases. Partial pressures are often used to describe concentrations of gases. If the gas is ideal, then the partial pressure is the same pressure that the gas would make if all the other components of the mixture weren't there, because:
\[p_{A} = \frac{n_{A}RT}{V}\]
In a real gas, this might not be true because the different gases might interact a little bit differently.


12.3.4: Procedure- Shampoo in Bed
Washing a patient’s hair helps to promote good hygiene, comfort, relaxation, and self-esteem. It also provides a chance for Home Health Aides/Personal Care Aides to assess the condition of their patient’s hair, skin, and scalp. When washing a patient’s hair in bed, Home Health Aides/Personal Care Aides should ensure that the bed linens and patient clothing are protected by using towels or waterproof pads under their shoulders. Always assess allergies to products being used, and style hair according to patient preference. Take care to not pull on hair, which could damage the patient’s scalp. Older patients may have thinner, more fragile hair, and extra care should be taken.
- Explain the procedure to the patient.
- Wash and dry your hands. Don gloves.
- Assemble equipment (shampoo, conditioner, bath towel, hand towel, pitcher, shampooing basin, or disposable shampoo cap).
- Ask the patient for preferences of products and ensure the patient is not allergic to products.
- Position the patient in a supine position. Place a waterproof pad or towel under the patient’s head and shoulders. Place a towel over shoulders and chest area to keep this area dry and warm. Ensure the rest of the patient’s body is kept warm and covered with a blanket.
- Protect the patient’s eyes and face from getting wet. Wet hair by pouring clean, warm water using a pitcher over the patient’s hair, starting from hairline at the scalp and working towards the neck.
- Apply shampoo to your hands and rub them together. Work shampoo into a lather, working from the front of the patient’s head to the ends of their hair.
- Use your fingertips to massage shampoo against the patient’s scalp, using a circular motion. Take care not to use your fingernails or scrape the patient’s skin or scalp with your nails. Ensure soap and water does not get into patient’s eyes or ears.
- Rinse hair thoroughly until water runs clear and no suds are visible. Rinse from the scalp line at the patient’s forehead to the ends of their hair, protecting the patient’s eyes and ears.
- If using conditioner, repeat steps 7 through 9.
- If using a shampoo cap, follow steps 1 through 5. Apply the shampoo cap to the patient’s hair, tucking in any loose hair ends so that all hair is within the cap.
- Massage scalp so the dry shampoo is evenly distributed throughout hair. Allow 1-5 minutes for shampoo to fully saturate hair. Remove cap and discard used cap. Dry and style patient’s hair as you normally would.
- Wipe water from patient’s face, head, and neck using a dry towel and a blotting motion.
- Dry and comb hair, according to patient preferences. If using a blow dryer, ensure that the hot air and the tip of the blow dryer is not placed onto or too close to the patient’s skin or you could cause a burn.
- When working on untangling hair, hold a section of hair above the tangle. This avoids painful pulling on the scalp. Gently comb through the tangle. Conditioner or a detangler could be applied to assist with removing tangles.
- When brushing hair, brush hair in sections, brushing from root to ends of hair. Be gentle with your strokes, taking care not to harshly scrape the patient’s scalp or to yank on hair, which could cause injury to the patient’s scalp.
- Once finished with hair care, lower bed to its lowest height. Ensure side rails are up for safety.
- Clean the area and store equipment.
- Remove your gloves. Wash and dry your hands.
- Document completion of task and record any changes in condition or behavior. Record any changes in condition of the patient’s skin, scalp, or hair.


2.6.9: The Compactness Theorem
One important consequence of the completeness theorem is the compactness theorem. The compactness theorem states that if each finite subset of a set of sentences is satisfiable, the entire set is satisfiable—even if the set itself is infinite. This is far from obvious. There is nothing that seems to rule out, at first glance at least, the possibility of there being infinite sets of sentences which are contradictory, but the contradiction only arises, so to speak, from the infinite number. The compactness theorem says that such a scenario can be ruled out: there are no unsatisfiable infinite sets of sentences each finite subset of which is satisfiable. Like the completeness theorem, it has a version related to entailment: if an infinite set of sentences entails something, already a finite subset does.
A set \(\Gamma\) of formulas is finitely satisfiable if and only if every finite \(\Gamma_0 \subseteq \Gamma\) is satisfiable.
The following hold for any sentences \(\Gamma\) and \(A\) :
- \(\Gamma \Entails A\) iff there is a finite \(\Gamma_0 \subseteq \Gamma\) such that \(\Gamma_0 \Entails A\) .
- \(\Gamma\) is satisfiable if and only if it is finitely satisfiable.
Proof. We prove (2). If \(\Gamma\) is satisfiable, then there is a structure \(\Struct{M}\) such that \(\Sat{M}{A}\) for all \(A \in \Gamma\) . Of course, this \({\Struct{M}}\) also satisfies every finite subset of \(\Gamma\) , so \(\Gamma\) is finitely satisfiable.
Now suppose that \(\Gamma\) is finitely satisfiable. Then every finite subset \(\Gamma_0 \subseteq \Gamma\) is satisfiable. By soundness (Corollaries 9.11.2 and 8.12.3 ), every finite subset is consistent. Then \(\Gamma\) itself must be consistent by Propositions 8.8.5 and 9.7.5 . By completeness ( Theorem 10.8.1 ), since \(\Gamma\) is consistent, it is satisfiable. ◻
Prove (1) of Theorem \(\PageIndex{1}\) .
In every model \(\Struct{M}\) of a theory \(\Gamma\) , each term \(t\) of course picks out an element of \(\Domain{M}\) . Can we guarantee that it is also true that every element of \(\Domain{M}\) is picked out by some term or other? In other words, are there theories \(\Gamma\) all models of which are covered? The compactness theorem shows that this is not the case if \(\Gamma\) has infinite models. Here’s how to see this: Let \(\Struct{M}\) be an infinite model of \(\Gamma\) , and let \(c\) be a constant symbol not in the language of \(\Gamma\) . Let \(\Delta\) be the set of all sentences \(\eqN[c][t]\) for \(t\) a term in the language \(\Lang{L}\) of \(\Gamma\) , i.e., \[\Delta = \Setabs{\eqN[c][t]}{t \in \Trm[L]}.\nonumber\] A finite subset of \(\Gamma \cup \Delta\) can be written as \(\Gamma' \cup \Delta'\) , with \(\Gamma' \subseteq \Gamma\) and \(\Delta' \subseteq \Delta\) . Since \(\Delta'\) is finite, it can contain only finitely many terms. Let \(a \in \Domain{M}\) be an element of \(\Domain{M}\) not picked out by any of them, and let \(\Struct{M'}\) be the structure that is just like \(\Struct{M}\) , but also \(\Assign{c}{M'} = a\) . Since \(a \neq \Value{t}{M}\) for all \(t\) occuring in \(\Delta'\) , \(\Sat{M'}{\Delta'}\) . Since \(\Sat{M}{\Gamma}\) , \(\Gamma' \subseteq \Gamma\) , and \(c\) does not occur in \(\Gamma\) , also \(\Sat{M'}{\Gamma'}\) . Together, \(\Sat{M'}{\Gamma' \cup \Delta'}\) for every finite subset \(\Gamma' \cup \Delta'\) of \(\Gamma \cup \Delta\) . So every finite subset of \(\Gamma \cup \Delta\) is satisfiable. By compactness, \(\Gamma \cup \Delta\) itself is satisfiable. So there are models \(\Sat{M}{\Gamma \cup \Delta}\) . Every such \(\Struct{M}\) is a model of \(\Gamma\) , but is not covered, since \(\Value{c}{M} \neq \Value{t}{M}\) for all terms \(t\) of \(\Lang{L}\) .
Consider a language \(\Lang{L}\) containing the predicate symbol \(<\) , constant symbols \(\Obj{0}\) , \(\Obj{1}\) , and function symbols \(+\) , \(\times\) , \(-\) , \(\div\) . Let \(\Gamma\) be the set of all sentences in this language true in \(\Struct{Q}\) with domain \(\Rat\) and the obvious interpretations. \(\Gamma\) is the set of all sentences of \(\Lang{L}\) true about the rational numbers. Of course, in \(\Rat\) (and even in \(\Real\) ), there are no numbers which are greater than \(0\) but less than \(1/k\) for all \(k \in \PosInt\) . Such a number, if it existed, would be an infinitesimal: non-zero, but infinitely small. The compactness theorem shows that there are models of \(\Gamma\) in which infinitesimals exist: Let \(\Delta\) be \(\{0<c\} \cup \Setabs{c < (\Obj{1} \div \num{k})}{k \in \PosInt}\) (where \(\num{k} = (\Obj{1} + (\Obj{1} + \dots + (\Obj{1} + \Obj{1})\dots))\) with \(k\) \(\Obj{1}\) ’s). For any finite subset \(\Delta_0\) of \(\Delta\) there is a \(K\) such that all the sentences \(c < (\Obj{1} \div \num{k})\) in \(\Delta_0\) have \(k < K\) . If we expand \(\Struct{Q}\) to \(\Struct{Q'}\) with \(\Assign{c}{Q'} = 1/K\) we have that \(\Sat{Q'}{\Gamma \cup \Delta_0}\) , and so \(\Gamma \cup \Delta\) is finitely satisfiable (Exercise: prove this in detail). By compactness, \(\Gamma \cup \Delta\) is satisfiable. Any model \(\Struct{S}\) of \(\Gamma \cup \Delta\) contains an infinitesimal, namely \(\Assign{c}{S}\) .
In the standard model of arithmetic \(\Struct{N}\) , there is no element \(k \in \Domain{N}\) which satisfies every formula \(\num{n} < x\) (where \(\num{n}\) is \(\Obj{0}^{\prime\dots\prime}\) with \(n\) \(\prime\) ’s). Use the compactness theorem to show that the set of sentences in the language of arithmetic which are true in the standard model of arithmetic \(\Struct{N}\) are also true in a structure \(\Struct{N'}\) that contains an element which does satisfy every formula \(\num{n} < x\) .
We know that first-order logic with identity predicate can express that the size of the domain must have some minimal size: The sentence \(A_{\ge n}\) (which says “there are at least \(n\) distinct objects”) is true only in structures where \(\Domain{M}\) has at least \(n\) objects. So if we take \[\Delta = \Setabs{A_{\ge n}}{n \ge 1}\nonumber\] then any model of \(\Delta\) must be infinite. Thus, we can guarantee that a theory only has infinite models by adding \(\Delta\) to it: the models of \(\Gamma \cup \Delta\) are all and only the infinite models of \(\Gamma\) .
So first-order logic can express infinitude. The compactness theorem shows that it cannot express finitude, however. For suppose some set of sentences \(\Lambda\) were satisfied in all and only finite structures. Then \(\Delta \cup \Lambda\) is finitely satisfiable. Why? Suppose \(\Delta' \cup \Lambda' \subseteq \Delta \cup \Lambda\) is finite with \(\Delta' \subseteq \Delta\) and \(\Lambda' \subseteq \Lambda\) . Let \(n\) be the largest number such that \(A_{\ge n} \in \Delta'\) . \(\Lambda\) , being satisfied in all finite structures, has a model \(\Struct{M}\) with finitely many but \(\ge n\) elements. But then \(\Sat{M}{\Delta' \cup \Lambda'}\) . By compactness, \(\Delta \cup \Lambda\) has an infinite model, contradicting the assumption that \(\Lambda\) is satisfied only in finite structures.


3.1: Nutrition Basics
What is your food made of?
Food provides the energy and nutrients you need to be healthy.
Nutrients include:
- protein
- carbohydrates
- fats
- vitamins
- minerals
- water
Energy of Food
When energy is used to describe the foods you consume, energy is referring to calories. Calories are what provides the body with the energy it needs to survive and stay healthy. Our body uses calories to breathe, think, and talk. We also use calories to exercise! The three categories of nutrients that provide us with calories, or energy, are Proteins, Carbohydrates, and Fats. If you were to go to McDonalds and eat a Big Mac you would be consuming 540 calories. How much of those calories come from Proteins, Carbohydrates, and Fats?
Protein
Protein is in every cell in the body. Our bodies need protein from the foods we eat to build and maintain bones, muscles and skin. We get proteins in our diet from meat, dairy products, nuts, and certain grains and beans. Proteins from meat and other animal products are complete proteins. This means they supply all of the amino acids the body can’t make on its own. Most plant proteins are incomplete. You should eat different types of plant proteins every day to get all of the amino acids your body needs.
It is important to get enough dietary protein.  How much you need depends on your age, sex, health, and level of physical activity. Most Americans eat enough protein in their diet.
Protein provides us with 4 calories per gram consumed. If you eat a Big Mac from McDonald's, it will provide you with 25 grams of protein. 25 grams of protein is equal to 100 calories, therefore 100 calories of the 540 total calories from a Big Mac come from proteins. Big Mac’s are 19% protein.
Carbohydrates
Carbohydrates are one of the main types of nutrients. They are the most important source of energy for your body. Your digestive system changes carbohydrates into glucose ( blood sugar ). Your body uses this sugar for energy for your cells, tissues and organs. It stores any extra sugar in your liver and muscles for when it is needed.
Carbohydrates are called simple or complex, depending on their chemical structure. Simple carbohydrates include sugars found naturally in foods such as fruits, vegetables, milk, and milk products. They also include sugars added during food processing and refining. Complex carbohydrates include whole grain breads and cereals, starchy vegetables and legumes. Many of the complex carbohydrates are good sources of fiber.
Fiber is commonly classified as soluble, which dissolves in water, or insoluble, which doesn’t dissolve.
- Soluble fiber. This type of fiber dissolves in water to form a gel-like material. It can help lower blood cholesterol and glucose levels. Soluble fiber is found in oats, barley, nuts, seeds, beans, lentils, peas, and some fruits and vegetables.
- Insoluble fiber. This type of fiber promotes the movement of material through your digestive system and adds bulk to the stool, so it can be of benefit to those who struggle with constipation or irregular stools. Insoluble fiber is found in foods such as wheat bran, vegetables, and whole grains.
For a healthy diet, limit the amount of added sugar that you eat and choose whole grains over refined grains.
Carbohydrates provide us with 4 calories per gram consumed. If you eat a Big Mac from McDonald's, it will provide you with 46 grams of carbohydrates. 46 grams of protein is equal to 184 calories, therefore 184 calories of the 540 total calories from a Big Mac come from carbohydrates. Big Mac’s are 34% carbohydrates.
Fats
We need a certain amount of fat in our diets to stay healthy. Fats provide needed energy in the form of calories. Fats help our bodies absorb important vitamins—called fat-soluble vitamins—including vitamins A, D and E. Fats also make foods more flavorful and help us feel full. Fats are especially important for infants and toddlers, because dietary fat contributes to proper growth and development.
Problems arise, though, if we eat too much fat. Dietary fats have more than twice as many calories per gram as either proteins or carbohydrates like sugar and starch. Excess calories, of course, can pack on the pounds and raise your risk for diabetes, cancer and other conditions.
Foods can contain a mixture of different fats. Unsaturated fats are considered “good” fats. They’re sometimes listed as “monounsaturated” and “polyunsaturated” fat on Nutrition Facts labels. These can promote health if eaten in the right amounts. They are generally liquid at room temperature, and are known as oils. You’ll find healthful unsaturated fats in fish, nuts and most vegetable oils, including canola, corn, olive and safflower oils.
The so-called “bad” fats are saturated fats and trans fats. They tend to be solid at room temperature. Solid fats include butter, meat fats, stick margarine, shortening, and coconut and palm oils. They’re often found in chocolates, baked goods, and deep-fried and processed foods.
Fats provide us with 9 calories per gram consumed. If you eat a Big Mac from McDonald's, it will provide you with 28 grams of fats. 28 grams of fat is equal to 252 calories, therefore 252 calories of the 540 total calories from a Big Mac come from fats. Big Mac’s are 47% fats.
Example: McDonald’s Big Mac
540 total calories
- Proteins = 25 grams = 100 calories = 19%
- Carbohydrates = 46 grams = 184 calories = 34%
- Fats = 28 grams = 252 calories = 47%
*Note: Many times the total calories from breaking down the macronutrients will not match the total calories and this is due to rounding the numbers.
We know the Big Mac provides us with a lot of Fat, but what kind of Fat is it? Is it good fat or bad fat? We can try to determine this by looking at the breakdown of Fats. The nutrition label tells us that 10 grams of the 28 grams comes from Saturated Fat and 1 grams comes from trans Fats.
Vitamins
Vitamins are substances that your body needs to grow and develop normally. There are 13 vitamins your body needs. They are:
- Vitamin A
- B vitamins (thiamine, riboflavin, niacin, pantothenic acid, biotin, vitamin B-6, vitamin B-12 and folate )
- Vitamin C
- Vitamin D
- Vitamin E
- Vitamin K
Vitamins are classified as either fat soluble (vitamins A, D, E and K) or water soluble (vitamins B and C). This difference between the two groups is very important as it determines how each vitamin acts within the body.
You can usually get all your vitamins from the foods you eat. Your body can also make vitamins D and K. People who eat a vegetarian diet may need to take a vitamin B12 supplement.
Each vitamin has specific jobs. If you have low levels of certain vitamins, you may get health problems. For example, if you don’t get enough vitamin C, you could become anemic. Some vitamins may help prevent medical problems. Vitamin A prevents night blindness.
The best way to get enough vitamins is to eat a balanced diet with a variety of foods. In some cases, you may need to take vitamin supplements. It’s a good idea to ask your healthcare provider first. High doses of some vitamins can cause problems.
Minerals
Minerals are important for your body to stay healthy. Your body uses minerals for many different jobs, including building bones, making hormones and regulating your heartbeat.
There are two kinds of minerals: macrominerals and trace minerals. Macrominerals are minerals your body needs in larger amounts. They include
calcium
, phosphorus, magnesium,
sodium
,
potassium
, chloride and sulfur. Your body needs just small amounts of trace minerals. These include
iron
, manganese, copper, iodine, zinc, cobalt, fluoride and selenium.
Water
Water is your body’s principal chemical component and makes up about 60 percent of your body weight. Every system in your body depends on water. For example, water flushes toxins out of vital organs, carries nutrients to your cells, and provides a moist environment for ear, nose and throat tissues.
Lack of water can lead to dehydration, a condition that occurs when you don’t have enough water in your body to carry out normal functions. Even mild dehydration can drain your energy and make you tired.
 For your body to function properly, you must replenish its water supply by consuming beverages and foods that contain water.
What are Antioxidants?
Antioxidants are substances we consume that may help to reduce cell damage. Antioxidants may come from the foods we eat or from dietary supplements.
Examples of antioxidants include
- Beta-carotene
- Lutein
- Lycopene
- Selenium
- Vitamin A
- Vitamin C
- Vitamin E
Antioxidants may help to reduce cell damage caused by free radicals. Free radicals are highly unstable molecules that are naturally formed when you exercise and when your body converts food into energy. Free radicals have been shown to cause “oxidative stress” in the body thus damaging healthy cells. Although not conclusive, research shows that antioxidants work to reduce the chances of cellular damage. Because antioxidants help to reduce cell damage, it had been theorized that they in turn help to reduce chances of many diseases, including cancer.
Query \(\PageIndex{1}\)
Try this Nutrition Facts Pre-Test to see how much you already know about nutrition.
Contributors and Attributions
Public domain content
- Nutrition Basics. Authored by: MedlinePlus. Provided by: National Institutes of Health. Located at: https://medlineplus.gov/nutrition.html . License: Public Domain: No Known Copyright
- Assortment of Fruit Image. Authored by: Daniel Sone. Provided by: National Cancer Institute. Located at: https://visualsonline.cancer.gov/details.cfm?imageid=8265 . License: Public Domain: No Known Copyright
- Antioxidants. Authored by: Medline Plus. Provided by: U.S. Department of Health and Human Services National Institutes of Health. Located at: https://medlineplus.gov/antioxidants.html License : Public Domain: No Known Copyright
- Antioxidants in Depth. Authored by: National Center for Complementary and Integrative Health (NCCIH). Provided by: U.S. Department of Health & Human Services, National Institutes of Health. Located at: https://nccih.nih.gov/health/antioxidants/introduction.htm License : Public Domain: No Known Copyright


4.4: Presenting Your Plan
If everything goes right, at some point you’ll find yourself presenting your plan to potential investors. This can be nerve-wracking for anyone, especially first-timers, but you can do a number of things to ensure your presentation comes off well.
Your objective: inspiration and distillation
When you present your plan, be enthusiastic, be confident and clearly illustrate the need for the product or service you plan to provide. Quickly evoke substantial interest in your venture. Once you’ve captured attention and interest, the audience will ask questions that allow you to expand on your ideas.
Think about your audience
How you present your business plan depends both on your audience and your situation. You really have two pitches: one for end-users (customers) and one for investors. The first focuses on price, performance, and ease of use that provides a sustainable competitive advantage. The second explains why the first one generates substantial return on investment (ROI) for investors or licensees.
And, although you may be formally presenting your plan to venture capitalists, don’t overlook the opportunity to present your ideas to the people you meet every day. In both cases it’s important to be socially astute and to recognize the needs and interests of the people with whom you are speaking.
Elevator pitch
Regardless of the situation, you have about thirty seconds to get the audience’s attention. One of the most important skills you need is to be able to explain your plan, out loud or in writing, in 30 seconds or less (the amount of time you might have riding an elevator with a prospective funder). Your elevator pitch is a clear, articulate, and concise description of your purpose that should also relay your passion for your venture. When you use the elevator pitch in a written document, the audience should immediately understand what your venture is about.
Brevity is key
Thoughtfully prepare your elevator pitch. You have about thirty seconds to grab the attention of your audience regardless of the situation. Bill Joos from Garage Technology Ventures1 (www.garage.com) recommends that you begin your pitch with an engaging tag line that incorporates your business’s product or service and purpose. A clever tag line can directly and simply convey your idea, and when you have a captive audience you can elaborate on your business. Your ability to clearly, concisely and passionately state your purpose establishes that you have well-defined goals and are adequately prepared to promote your ideas. This also allows you to get your point across before your listener has time to get bored.
Rules of public speaking
Make sure that you tell your audience what you are going to tell them, tell them what you want them to know and then tell them what you told them. Emphasize a few key points throughout your presentation and do not overwhelm your audience with too much information. Help the audience retain what you’ve said by strategically repeating the most important information. If you’ve covered a few main points, you’ve probably given your audience enough information—again, if members of the audience are interested in learning more, they will ask questions.
Main points of a presentation
Bill Joos recommends using the following outline for your business plan presentation:
Summary
—a modified version of your elevator pitch. Tell your audience your mission, quickly describe the product and, if appropriate, tell them how much funding you need.
Market
—Establish your market by introducing the problem that you will solve with your product or service.
Solution
—Explain your proposed venture and how it will solve the problem. Include a description of your idea, a brief description of how you are going to implement this idea, your awareness of major competitors, how you will market this service or product and how you plan to profit from this venture.
Team
—Establish that you have a competent team with past experience that makes them ideal for your business venture.
Use of Funds
—Explain how you plan to use acquired funds to implement your venture.
Recap
—Briefly summarize the main points of what you just finished telling your audience, leaving key points of your presentation fresh in their minds as you ask them to invest in your venture.
End with action
At the end of your presentation, tell your audience what you want them to do. Directly invite your listeners to become a part of your venture and let them know how to go about getting involved.
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Example of a great pitch
“ConstructionBoots.com is an e-commerce website that sells construction boots on a b2c and a b2b basis. Our primary market consists of construction workers, with secondary markets including other individuals and companies in the construction trade. We offer the highest quality products and drive traffic to the site by linking to other websites related to the construction industry. We believe the customer would find purchasing and direct delivery of construction boots through our website easier than purchasing via traditional retail outlets. We believe we will be the only pure e-commerce construction boot site, but will face indirect competition from traditional brick and mortar b2b retailers who target the trade as well as traditional mass merchandisers. If all goes as planned, we would look to sell ConstructionBoots.com to an industry retailer who sells construction gear.”
Tips for your elevator pitch
From “How to Deliver the Big Pitch,” by Todd Balf. Fast Company, June, 1999. “Prepare what you’re going to say—don’t wing it! Once you get the material down, and say it out loud, try it in front of your co-workers—but make sure they are able to give (and that you are able to take) criticism.” —Steven Bruner “I didn’t have time to write you a short letter, so I wrote you a long one.” —Mark Twain |