2.2: Discount Problems
Learning outcome
- Use mathematical notation to solve discount problems
A store called Feminine Furnishings is having a sale on bedding. Their queen sheet sets have a list price of \($126\). During the first two weeks of February, the store has a—Snuggle Up In Love Sale— where customers save \(14\%\) on any white, pink, or red bedding set. Carly selects a bedding set with pink stripes and pays \($108.36\).
Applications of discount are very common in retail settings. When you buy an item on sale, the original or list price of the item has been reduced by some dollar amount. The discount rate , usually given as a percent, is used to determine the amount of the discount. To determine the amount of discount , we multiply the discount rate by the original price. We summarize the discount model in the box below.
Discount
An amount of discount is subtracted from the original price.
amount of discount = discount rate \(\cdot\) original price
sale price = original price \(-\) discount
The sale price should always be less than the original price.
In some cases, the amount of discount is a fixed dollar amount. Then we just find the sale price by subtracting the amount of discount from the original price. For example, as you walk into a store you may see a sign that says “Spend \($100\) or more, and receive a \($20\) discount!”
example
Jason bought a pair of sunglasses from a rack that was labeled \(\text{\$10}\) off all Retrop brand glasses. The original price of the sunglasses was \(\text{\$39}\). What was the sale price of the sunglasses?
[reveal-answer q=”967734″]Show Answer[/reveal-answer]
[hidden-answer a=”967734″]
Solution
| Identify what you are asked to find. | What is the sale price? |
| Choose a variable to represent it. | Let \(s=\) the sale price. |
| Write a sentence that gives the information to find it. | The sale price is the original price minus the discount. |
| Translate into an equation. | |
| Simplify. | \(s=29\) |
| Check if this answer is reasonable. | |
| Yes. The sale price, \(\text{\$29}\), is less than the original price, \(\text{\$39}\). | |
| Write a complete sentence that answers the question. | The sale price of the sunglasses was \(\text{\$29}\). |
[/hidden-answer]
try it
[ohm_question]146772[/ohm_question]
In the first example, the amount of discount was a set or static amount. In the next example, the discount is given as a percent of the original price.
Example
Elise bought a dress that was discounted \(\text{35%}\) off of the original price of \(\text{\$140}\). What was the amount of discount and the sale price of the dress?
[reveal-answer q=”967374″]Show Answer[/reveal-answer]
[hidden-answer a=”967374″]
Solution
ⓐ Before beginning, you may find it helpful to organize the information in a list.
Original price = \(\text{\$140}\)
Discount rate = \(35\text{%}\)
Amount of discount = ?
| Identify what you are asked to find. | What is the amount of discount? |
| Choose a variable to represent it. | Let \(d=\) the amount of discount. |
| Write a sentence that gives the information to find it. | The discount is \(35\text{%}\) of the original price. |
| Translate into an equation. | |
| Simplify. | \(d=49\) |
| Check if this answer is reasonable. | |
| Yes. A \(\text{\$49}\) discount is reasonable for a \(\text{\$140}\) dress. | |
| Write a complete sentence that answers the question. | The amount of discount was \(\text{\$49}\). |
ⓑ
Original price = \(\text{\$140}\)
Amount of discount = \(\text{\$49}\)
Sale price = ?
| Identify what you are asked to find. | What is the sale price of the dress? |
| Choose a variable to represent it. | Let \(s=\) the sale price. |
| Write a sentence that gives the information to find it. | The sale price is the original price minus the discount. |
| Translate into an equation. | |
| Simplify. | \(s=91\) |
| Check if this answer is reasonable. | |
| Yes. The sale price, \(\text{\$91}\), is less than the original price, \(\text{\$140}\). | |
| Write a complete sentence that answers the question. | The sale price of the dress was \(\text{\$91}\). |
[/hidden-answer]
try it
[ohm_question]146775[/ohm_question]
There may be times when you buy something on sale and want to know the discount rate. The next example will show this case.
example
Jeannette bought a swimsuit at a sale price of \(\text{\$13.95}\). The original price of the swimsuit was \(\text{\$31}\). Find the ⓐ amount of discount and ⓑ discount rate.
[reveal-answer q=”123339″]Show Answer[/reveal-answer]
[hidden-answer a=”123339″]
Solution
ⓐ Before beginning, you may find it helpful to organize the information in a list.
Original price = \(\text{\$31}\)
Amount of discount = ?
Sale price = \(\text{\$13.95}\)
| Identify what you are asked to find. | What is the amount of discount? |
| Choose a variable to represent it. | Let \(d=\) the amount of discount. |
| Write a sentence that gives the information to find it. | The discount is the original price minus the sale price. |
| Translate into an equation. | |
| Simplify. | \(d=17.05\) |
| Check if this answer is reasonable. | |
| Yes. The \(\text{\$17.05}\) discount is less than the original price. | |
| Write a complete sentence that answers the question. | The amount of discount was \($17.05\). |
ⓑ Before beginning, you may find it helpful to organize the information in a list.
Original price = \($31\)
Amount of discount = \($17.05\)
Discount rate = ?
| Identify what you are asked to find. | What is the discount rate? |
| Choose a variable to represent it. | Let \(r=\) the discount rate. |
| Write a sentence that gives the information to find it. | The discount is what percent of the original price? |
| Translate into an equation. | |
| Divide. | \(\Large\frac{17.05}{31}\normalsize =\Large\frac{r(31)}{31}\) |
| Simplify. | \(0.55=r\) |
| Check if this answer is reasonable. | |
| The rate of discount was a little more than \(50\text{%}\) and the amount of discount is a little more than half of \(\text{\$31}\). | |
| Write a complete sentence that answers the question. | The rate of discount was \(55\text{%}\). |
[/hidden-answer]
try it
[ohm_question]156971[/ohm_question]
In the following video we show another example of how to find the discount rate (also called the percent of change) given the original price and the marked-down price.


10: Quadratic Equations Last updated Save as PDF Page ID 49290 Denny Burzynski & Wade Ellis, Jr. College of Southern Nevada via OpenStax CNX 10.1: Objectives 10.2: Solving Quadratic Equations 10.3: Solving Quadratic Equations by Factoring 10.4: Solving Quadratic Equations Using the Method of Extraction of Roots 10.5: Solving Quadratic Equations Using the Method of Completing the Square We need another method for solving quadratic equations. The method we shall study is based on perfect square trinomials and extraction of roots. The method is called solving quadratic equations by completing the square. 10.6: Solving Quadratic Equations Using the Quadratic Formula 10.7: Applications 10.8: Graphing Quadratic Solutions 10.9: Summary of Key Concepts 10.10: Exercise Supplement 10.11: Proficiency Exam


15.2: Prokaryotic Transcription
Skills to Develop
- List the different steps in prokaryotic transcription
- Discuss the role of promoters in prokaryotic transcription
- Describe how and when transcription is terminated
The prokaryotes, which include bacteria and archaea, are mostly single-celled organisms that, by definition, lack membrane-bound nuclei and other organelles. A bacterial chromosome is a covalently closed circle that, unlike eukaryotic chromosomes, is not organized around histone proteins. The central region of the cell in which prokaryotic DNA resides is called the nucleoid. In addition, prokaryotes often have abundant plasmids , which are shorter circular DNA molecules that may only contain one or a few genes. Plasmids can be transferred independently of the bacterial chromosome during cell division and often carry traits such as antibiotic resistance.
Transcription in prokaryotes (and in eukaryotes) requires the DNA double helix to partially unwind in the region of mRNA synthesis. The region of unwinding is called a transcription bubble. Transcription always proceeds from the same DNA strand for each gene, which is called the template strand . The mRNA product is complementary to the template strand and is almost identical to the other DNA strand, called the nontemplate strand . The only difference is that in mRNA, all of the T nucleotides are replaced with U nucleotides. In an RNA double helix, A can bind U via two hydrogen bonds, just as in A–T pairing in a DNA double helix.
The nucleotide pair in the DNA double helix that corresponds to the site from which the first 5' mRNA nucleotide is transcribed is called the +1 site, or the initiation site . Nucleotides preceding the initiation site are given negative numbers and are designated upstream . Conversely, nucleotides following the initiation site are denoted with “+” numbering and are called downstream nucleotides.
Initiation of Transcription in Prokaryotes
Prokaryotes do not have membrane-enclosed nuclei. Therefore, the processes of transcription, translation, and mRNA degradation can all occur simultaneously. The intracellular level of a bacterial protein can quickly be amplified by multiple transcription and translation events occurring concurrently on the same DNA template. Prokaryotic transcription often covers more than one gene and produces polycistronic mRNAs that specify more than one protein.
Our discussion here will exemplify transcription by describing this process in Escherichia coli , a well-studied bacterial species. Although some differences exist between transcription in E. coli and transcription in archaea, an understanding of E. coli transcription can be applied to virtually all bacterial species.
Prokaryotic RNA Polymerase
Prokaryotes use the same RNA polymerase to transcribe all of their genes. In E. coli , the polymerase is composed of five polypeptide subunits, two of which are identical. Four of these subunits, denoted α , α , β , and β' comprise the polymerase core enzyme . These subunits assemble every time a gene is transcribed, and they disassemble once transcription is complete. Each subunit has a unique role; the two α -subunits are necessary to assemble the polymerase on the DNA; the β -subunit binds to the ribonucleoside triphosphate that will become part of the nascent “recently born” mRNA molecule; and the β' binds the DNA template strand. The fifth subunit, σ , is involved only in transcription initiation. It confers transcriptional specificity such that the polymerase begins to synthesize mRNA from an appropriate initiation site. Without σ , the core enzyme would transcribe from random sites and would produce mRNA molecules that specified protein gibberish. The polymerase comprised of all five subunits is called the holoenzyme .
Prokaryotic Promoters
A promoter is a DNA sequence onto which the transcription machinery binds and initiates transcription. In most cases, promoters exist upstream of the genes they regulate. The specific sequence of a promoter is very important because it determines whether the corresponding gene is transcribed all the time, some of the time, or infrequently. Although promoters vary among prokaryotic genomes, a few elements are conserved. At the -10 and -35 regions upstream of the initiation site, there are two promoter consensus sequences, or regions that are similar across all promoters and across various bacterial species (Figure \(\PageIndex{1}\)). The -10 consensus sequence, called the -10 region, is TATAAT. The -35 sequence, TTGACA, is recognized and bound by σ . Once this interaction is made, the subunits of the core enzyme bind to the site. The A–T-rich -10 region facilitates unwinding of the DNA template, and several phosphodiester bonds are made. The transcription initiation phase ends with the production of abortive transcripts, which are polymers of approximately 10 nucleotides that are made and released.
Link to Learning
View this MolecularMovies animation to see the first part of transcription and the base sequence repetition of the TATA box.
Elongation and Termination in Prokaryotes
The transcription elongation phase begins with the release of the σ subunit from the polymerase. The dissociation of σ allows the core enzyme to proceed along the DNA template, synthesizing mRNA in the 5' to 3' direction at a rate of approximately 40 nucleotides per second. As elongation proceeds, the DNA is continuously unwound ahead of the core enzyme and rewound behind it (Figure \(\PageIndex{2}\)). The base pairing between DNA and RNA is not stable enough to maintain the stability of the mRNA synthesis components. Instead, the RNA polymerase acts as a stable linker between the DNA template and the nascent RNA strands to ensure that elongation is not interrupted prematurely.
Prokaryotic Termination Signals
Once a gene is transcribed, the prokaryotic polymerase needs to be instructed to dissociate from the DNA template and liberate the newly made mRNA. Depending on the gene being transcribed, there are two kinds of termination signals. One is protein-based and the other is RNA-based. Rho-dependent termination is controlled by the rho protein, which tracks along behind the polymerase on the growing mRNA chain. Near the end of the gene, the polymerase encounters a run of G nucleotides on the DNA template and it stalls. As a result, the rho protein collides with the polymerase. The interaction with rho releases the mRNA from the transcription bubble.
Rho-independent termination is controlled by specific sequences in the DNA template strand. As the polymerase nears the end of the gene being transcribed, it encounters a region rich in C–G nucleotides. The mRNA folds back on itself, and the complementary C–G nucleotides bind together. The result is a stable hairpin that causes the polymerase to stall as soon as it begins to transcribe a region rich in A–T nucleotides. The complementary U–A region of the mRNA transcript forms only a weak interaction with the template DNA. This, coupled with the stalled polymerase, induces enough instability for the core enzyme to break away and liberate the new mRNA transcript.
Upon termination, the process of transcription is complete. By the time termination occurs, the prokaryotic transcript would already have been used to begin synthesis of numerous copies of the encoded protein because these processes can occur concurrently. The unification of transcription, translation, and even mRNA degradation is possible because all of these processes occur in the same 5' to 3' direction, and because there is no membranous compartmentalization in the prokaryotic cell (Figure \(\PageIndex{3}\)). In contrast, the presence of a nucleus in eukaryotic cells precludes simultaneous transcription and translation.
Link to Learning
Visit this BioStudio animation to see the process of prokaryotic transcription.
Summary
In prokaryotes, mRNA synthesis is initiated at a promoter sequence on the DNA template comprising two consensus sequences that recruit RNA polymerase. The prokaryotic polymerase consists of a core enzyme of four protein subunits and a σ protein that assists only with initiation. Elongation synthesizes mRNA in the 5' to 3' direction at a rate of 40 nucleotides per second. Termination liberates the mRNA and occurs either by rho protein interaction or by the formation of an mRNA hairpin.
Glossary
- consensus
- DNA sequence that is used by many species to perform the same or similar functions
- core enzyme
- prokaryotic RNA polymerase consisting of α , α , β , and β' but missing σ ; this complex performs elongation
- downstream
- nucleotides following the initiation site in the direction of mRNA transcription; in general, sequences that are toward the 3' end relative to a site on the mRNA
- hairpin
- structure of RNA when it folds back on itself and forms intramolecular hydrogen bonds between complementary nucleotides
- holoenzyme
- prokaryotic RNA polymerase consisting of α , α , β , β' , and σ ; this complex is responsible for transcription initiation
- initiation site
- nucleotide from which mRNA synthesis proceeds in the 5' to 3' direction; denoted with a “+1”
- nontemplate strand
- strand of DNA that is not used to transcribe mRNA; this strand is identical to the mRNA except that T nucleotides in the DNA are replaced by U nucleotides in the mRNA
- plasmid
- extrachromosomal, covalently closed, circular DNA molecule that may only contain one or a few genes; common in prokaryotes
- promoter
- DNA sequence to which RNA polymerase and associated factors bind and initiate transcription
- Rho-dependent termination
- in prokaryotes, termination of transcription by an interaction between RNA polymerase and the rho protein at a run of G nucleotides on the DNA template
- Rho-independent
- termination sequence-dependent termination of prokaryotic mRNA synthesis; caused by hairpin formation in the mRNA that stalls the polymerase
- TATA box
- conserved promoter sequence in eukaryotes and prokaryotes that helps to establish the initiation site for transcription
- template strand
- strand of DNA that specifies the complementary mRNA molecule
- transcription bubble
- region of locally unwound DNA that allows for transcription of mRNA
- upstream
- nucleotides preceding the initiation site; in general, sequences toward the 5' end relative to a site on the mRNA


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paternalism
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initiatives that aim to prevent an adverse health event from occurring, such as immunizations and health promotion education
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5.8: Force, Energy, and Potential Difference
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The force \({\bf F}_e\) experienced by a particle at location \({\bf r}\) bearing charge \(q\) in an electric field intensity \({\bf E}\) is
\[{\bf F}_e = q {\bf E}({\bf r}) \label{m0061_eFeqE} \]
If left alone in free space, this particle would immediately begin to move. The resulting displacement represents a loss of potential energy. This loss can quantified using the concept of work , \(W\). The incremental work \(\Delta W\) done by moving the particle a short distance \(\Delta l\), over which we assume the change in \({\bf F}_e\) is negligible, is
\[\Delta W \approx -{\bf F}_e\cdot\hat{\bf l}\Delta l \label{m0061_WeFdl} \]
where in this case \(\hat{\bf l}\) is the unit vector in the direction of the motion; i.e., the direction of \({\bf F}_e\). The minus sign indicates that potential energy of the system consisting of the electric field and the particle is being reduced. Like a spring that was previously compressed and is now released, the system is “relaxing.”
To confirm that work defined in this way is an expression of energy, consider the units. The product of force (units of N) and distance (units of m) has units of N\(\cdot\)m, and 1 N\(\cdot\)m is 1 J of energy.
Now, what if the motion of the particle is due to factors other than the force associated with the electric field? For example, we might consider “resetting” the system to it’s original condition by applying an external force to overcome \({\bf F}_e\). Equation \ref{m0061_WeFdl} still represents the change in potential energy of the system, but now \(\hat{\bf l}\) changes sign. The same magnitude of work is done, but now this work is positive. In other words, positive work requires the application of an external force that opposes and overcomes the force associated with the electric field, thereby increasing the potential energy of the system. With respect to the analogy of a mechanical spring used above, positive work is achieved by compressing the spring.
It is also worth noting that the purpose of the dot product in Equation \ref{m0061_WeFdl} is to ensure that only the component of motion parallel to the direction of the electric field is included in the energy tally. This is simply because motion in any other direction cannot be due to \({\bf E}\), and therefore does not increase or decrease the associated potential energy.
We can make the relationship between work and the electric field explicit by substituting Equation \ref{m0061_eFeqE} into Equation \ref{m0061_WeFdl}, yielding
\[\Delta W \approx -q {\bf E}({\bf r})\cdot\hat{\bf l}\Delta l \label{m0061_WqEdl} \]
Equation \ref{m0061_WqEdl} gives the work only for a short distance around \({\bf r}\). Now let us try to generalize this result. If we wish to know the work done over a larger distance, then we must account for the possibility that \({\bf E}\) varies along the path taken. To do this, we may sum contributions from points along the path traced out by the particle, i.e.,
\[W \approx \sum_{n=1}^N \Delta W ({\bf r}_n) \nonumber \]
where \({\bf r}_n\) are positions defining the path. Substituting Equation \ref{m0061_WqEdl}, we have
\[W \approx -q \sum_{n=1}^N {\bf E}({\bf r}_n)\cdot\hat{\bf l}({\bf r}_n)\Delta l \nonumber \]
Taking the limit as \(\Delta l\to 0\) we obtain
\[W = -q \int_{\mathcal C} {\bf E}({\bf r})\cdot\hat{\bf l}({\bf r}) dl \nonumber \]
where \(\mathcal{C}\) is the path (previously, the sequence of \({\bf r}_n\)’s) followed. Now omitting the explicit dependence on \({\bf r}\) in the integrand for clarity:
\[W = -q \int_{\mathcal C} {\bf E}\cdot d{\bf l} \label{m0061_eWqint} \]
where \(d{\bf l} = \hat{\bf l}dl\) as usual. Now, we are able to determine the change in potential energy for a charged particle moving along any path in space, given the electric field.
At this point, it is convenient to formally define the electric potential difference \(V_{21}\) between the start point (1) and end point (2) of \({\mathcal C}\). \(V_{21}\) is defined as the work done by traversing \({\mathcal C}\), per unit of charge: \[V_{21} \triangleq \frac{W}{q} \nonumber \] This has units of J/C, which is volts (V). Substituting Equation \ref{m0061_eWqint}, we obtain:
\[\boxed{ V_{21} = - \int_{\mathcal C} {\bf E} \cdot d{\bf l} } \label{m0062_eVAB} \]
An advantage of analysis in terms of electrical potential as opposed to energy is that we will no longer have to explicitly state the value of the charge involved.
The potential difference \(V_{21}\) between two points in space, given by Equation \ref{m0062_eVAB}, is the change in potential energy of a charged particle divided by the charge of the particle. Potential energy is also commonly known as “voltage” and has units of V.
Example \(\PageIndex{1}\): Potential difference in a uniform electric field
Consider an electric field \({\bf E}({\bf r}) = \hat{\bf z}E_0\), which is constant in both magnitude and direction throughout the domain of the problem. The path of interest is a line beginning at \(\hat{\bf z}z_1\) and ending at \(\hat{\bf z}z_2\). What is \(V_{21}\)? (It’s worth noting that the answer to this problem is a building block for a vast number of problems in electromagnetic analysis.)
Solution
From Equation \ref{m0062_eVAB} we have
\[V_{21} = - \int_{z_1}^{z_2} \left( \hat{\bf z}E_0 \right) \cdot \hat{\bf z}dz = -E_0 (z_2 - z_1) \nonumber \]
Note \(V_{21}\) is simply the electric field intensity times the distance between the points. This may seem familiar. For example, compare this to the findings of the battery-charged capacitor experiment described in Section 2.2. There too we find that potential difference equals electric field intensity times distance, and the signs agree.
The solution to the preceding example is simple because the direct path between the two points is parallel to the electric field. If the path between the points had been perpendicular to \({\bf E}\), then the solution is even easier – \(V_{21}\) is simply zero. In all other cases, \(V_{21}\) is proportional to the component of the direct path between the start and end points that is parallel to \({\bf E}\), as determined by the dot product .


5.5: Two-Way Tables (3 of 5)
Learning Objectives
- Calculate marginal, joint, and conditional percentages and interpret them as probability estimates.
At this point, we know how to determine marginal probabilities , such as the probability that a randomly selected student is female: P (female).
And we know how to calculate conditional probabilities , such as the probability that a randomly selected female student is in the Health Science program: P (Health Science | female)
But we do not know how to calculate joint probabilities , such as the probability that a randomly selected student is both a female and in the Health Sciences program.
We write this joint probability as P (female and Health Sciences).
The following example illustrates how to calculate a joint probability.
Example
Joint Probability
Question: If we select a student at random, what is the probability that the student is both a male and in the Info Tech program?
Answer This question involves male students who are in the Info Tech program, but it is NOT a conditional probability. We are picking a student at random from the entire population of 12,000 students , so there is no condition. Our shorthand notation for this probability is:
- P (male and Info Tech)
Since 564 of the 12,000 students enrolled at the college are both male and in the Info Tech program (see table), the probability P (male and Info Tech) is:
| Arts-Sci | Bus-Econ | Info Tech | Health Science | Graphics Design | Culinary Arts | Row Totals | |
| Female | 4,660 | 435 | 494 | 421 | 105 | 83 | 6,198 |
| Male | 4,334 | 490 | 564 | 223 | 97 | 94 | 5,802 |
| Column Totals | 8,994 | 925 | 1,058 | 644 | 202 | 177 | 12,000 |
We call this calculation a joint probability . Note that when we calculate a joint probability, we divide the count from an inner cell of the table by the overall total count in the lower right corner.
The following table is used for the next Try It and Did I Get This? activities.
| Arts-Sci | Bus-Econ | Info Tech | Health Science | Graphics Design | Culinary Arts | Row Totals | |
| Female | 4,660 | 435 | 494 | 421 | 105 | 83 | 6,198 |
| Male | 4,334 | 490 | 564 | 223 | 97 | 94 | 5,802 |
| Column Totals | 8,994 | 925 | 1,058 | 644 | 202 | 177 | 12,000 |
Contributors and Attributions
- Concepts in Statistics. Provided by : Open Learning Initiative. Located at : http://oli.cmu.edu . License : CC BY: Attribution


3.1: Overview of Weather and Climate
In seeking to learn the climate of a country we first think of its latitude, since that is usually the most important factor. In the case of California, however, this inquiry does not help us very much. California has a coastline nearly 1000 miles in length, reaching through ten degrees of latitude, and we would expect that its northern part, which is nearly the latitude of Chicago, would be cold in winter, and that the southern part, which reaches to about the latitude of Savannah Georgia, would be very warm, but there is, near the coast, only a few degrees difference in temperature between the north and the south. Spring fruits appear first, and oranges ripen earlier in Northern rather than in Southern California.
Want to learn more? Either scan the QR code or visit this link to watch a lecture that introduces the basics of California’s weather & climate (Video length: 23 min).
Regarding the small range in temperature as we go north or south along the coast, the temperature of the ocean changes but little from winter to summer. The California current is a cold ocean current, which makes the west coast of the USA much drier than coasts with warm oceans. We also know that California, being in the temperate zone, is situated in the belt of prevailing westerly winds. The temperature of the air over the ocean is determined, to a large extent, by that of the water, and since the ocean varies but little throughout the year, and the winds blow mostly from the ocean toward the land, the latter is going to be cooler in summer and warmer in winter than it otherwise would be.
If not for mountain barriers, the cool ocean winds would sweep far inland and temper the climate of the whole State. The fact that there are mountain ranges lying close to and parallel to the coast has resulted has aided in making the climate of the interior subject to much greater extremes of temperature, as well as decreasing its rainfall. By the time the winds have passed the Coast Ranges their moisture and coolness have been greatly reduced, while still farther eastward, on the opposite side of the Sierra Nevada, the summers are not only extremely hot, but the lack of moisture makes the region a desert.
During the summer, except for the thunderstorms in the mountains, it is very rare that rain falls over most of the State, although the air sweeping in from the sea is saturated with moisture, as shown by the fog it bears, but if the Pacific had warmer ocean waters and currents—like the Gulf of Mexico or Atlantic, California would experience more rain in the summer, as warmer water provides more humidity than colder water. To have rain, air must not only be cooled to the dew point, but below that point, and the only thing which will do that is exemplified in those irregular and violent disturbances of the atmosphere which set up currents carrying the moisture-laden air to a great elevation where the temperature is sufficiently low to bring this about.
Many storms that pass across Northern California fail to reach the southern portion, and they also usually decrease in intensity toward the south, so that outside of the mountain districts the southern portion of the State has a very light rainfall. The influence of mountains on precipitation is extremely important because of the low temperature of their lofty tops. In the case of many storms in Southern California which pass over the lowland regions with but a slight rainfall, when they encounter the mountains there is a heavy fall of snow or rain. It is because of this fact that we find such great differences in the rainfall during a few miles.
During the summer there generally exists an area of low air pressure over the Gulf of California, and here originates the "Sonora" (so-called from the province of Sonora, in Mexico) storms which bring frequent rains to Southern Arizona and New Mexico. These storms sometimes reach into Southern California and give heavy summer rains in the mountains and in the deserts. In fact, the heaviest rainfall of the whole year may occur in the Colorado desert during summer.
Summer thunderstorms are frequent in all the higher mountain regions of the State. They are partly due to the low-pressure areas just mentioned and in part to the influence of the cool mountain tops on the upward-moving air currents. They add quite substantially to the summer water supply, and some monsoonal moisture from the south.
During the clear cool periods of winter, a heavy blanket of fog, known as "tule fog," occurs in nearly all the lowland valleys to a greater or less extent. This generally breaks away during the day, but in the lower San Joaquin-Sacramento Valley, it may last continuously for weeks at a time, completely shutting out the sun. The name is derived from its prevalence in the tule region of the district just mentioned. This fog is the result of the settling of the heavier and cooler air into the hollows of the land, where the evaporation from the moist earth following the early winter rains finally produces a saturated condition.
Destructive winds of cyclonic character are rarely known in California. The most disagreeable, as well as harmful, winds occur in the spring and fall. They are dry and hot, and from their direction are known as ‘northers"’ or diablo winds. In Southern California, this wind is locally known as the ‘Santa Ana’. During its occurrence, the air is filled with dust, and for this reason, is often called a dust storm in the drier parts of the State.


3.5: Spec Work, Prototypes, Pretesting, Pilots (Brand and Franchise Fodder)
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I research speculation work because corporate/professional apologists for free/gifted labor provoke my long-standing interests in industrial aesthetics, production’s cultural politics, multimedia branding rationality, and industrial reflexivity. 13 Those concerns resonate with many current labor practices: the spec script, the pitch aesthetic, the craft-worker’s Facebook network, the technician’s how-to demo, the underemployed editor’s clip reel, the disgruntled crew member’s theoretical deconstruction of executives, the creative producer’s fan-pandering Twitterverse, and the endless proliferation of reps, agents, middlemen, “contact men,” and handlers. Such mediators and facilitators complicate the para-industry. Yet they also provide scholars with many new opportunities for para-industrial research.
In some ways, the pilot is no longer just a preliminary artifact setting up more durable or primary forms of lasting screen content. Rather, the pilot now arguably defines all film and television production. Or, said differently, all film and television productions now ideally function as pilots, in the broad sense of the term. This is because most films and shows (even year-long series) merely stand in as prototypes that create the possibility of endless systematic iterations of the same concept. This posturing in turn heightens the prospects that a corporation can endlessly monetize its proprietary IP. For only through endless speculation, conceptual pretesting, work-shopping, and “piloting” can a brand or franchise succeed. Such is the spec world. The fact that much of both the material burden and the justification for spec, prototyping, pretesting, and piloting has been financially off-loaded onto workers means that labor will continue to persist as a nagging but important complication in media studies.


4.5: 8chan
8chan (also known as infinitychan or infinitechan) originated in October 22, 2013 as a response to the supposed “authoritarian” development of the imageboard 4chan according to its developer Frederick Brennen , otherwise known by his online pseudonym “Hotwheels”. 8chan is an imageboard designed to allow for the unabridged free speech of its anonymous users. It has a small user base when compared to social media giants like Facebook, but ranks 3776th in global user visits. The site requires no registration for its use, and claims to hold no information on its users (a claim doubted by some users), with users being identified only by IP address and a randomly generated numeric code. It is only moderated by the individual board’s owner, allowing difficulty in holding individual rule-breakers accountable outside of removing their rule-breaking posts & banning their IP addresses.
There is one guiding rule for the entirety of the site: “ Do not post, request, or link to any content that is illegal in the United States of America and do not create boards with the purpose of posting or spreading such content. ” The site accepts advertisement , allowing for threads’ placement at the top of board pages with payment. Despite these routes, the site is bankrolled by the owner of the site, Jim Watkins. Watkins got his start in the online pornography business in the early days of the internet, and owns NT Technology, a server hosting business which he used to repossess the domain of 2chan. The website has yet to make profit, instead surviving due to Watkins’ patronage, for better or worse. 8chan has had some of its largest struggles with policing its own community; many cases of legal offenses and even some terroristic events have occurred.
Media Spotlight
While 8chan itself is far from a ‘news site’ in any classic definition of the phrase, it certainly does its fair share to earn itself a name in the news. Its continual gain in attraction to nefarious counter-culture groups like the Alt-right, the site even hosts a board which provides a space for pedophiles to create dialogue, some users even sharing links to child pornography images or sites. The track record is not good, and appears as though the site is making no genuine efforts to correct the actions that have been made clear to them. Some would argue, including Brennan himself, that ‘ it is simply the cost of free speech …’. But the crackdowns below are not the first, nor the last of 8chan’s problems with the law, nor are they exhaustive at this point.
/Baphomet/ & Swatting: An escalation of Gamergate
Baphomet, the supposed idol of the Knights of Templar turned symbol of the Church of Satan, was co-opted by 8chan users in 2015 on the tail end of the gamergate scandal. The group was a hub of people who desired to ‘ SWAT ’ on those that the community of the board deemed threatening/critical of the goals of gamergate: the increase in numbers of female video game developers and producers. Eventually, much of the thread was expunged from 8chan, but only after a user of the board attempted to ‘ doxx ’ Judge Katherine Forrest , who preceded over the influential Silk Road case.
8chan Removed From Google Search Results Over Reports of Child Abuse
Later in the same year as the SWATing incident, 8chan was removed from the search results of Google’s search engine during an investigation into allegations of child abuse, ranging from images of children that were just on the close side of the law to explicitly sexual images of children and the discussion of pedophile’s lust for children, including their tips and tricks for dealing with their sexual appetites, and even discussions of what they felt was their ‘persecution’.
Louisiana State Police and Alleged Antifa Membership Roster
The Louisiana state P.D. is being sued over its refusal to allow the public release of a supposed Antifa roster which some argue has been harvested from the boards of 8chan. Knowing the reputation of this site concerning false sources, pranks, and harassment, the factual validity of the document is questionable, at best. This document has been circulated throughout the Louisiana Police Dept. and appears to be part of an active investigation.
Shooter’s Manifestos Posted to 8chan
In April of 2019, two seperate terrorists posted manifestos to 8chan before engaging in violent actions that left over 50 dead, collectively. Both of these actions were politically motivated, and inspired, at least in part, by the extremity of 8chan’s white nationalist population. In New Zealand, the shooter’s anti-Muslim bigotry inspired him to open fire on two separate religious establishments, with catastrophic results. Shortly afterward, another gunman mimicked the New Zealand terrorist, posting his own manifesto in which he praised the New Zealand shooter. He then traveled to a synagogue to act out his own attack on one of Powey, California’s Jewish communities.
8chan’s Culture
Having been popularized during an exodus of extremist users from 4chan and other message board sites, 8chan has only one intention: to be a haven of unfettered free speech rights. As mentioned in the introduction, there is only one universal rule for using the site, and that is to avoid posting/linking services and content that is illegal in the United States. This rudimentary set of guidelines is still too stringent for the admins of 8chan, and as a result they only seem to respond to their own rules when violations of U.S. laws are waved before their faces or when they are threatened with legal action. All marginalized groups are fair game on this website, which is resistant to political correctness, anti-feminist, and home to radical voices from many ideologies.
I don’t have a problem with white supremacists talking on 8chan.
—
Jim Watkins
, 8chan owner
8chan also allows for complete anonymity for its users, requiring no registration, log in, or verification of identity. Users are instead identified merely by a number serial which is random, resulting in a loss of personal identification and accountability. The 8chan administration can view what IP address that users are browsing with, and ban them from the site, but users are otherwise protected from punishment. While in line with the goal of the site, these facts make it no easy task to hold users accountable, and emboldens them to behave in ways which they would not be able to on other, more moderated platforms.
“Free speech” in the case of 8chan, has lead to a prevalence of conspiracy theories due to a complete lack of moderation. From claims that Hillary Clinton ran a child sex trafficking ring from the basement of a pizza parlour, to assertions that there is a deep-state government controlling the heads of state (specifically those opposed to the sitting president), many subversive opinions and theories gain traction on this site, and some even seep into the pores of more credible sources. This muddling of people’s worldview is part and parcel of the overall ‘Troll’ mentality of the user base, which consistently uses disinformation campaigns, exploitation of technology, and online mob-tactics to spread its ideology.
A quick key to imageboard vernacular
- fullchan: 8chan
- halfchan: 4chan
- normalf*g or normaln*****: normal person, especially one who follows/subscribes to mainstream beliefs and popular culture
- Xf*g: person overly obsessed with X thing
- >>>/out/ or >>>/reddit/ : used in a reply when a person does not put enough effort into their post. the Reddit reference comes from the popular idea on 8chan that Reddit users come to 8chan to find memes and flood the board with low-quality, low-effort posts
- boomer: pretty much anyone over the age of 40; derogatory for someone who is out of touch with the ongoings of the world
- zoomer: a person in Generation Z; derogatory for a young person interested or obsessed with mainstream culture
- doomer: a depressed person who has given up on the world or otherwise believes the world is doomed, usually because of “degeneracy”. mostly bunkers in the /doomer/ board on 8chan
- fed: anyone who advocates for governmental control over imageboards and other parts of the internet, or is believed to be a member of law enforcement attempting data collection on the users of the site
- tripf*g: a person who uses the tripcode system in order to have a persistent username on the site. Tripcodes are cryptographically generated from a password, which is entered every time one makes a post or reply on the site. derogatory as “tripf*gging”, the act of using a tripcode to identify oneself across posts, goes against the board culture of anonymity
- avatarf*gging: including an image of the same character or person across all of one’s posts, much like one would have an avatar or profile picture on a traditional social media site
- “glow-in-the-dark n***** from the CIA”: a person who advocates for governmental surveillance and backdoored online services, particularly on /tech/ where the prevailing board culture values libre software, security, and privacy. comes from a popular verbal tic of Terry Davis, a programmer revered by imageboards for his frequent racist screeds and singlehandedly creating the computer operating system TempleOS because be believed God told him to
- lolcow: a person who can be easily goaded into doing embarrassing things on the internet for trolls’ amusement
8chan Iconography and Dog-Whistles
A dog-whistle in a political sense is coded language employed in a way so that the general public cannot fully understand the true meaning that the ingroup understands it. Dog whistles are often disguised as completely mundane and innocuous language as to allow those in the ingroup to completely disavow the dog whistle’s true meaning and say that they were using the normal usage of it. Both 4 and 8 chan have created multiple dog-whistles and have worked them into their existing iconography.
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Pepe
- Probably the oldest and best-known image coming from 4 and 8 Chan. The character originated from the comic Boy’s Club written by Matt Furie but quickly was co opted by the Chans and became a mascot of sorts. But as they moved further towards extremism and bigotry so did Pepe leading to the Anti-Defamation League classifying it as a hate symbol .
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NPC
- The NPC meme was created to mock progressives and pretty much everyone else left of center by comparing them to NPCs (non-player characters) from video games.  Members of 4 and 8 Chan compare their political adversaries to them in order to dehumanize them, which could potentially lead to violence.
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Kekistan
- A fake nation created in 4chan around 2017 as a home for the members of site. It became a symbol for /pol/, and as time went on the flag started to show up at right wing rallies such as the “Unite the Right Rally” where Heather Heyer was killed. The flag itself looks like an altered nazi flag with the swastikas replaced with the word “Kek” and the flag itself recolored to green, doubtlessly referencing Pepe.
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The “Ok Hand”
- One of the older dog whistles but one that is still being used today. It was originally created to make people who called them out on it look absurd. The sign means white power, the three fingers are the W and the thumb and the pointer finger along with the wrist being the P. The members of 4chan showed an image of Mel Gibson (who famously made multiple anti-Semitic remarks) making the sign alongside an image explaining it to give the fake dog whistle credibility. As time has passed, the hand sign has developed from a meme into a disparaging symbol, as shown with the Christchurch shooter making it during his shooting and in court .
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Any common noun (who, they, etc.) surrounded with three sets of parentheses or asterisks
- This is a way for them to discuss their Jewish deep state conspiracy without being too overt. Many members on the Chans believe that there is a vast Jewish conspiracy that has control of the world governments and mainstream media. Replace the noun in the parenthesis or asterisks with “The Jews.”
What Can Be Done?
To ban or not to ban, that is the question, and around that question there is much debate. Hate groups, like white nationalist organizations and anti-gender-equality groups, often espouse the message that they are woefully oppressed and suppressed by the government and liberals, hence their migration to platforms like 8chan to escape accountability. In a climate such as this, marginalizing them further may lead to deeper convictions . Unfortunately, as the administrative leaders of 8chan are reluctant to acknowledge their role in the real-life consequences of their cyber laissez-faire, there are not many courses that this website will take. This problem is exacerbated further by the fact that while the website has servers in the United States, those in control of the site itself reside outside the legal bounds of the U.S. system.
Would government action restricting content on the site violate the First Amendment? A great deal of the population would refer to the website as the darkest place on the internet, which some would use to argue for the censorship of its content. The First Amendment states “Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.” At the time of its creation, the First Amendment was devised to protect the individual from having their civil liberties infringed upon by a tyrannical government. Acts of violence encouraged by a space that does not have an underlying ethical conformity besides freely speaking like this site poses a challenge: is this speech legally protected? Cases such as of Miller v. California (1973) which proposed a test for whether speech is obscene and therefore not protected and Chaplinsky v. New Hampshire (1942), concerning speech that provokes violence, suggest some of the speech expressed on 8chan is not necessarily protected under the First Amendment. However, the site’s administrators live abroad and might claim immunity is provided by Section 230 of the Telecommunications Act of 1996.
Commercial constraints are not likely to moderate 8chan. This is not a normal case of social media management, and therefore will be near impervious to economic constraints, seeing as it already appears as though the site doesn’t earn enough money itself to stay in the dark. Social pressure also will not alleviate this problem, as 8channers are the type to feed off of detraction. Hopefully, as this site grows in its influence and popularity, its administration will be forced to seek new employees, some of whom may see this problem for what it is, not as some bastion of free speech, but a host for those who are willing to weaponize it to prove a point.
Some countries, like New Zealand, that have seen extreme violence as a result of the radicalization of the site’s users are blocking accessibility to the site, taking the only recourse left to them by a website that continually pushes the envelope. Unfortunately, users in these countries may be empowered by this silencing of their counter culture, but the world may have to cross each bridge as we get to them in cases like these.
Recommended Reading and Viewing
“ Meet the Man Keeping 8chan, The World’s Most Vile Website, Alive ” by Ethan Chiel, Splinter , April 19, 2016.
The Other America ‘Frederick Brennan’ Al Jazeera America , n.d.
“ The Cops Want to Know What’s Happening on 8Chan ” by Ali Breland, Mother Jones , April 5, 2019.
“ Why Banning the Toxic, Racist 8chan Message Board Could Backfire ” by Ali Breland, Mother Jones , May 1, 2019.


9.8: One-on-One Audio Calls
- Identify strategies to increase comprehension and reduce misunderstanding in one-on-one telephone / VOIP communications
In many ways, one-on-one calls are the easiest because they are the most familiar. However, this familiarity can also lead to people being underprepared for the call and wasting time, which is frustrating for both parties. Needless to say, you shouldn’t eat or chew gum during the call; a quiet sip of water now and then is fine. You should also make sure you complete all five stages of the call.
If the call is planned and on the calendar, make sure you call on time. It’s human nature to feel more pressure when several people are waiting rather than just one, but it’s no less rude to that one person when you’re late. If the call is unplanned and it’s likely to take more than a few minutes, it’s courteous to send an IM or email asking whether the person is available now and letting them know how long the call may take: “Hi Dan, are you free to talk for about 20 minutes right now? If not, might you have some time before the end of the day? Thanks.”
Listen as actively as you talk . No matter what means of communication you are using, this is one of your most important guidelines. A lot of time and confusion is saved when people actively listen to one another rather than thinking about what they’re going to say next.
Because of quirks in the technology, using more complex systems such as VOIP on your laptop or conferencing applications can make calls a bit more complicated even when it’s just you and one other person. As we have already discussed, allow a bit of time when scheduling the call to make sure that you can attend to technology issues and still get your important business done.
If there’s a staticky or hard-to-hear line, there are a couple of things to do:
- Find out where the other person is calling from. If they are outside or at a busy coffee shop, the background noise behind them may be what’s making your call hard to hear. To fix this, they can either move to a quieter place (which may mean rescheduling the call), or mute their phone when they are not actively talking. However, muting can be pretty inconvenient if there are only two people are on the call since there will likely be a lot of back-and-forth conversation.
- If it’s the line itself, hang up the call and dial back in. You are likely to get a clearer line on your second try.
If one person cannot hear the other, there are a few things you can try. Let’s go back to Dave and Lanie’s call and assume they are using VOIP through their laptops. If Lanie can hear Dave just fine but he can’t hear her, he might try the following solutions:
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Dave should check to make sure that his speakers are on and the volume turned up. There are a few places on a laptop to check this.
- On a PC, at the bottom-right corner of the screen, there’s a speaker icon. If that icon has an X (or a circle with a line through it) next to it, that means the speaker is on Mute. If there’s no X, click on the speaker anyway to see how far the volume is turned up.
- On a Mac, the volume control icon is at the top right of the screen. If there are no waves coming out of the speaker icon, your Mac is muted.
- If either Dave or Lanie is using a headset or headphones with a microphone, they should both make sure that the headphones are plugged all the way into the proper jack on the laptop. If they’re using Bluetooth headphones, they should make sure the Bluetooth connection is established.
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If the problem is not with Dave’s speakers or anyone’s headset, Lanie should check her microphone settings.
- If Lanie is on a PC, she’ll go to Settings in the Windows menu and search on Microphone. She’ll make sure the mic is set up. Then she’ll check her microphone privacy settings to be sure she hasn’t blocked the app she’s using from access to the microphone.
- If she’s on a Mac, she’ll click on the System Preferences icon and then click the Sound icon. She’ll make sure the Internal Microphone is chosen and then adjust the Input Volume to be sure she can be heard.
- If none of that works, they may need to start over with a new line or switch to a regular phone call.
If there’s an echo on the line that makes it hard for one or both people to hear, this can really mess with the pacing of the call and be frustrating for those involved. There are a few steps you can take to eliminate this problem.
- Ask whether either person is using their speaker instead of their handset. If multiple people are using speakers, this can cause an echo. The more people on the call, the worse this can get. The solution is to ask people who don’t absolutely need to use their speakers to switch to their handsets. Using cell phones can sometimes make this even worse.
- Restart the call to get another line.
One more thing to take into account when using VOIP, especially through a laptop or tablet, is that there may be a delay between what the speaker says and when the hearer hears it. This is why active listening is so important. Take the time to be sure the other person has finished speaking, and have some phrases ready to use if you get interrupted because of the delay. Here’s what to do:
- Acknowledge the delay: “We seem to have a little bit of a lag in the audio. I want to make sure you get to finish your thoughts before I start talking, so please let me know if I interrupt you.”
- When you step on someone else’s conversation: “Sorry, please continue.”
- When someone steps on your conversation: “I’d like to finish that thought, and the sound delay got in the way. If I could have one more minute . . .”
Contributors and Attributions
- One-on-One Audio Calls. Authored by : Barbara Egel. Provided by : Lumen Learning. License : CC BY: Attribution
- Modification of Active listening chart. Authored by : Imelda Bickham. Provided by : Wikimedia. Located at : https://commons.wikimedia.org/wiki/File:Active-listening-chart.png . License : CC BY-SA: Attribution-ShareAlike


13.9.10: Chapter 8 Review Exercises
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Chapter Review Exercises
Simplify Rational Expressions
Determine the Values for Which a Rational Expression is Undefined
In the following exercises, determine the values for which the rational expression is undefined.
Exercise \(\PageIndex{1}\)
\(\dfrac{2a+1}{3a−2}\)
- Answer
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\(a \ne \dfrac{2}{3}\)
Exercise \(\PageIndex{2}\)
\(\dfrac{b−3}{b^2−16}\)
Exercise \(\PageIndex{3}\)
\(\dfrac{3xy^2}{5y}\)
- Answer
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\(y \ne 0\)
Exercise \(\PageIndex{4}\)
\(\dfrac{u−3}{u^2−u−30}\)
Evaluate Rational Expressions
In the following exercises, evaluate the rational expressions for the given values.
Exercise \(\PageIndex{5}\)
\(\dfrac{4p−1}{p^2+5}\) when \(p=−1\)
- Answer
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\(−\dfrac{5}{6}\)
Exercise \(\PageIndex{6}\)
\(\dfrac{q^2−5}{q+3}\) when \(q=7\)
Exercise \(\PageIndex{7}\)
\(\dfrac{y^2−8}{y^2−y−2}\) when \(y=1\)
- Answer
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\(\dfrac{7}{2}\)
Example \(\PageIndex{8}\)
\(\dfrac{z^2+2}{4z−z^2}\) when \(z=3\)
In the following exercises, simplify.
Exercise \(\PageIndex{9}\)
\(\dfrac{10}{24}\)
- Answer
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\(\dfrac{5}{12}\)
Exercise \(\PageIndex{10}\)
\(\dfrac{8m^4}{16mn^3}\)
Exercise \(\PageIndex{11}\)
\(\dfrac{14a−14}{a−1}\)
- Answer
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\(14\)
Exercise \(\PageIndex{12}\)
\(\dfrac{b^2+7b+12}{b^2+8b+16}\)
Simplify Rational Expressions with Opposite Factors
In the following exercises, simplify.
Exercise \(\PageIndex{13}\)
\(\dfrac{c^2−c−2}{4−c^2}\)
- Answer
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\(-\dfrac{c+1}{c+2}\)
Exercise \(\PageIndex{14}\)
\(\dfrac{d−16}{16−d}\)
Exercise \(\PageIndex{15}\)
\(\dfrac{7v−35}{25−v^2}\)
- Answer
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\(−\dfrac{7}{5+v}\)
Exercise \(\PageIndex{16}\)
\(\dfrac{w^2−3w−28}{49−w^2}\)
Multiply and Divide Rational Expressions
Multiply Rational Expressions
In the following exercises, multiply.
Exercise \(\PageIndex{17}\)
\(\dfrac{3}{8}·\dfrac{2}{15}\)
- Answer
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\(\dfrac{1}{20}\)
Exercise \(\PageIndex{18}\)
\(\dfrac{2xy^2}{8y^3}·\dfrac{16y}{24x}\)
Exercise \(\PageIndex{19}\)
\(\dfrac{3a^2+21a}{a^2+6a−7}·\dfrac{a−1}{ab}\)
- Answer
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\(\dfrac{3}{b}\)
Exercise \(\PageIndex{20}\)
\(\dfrac{5z^2}{5z^2+40z+35}·\dfrac{z^2−1}{3z}\)
Divide Rational Expressions
In the following exercises, divide.
Exercise \(\PageIndex{21}\)
\(\dfrac{t^2−4t-12}{t^2+8t+12}÷\dfrac{t^2−36}{6t}\)
- Answer
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\(\dfrac{6t}{(t+6)^2}\)
Exercise \(\PageIndex{22}\)
\(\dfrac{r^2−16}{4}÷\dfrac{r^3−64}{2r^2−8r+32}\)
Exercise \(\PageIndex{23}\)
\(\dfrac{11+w}{w−9}÷\dfrac{121−w^2}{9−w}\)
- Answer
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\(\dfrac{1}{11+w}\)
Exercise \(\PageIndex{24}\)
\(\dfrac{3y^2−12y−63}{4y+3}÷(6y^2−42y)\)
Exercise \(\PageIndex{25}\)
\(\dfrac{\dfrac{c^2−64}{3c^2+26c+16}}{\dfrac{c^2−4c−32}{15c+10}}\)
- Answer
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\(5c+4\)
Exercise \(\PageIndex{26}\)
\(\dfrac{8m^2−8m}{m−4}·\dfrac{m^2+2m−24}{m^2+7m+10}÷\dfrac{2m^2−6m}{m+5}\)
Add and Subtract Rational Expressions with a Common Denominator
Add Rational Expressions with a Common Denominator
In the following exercises, add.
Exercise \(\PageIndex{27}\)
\(\dfrac{3}{5}+\dfrac{2}{5}\)
- Answer
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\(1\)
Exercise \(\PageIndex{28}\)
\(\dfrac{4a^2}{2a−1}−\dfrac{1}{2a−1}\)
Exercise \(\PageIndex{29}\)
\(\dfrac{p^2+10p}{p+5}+\dfrac{25}{p+5}\)
- Answer
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\(p+5\)
Exercise \(\PageIndex{30}\)
\(\dfrac{3x}{x−1}+\dfrac{2}{x−1}\)
Subtract Rational Expressions with a Common Denominator
In the following exercises, subtract.
Exercise \(\PageIndex{31}\)
\(\dfrac{d^2}{d+4}−\dfrac{3d+28}{d+4}\)
- Answer
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\(d-7\)
Exercise \(\PageIndex{32}\)
\(\dfrac{z^2}{z+10}−\dfrac{100}{z+10}\)
Exercise \(\PageIndex{33}\)
\(\dfrac{4q^2−q+3}{q^2+6q+5}−\dfrac{3q^2+q+6}{q^2+6q+5}\)
- Answer
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\(\dfrac{q−3}{q+5}\)
Exercise \(\PageIndex{34}\)
\(\dfrac{5t+4t+3}{t^2−25}−\dfrac{4t^2−8t−32}{t^2−25}\)
In the following exercises, add and subtract.
Exercise \(\PageIndex{35}\)
\(\dfrac{18w}{6w−1}+\dfrac{3w−2}{1−6w}\)
- Answer
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\(\dfrac{15w+2}{6w−1}\)
Exercise \(\PageIndex{36}\)
\(\dfrac{a^2+3a}{a^2−4}−\dfrac{3a−8}{4−a^2}\)
Exercise \(\PageIndex{37}\)
\(\dfrac{2b^2+3b−15}{b^2−49}−\dfrac{b^2+16b−1}{49−b^2}\)
- Answer
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\(\dfrac{3b−2}{b+7}\)
Exercise \(\PageIndex{38}\)
\(\dfrac{8y^2−10y+7}{2y−5}+\dfrac{2y^2+7y+2}{5−2y}\)
Add and Subtract Rational Expressions With Unlike Denominators
Find the Least Common Denominator of Rational Expressions
In the following exercises, find the LCD.
Exercise \(\PageIndex{38}\)
\(\dfrac{4}{m^2−3m−10},\quad\dfrac{2m}{m^2−m−20}\)
- Answer
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\((m+2)(m−5)(m+4)\)
Exercise \(\PageIndex{39}\)
\(\dfrac{6}{n^2−4},\quad\dfrac{2n}{n^2−4n+4}\)
Exercise \(\PageIndex{40}\)
\(\dfrac{5}{3p^2+17p−6},\quad\dfrac{2m}{3p^2−23p−8}\)
- Answer
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\((3p+1)(p+6)(p+8)\)
In the following exercises, rewrite as equivalent rational expressions with the given denominator.
Exercise \(\PageIndex{41}\)
Rewrite as equivalent rational expressions with denominator \((m+2)(m−5)(m+4)\)
\(\dfrac{4}{m^2−3m−10},\quad\dfrac{2m}{m^2−m−20}\).
Exercise \(\PageIndex{42}\)
Rewrite as equivalent rational expressions with denominator \((n−2)(n−2)(n+2)\)
\(\dfrac{6}{n^2−4n+4},\quad\dfrac{2n}{n^2−4}\).
- Answer
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\(\dfrac{6n+12}{(n−2)(n−2)(n+2)},\quad\dfrac{2n^2−4n}{(n−2)(n−2)(n+2)}\)
Exercise \(\PageIndex{43}\)
Rewrite as equivalent rational expressions with denominator \((3p+1)(p+6)(p+8)\)
\(\dfrac{5}{3p^2+19p+6},\quad\dfrac{7p}{3p^2+25p+8}\)
In the following exercises, add.
Exercise \(\PageIndex{44}\)
\(\dfrac{2}{3}+\dfrac{3}{5}\)
- Answer
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\(\dfrac{19}{15}\)
Exercise \(\PageIndex{45}\)
\(\dfrac{7}{5a}+\dfrac{3}{2b}\)
Exercise \(\PageIndex{46}\)
\(\dfrac{2}{c−2}+\dfrac{9}{c+3}\)
- Answer
-
\(\dfrac{11c−12}{(c−2)(c+3)}\)
Exercise \(\PageIndex{47}\)
\(\dfrac{3d}{d^2−9}+\dfrac{5}{d^2+6d+9}\)
Exercise \(\PageIndex{48}\)
\(\dfrac{2x}{x^2+10x+24}+\dfrac{3x}{x^2+8x+16}\)
- Answer
-
\(\dfrac{5x^2+26x}{(x+4)(x+4)(x+6)}\)
Exercise \(\PageIndex{49}\)
\(\dfrac{5q}{p^{2}q−p^2}+\dfrac{4q}{q^2−1}\)
In the following exercises, subtract and add.
Exercise \(\PageIndex{50}\)
\(\dfrac{3v}{v+2}−\dfrac{v+2}{v+8}\)
- Answer
-
\(\dfrac{2(v^2+10v−2)}{(v+2)(v+8)}\)
Exercise \(\PageIndex{51}\)
\(\dfrac{−3w−15}{w^2+w−20}−\dfrac{w+2}{4−w}\)
Exercise \(\PageIndex{52}\)
\(\dfrac{7m+3}{m+2}−5\)
- Answer
-
\(\dfrac{2m−7}{m+2}\)
Exercise \(\PageIndex{53}\)
\(\dfrac{n}{n+3}+\dfrac{2}{n−3}−\dfrac{n−9}{n^2−9}\)
Exercise \(\PageIndex{54}\)
\(\dfrac{8d}{d^2−64}−\dfrac{4}{d+8}\)
- Answer
-
\(4d−8\)
Exercise \(\PageIndex{55}\)
\(\dfrac{5}{12x^{2}y}+\dfrac{7}{20xy^3}\)
Simplify Complex Rational Expressions
Simplify a Complex Rational Expression by Writing it as Division
In the following exercises, simplify.
Exercise \(\PageIndex{56}\)
\(\dfrac{\dfrac{5a}{a+2}}{\dfrac{10a^2}{a^2−4}}\)
- Answer
-
\(\dfrac{a−2}{2a}\)
Exercise \(\PageIndex{57}\)
\(\dfrac{\dfrac{2}{5}+\dfrac{5}{6}}{\dfrac{1}{3}+\dfrac{1}{4}}\)
Exercise \(\PageIndex{58}\)
\(\dfrac{x−\dfrac{3x}{x+5}}{\dfrac{1}{x+5}+\dfrac{1}{x−5}}\)
- Answer
-
\(\dfrac{(x−8)(x−5)}{2}\)
Exercise \(\PageIndex{59}\)
\(\dfrac{\dfrac{2}{m}+\dfrac{m}{n}}{\dfrac{n}{m}−\dfrac{1}{n}}\)
In the following exercises, simplify.
Exercise \(\PageIndex{60}\)
\(\dfrac{6+\dfrac{2}{q−4}}{\dfrac{5}{q}+4}\)
- Answer
-
\(\dfrac{(q−2)(q+4)}{5(q−4)}\)
Exercise \(\PageIndex{61}\)
\(\dfrac{\dfrac{3}{a^2}−\dfrac{1}{b}}{\dfrac{1}{a}+\dfrac{1}{b^2}}\)
Exercise \(\PageIndex{62}\)
\(\dfrac{\dfrac{2}{z^2−49}+\dfrac{1}{z+7}}{\dfrac{9}{z+7}+\dfrac{12}{z−7}}\)
- Answer
-
\(\dfrac{z−5}{21z+21}\)
Exercise \(\PageIndex{63}\)
\(\dfrac{\dfrac{3}{y^2−4y−32}}{\dfrac{2}{y−8}+\dfrac{1}{y+4}}\)
Solve Rational Equations
Solve Rational Equations
In the following exercises, solve.
Exercise \(\PageIndex{64}\)
\(\dfrac{1}{2}+\dfrac{2}{3}=\dfrac{1}{x}\)
- Answer
-
\(\dfrac{6}{7}\)
Exercise \(\PageIndex{65}\)
\(1−\dfrac{2}{m}=\dfrac{8}{m^2}\)
Exercise \(\PageIndex{66}\)
\(\dfrac{1}{b−2}+\dfrac{1}{b+2}=\dfrac{3}{b^2−4}\)
- Answer
-
\(\dfrac{3}{2}\)
Exercise \(\PageIndex{67}\)
\(\dfrac{3}{q+8}−\dfrac{2}{q−2}=1\)
Exercise \(\PageIndex{68}\)
\(\dfrac{v−15}{v^2−9v+18}=\dfrac{4}{v−3}+\dfrac{2}{v−6}\)
- Answer
-
no solution
Exercise \(\PageIndex{69}\)
\(\dfrac{z}{12}+\dfrac{z+3}{3z}=\dfrac{1}{z}\)
Solve a Rational Equation for a Specific Variable
In the following exercises, solve for the indicated variable.
Exercise \(\PageIndex{70}\)
\(\dfrac{V}{l}=hw\) for \(l\)
- Answer
-
\(l=\dfrac{V}{hw}\)
Exercise \(\PageIndex{71}\)
\(\dfrac{1}{x}−\dfrac{2}{y}=5\) for \(y\)
Exercise \(\PageIndex{72}\)
\(x=\dfrac{y+5}{z−7}\) for \(z\)
- Answer
-
\(z=\dfrac{y+5+7x}{x}\)
Exercise \(\PageIndex{73}\)
\(P=\dfrac{k}{V}\) for \(V\)
Solve Proportion and Similar Figure Applications Similarity
Solve Proportions
In the following exercises, solve.
Exercise \(\PageIndex{74}\)
\(\dfrac{x}{4}=\dfrac{3}{5}\)
- Answer
-
\(\dfrac{12}{5}\)
Exercise \(\PageIndex{75}\)
\(\dfrac{3}{y}=\dfrac{9}{5}\)
Exercise \(\PageIndex{76}\)
\(\dfrac{s}{s+20}=\dfrac{3}{7}\)
- Answer
-
\(15\)
Exercise \(\PageIndex{77}\)
\(\dfrac{t−3}{5}=\dfrac{t+2}{9}\)
In the following exercises, solve using proportions.
Exercise \(\PageIndex{78}\)
Rachael had a \(21\) ounce strawberry shake that has \(739\) calories. How many calories are there in a \(32\) ounce shake?
- Answer
-
\(1161\) calories
Exercise \(\PageIndex{79}\)
Leo went to Mexico over Christmas break and changed \($525\) dollars into Mexican pesos. At that time, the exchange rate had \($1\) US is equal to \(16.25\) Mexican pesos. How many Mexican pesos did he get for his trip?
In the following exercises, solve.
Exercise \(\PageIndex{80}\)
\(∆ABC\) is similar to \(∆XYZ\). The lengths of two sides of each triangle are given in the figure. Find the lengths of the third sides.
- Answer
-
\(b=9\); \(x=2\dfrac{1}{3}\)
Exercise \(\PageIndex{81}\)
On a map of Europe, Paris, Rome, and Vienna form a triangle whose sides are shown in the figure below. If the actual distance from Rome to Vienna is \(700\) miles, find the distance from
- a. Paris to Rome
- b. Paris to Vienna
Exercise \(\PageIndex{82}\)
Tony is \(5.75\) feet tall. Late one afternoon, his shadow was \(8\) feet long. At the same time, the shadow of a nearby tree was \(32\) feet long. Find the height of the tree.
- Answer
-
\(23\) feet
Exercise \(\PageIndex{83}\)
The height of a lighthouse in Pensacola, Florida is \(150\) feet. Standing next to the statue, \(5.5\) foot tall Natalie cast a \(1.1\) foot shadow How long would the shadow of the lighthouse be?
Solve Uniform Motion and Work Applications Problems
Solve Uniform Motion Applications
In the following exercises, solve.
Exercise \(\PageIndex{84}\)
When making the 5-hour drive home from visiting her parents, Lisa ran into bad weather. She was able to drive \(176\) miles while the weather was good, but then driving \(10\) mph slower, went \(81\) miles in the bad weather. How fast did she drive when the weather was bad?
- Answer
-
45 mph
Exercise \(\PageIndex{85}\)
Mark is riding on a plane that can fly \(490\) miles with a tailwind of \(20\) mph in the same time that it can fly \(350\) miles against a tailwind of \(20\) mph. What is the speed of the plane?
Exercise \(\PageIndex{86}\)
John can ride his bicycle \(8\) mph faster than Luke can ride his bike. It takes Luke \(3\) hours longer than John to ride \(48\) miles. How fast can John ride his bike?
- Answer
-
\(16\) mph
Exercise \(\PageIndex{87}\)
Mark was training for a triathlon. He ran \(8\) kilometers and biked \(32\) kilometers in a total of \(3\) hours. His running speed was \(8\) kilometers per hour less than his biking speed. What was his running speed?
In the following exercises, solve.
Exercise \(\PageIndex{88}\)
Jerry can frame a room in \(1\) hour, while Jake takes \(4\) hours. How long could they frame a room working together?
- Answer
-
\(\dfrac{4}{5}\) hour
Exercise \(\PageIndex{89}\)
Lisa takes \(3\) hours to mow the lawn while her cousin, Barb, takes \(2\) hours. How long will it take them working together?
Exercise \(\PageIndex{90}\)
Jeffrey can paint a house in \(6\) days, but if he gets a helper he can do it in \(4\) days. How long would it take the helper to paint the house alone?
- Answer
-
\(12\) days
Exercise \(\PageIndex{91}\)
Sue and Deb work together writing a book that takes them \(90\) days. If Sue worked alone it would take her \(120\) days. How long would it take Deb to write the book alone?
Use Direct and Inverse Variation
Solve Direct Variation Problems
In the following exercises, solve.
Exercise \(\PageIndex{92}\)
If \(y\) varies directly as \(x\), when \(y=9\) and \(x=3\), find \(x\) when \(y=21\).
- Answer
-
\(7\)
Exercise \(\PageIndex{93}\)
If \(y\) varies directly as \(x\), when \(y=20\) and \(x=2\), find \(y\) when \(x=4\).
Exercise \(\PageIndex{94}\)
If \(m\) varies inversely with the square of \(n\), when \(m=4\) and \(n=6\), find \(m\) when \(n=2\).
- Answer
-
\(36\)
Exercise \(\PageIndex{95}\)
Vanessa is traveling to see her fiancé. The distance, \(d\), varies directly with the speed, \(v\), she drives. If she travels \(258\) miles driving \(60\) mph, how far would she travel going \(70\) mph?
Exercise \(\PageIndex{96}\)
If the cost of a pizza varies directly with its diameter, and if an \(8\)” diameter pizza costs \($12\), how much would a \(6\)” diameter pizza cost?
- Answer
-
\($9\)
Exercise \(\PageIndex{97}\)
The distance to stop a car varies directly with the square of its speed. It takes \(200\) feet to stop a car going \(50\) mph. How many feet would it take to stop a car going \(60\) mph?
In the following exercises, solve.
Exercise \(\PageIndex{98}\)
The number of tickets for a music fundraiser varies inversely with the price of the tickets. If Madelyn has just enough money to purchase \(12\) tickets for \($6\), how many tickets can Madelyn afford to buy if the price increased to \($8\)?
- Answer
-
\(97\) tickets
Exercise \(\PageIndex{99}\)
On a string instrument, the length of a string varies inversely with the frequency of its vibrations. If an \(11\)-inch string on a violin has a frequency of \(360\) cycles per second, what frequency does a \(12\)-inch string have?
Practice Test
In the following exercises, simplify.
Exercise \(\PageIndex{1}\)
\(\dfrac{3a^{2}b}{6ab^2}\)
- Answer
-
\(\dfrac{a}{2b}\)
Exercise \(\PageIndex{2}\)
\(\dfrac{5b−25}{b^2−25}\)
In the following exercises, perform the indicated operation and simplify.
Exercise \(\PageIndex{3}\)
\(\dfrac{4x}{x+2}·\dfrac{x^2+5x+6}{12x^2}\)
- Answer
-
\(\dfrac{x+3}{3x}\)
Exercise \(\PageIndex{4}\)
\(\dfrac{5y}{4y−8}·\dfrac{y^2−4}{10}\)
Exercise \(\PageIndex{5}\)
\(\dfrac{4p}{q}+\dfrac{5}{p}\)
- Answer
-
\(\dfrac{4+5q}{pq}\)
Exercise \(\PageIndex{6}\)
\(\dfrac{1}{z−9}−\dfrac{3}{z+9}\)
Exercise \(\PageIndex{7}\)
\(\dfrac{\dfrac{2}{3}+\dfrac{3}{5}}{\dfrac{2}{5}}\)
- Answer
-
\(\dfrac{19}{16}\)
Exercise \(\PageIndex{8}\)
\(\dfrac{\dfrac{1}{m}−\dfrac{1}{n}}{\dfrac{1}{n}+\dfrac{1}{m}}\)
In the following exercises, solve each equation.
Exercise \(\PageIndex{9}\)
\(\dfrac{1}{2}+\dfrac{2}{7}=\dfrac{1}{x}\)
- Answer
-
\(x = \dfrac{14}{11}\)
Exercise \(\PageIndex{10}\)
\(\dfrac{5}{y−6}=\dfrac{3}{y+6}\)
Exercise \(\PageIndex{11}\)
\(\dfrac{1}{z−5}+\dfrac{1}{z+5}=\dfrac{1}{z^2−25}\)
- Answer
-
\(z = \dfrac{1}{2}\)
Exercise \(\PageIndex{12}\)
\(\dfrac{t}{4}=\dfrac{3}{5}\)
Exercise \(\PageIndex{13}\)
\(\dfrac{2}{r−2}=\dfrac{3}{r−1}\)
- Answer
-
\(r = 4\)
In the following exercises, solve.
Exercise \(\PageIndex{14}\)
If \(y\) varies directly with \(x\), and \(x=5\) when \(y=30\), find \(x\) when \(y=42\).
Exercise \(\PageIndex{15}\)
If \(y\) varies inversely with \(x\) and \(x=6\) when \(y=20\), find \(y\) when \(x=2\).
- Answer
-
\(y=60\)
Exercise \(\PageIndex{16}\)
If \(y\) varies inversely with the square of \(x\) and \(x=3\) when \(y=9\), find \(y\) when \(x=4\).
Exercise \(\PageIndex{17}\)
The recommended erythromycin dosage for dogs, is \(5\) mg for every pound the dog weighs. If Daisy weighs \(25\) pounds, how many milligrams of erythromycin should her veterinarian prescribe?
- Answer
-
\(125\) mg
Exercise \(\PageIndex{18}\)
Julia spent \(4\) hours Sunday afternoon exercising at the gym. She ran on the treadmill for \(10\) miles and then biked for \(20\) miles. Her biking speed was \(5\) mph faster than her running speed on the treadmill. What was her running speed?
Exercise \(\PageIndex{19}\)
Kurt can ride his bike for \(30\) miles with the wind in the same amount of time that he can go \(21\) miles against the wind. If the wind’s speed is \(6\) mph, what is Kurt’s speed on his bike?
- Answer
-
\(14\) mph
Exercise \(\PageIndex{20}\)
Amanda jogs to the park \(8\) miles using one route and then returns via a \(14\)-mile route. The return trip takes her \(1\) hour longer than her jog to the park. Find her jogging rate.
Exercise \(\PageIndex{21}\)
An experienced window washer can wash all the windows in Mike’s house in \(2\) hours, while a new trainee can wash all the windows in \(7\) hours. How long would it take them working together?
- Answer
-
\(1\frac{5}{9}\) hour
Exercise \(\PageIndex{22}\)
Josh can split a truckload of logs in \(8\) hours, but working with his dad they can get it done in \(3\) hours. How long would it take Josh’s dad working alone to split the logs?
Exercise \(\PageIndex{23}\)
The price that Tyler pays for gas varies directly with the number of gallons he buys. If \(24\) gallons cost him \($59.76\), what would \(30\) gallons cost?
- Answer
-
\($74.70\)
Exercise \(\PageIndex{24}\)
The volume of a gas in a container varies inversely with the pressure on the gas. If a container of nitrogen has a volume of \(29.5\) liters with \(2000\) psi, what is the volume if the tank has a \(14.7\) psi rating? Round to the nearest whole number.
Exercise \(\PageIndex{25}\)
The cities of Dayton, Columbus, and Cincinnati form a triangle in southern Ohio, as shown on the figure below, that gives the map distances between these cities in inches.
The actual distance from Dayton to Cincinnati is \(48\) miles. What is the actual distance between Dayton and Columbus?
- Answer
-
\(64\) miles


3.12: Personal Values and Ethics
What is the role of ethical behavior in managerial actions?
A factor that has surprised many business leaders is the alarming rise in accusations of unethical or disreputable behavior in today’s companies. We hear with increasing regularity of stock market manipulations, disregard of environmental hazards, bribes, and kickbacks. To understand these behaviors, we must examine the role of values and personal ethics in the workplace. We begin with the concept of values.
A value may be defined as “an enduring belief that a specific mode of conduct or end-state of existence is personally or socially preferable to an opposite or converse mode of conduct or end-state of existence.” 23 In other words, a value represents a judgment by an individual that certain things are “good” or “bad,” “important” or “unimportant,” and so forth. As such, values serve a useful function in providing guidelines or standards for choosing one’s own behavior and for evaluating the behavior of others.
Characteristics of Values
The values people have tend to be relatively stable over time. The reason for this lies in the manner in which values are acquired in the first place. That is, when we first learn a value (usually at a young age), we are taught that such-and-such behavior is always good or always bad. For instance, we may be taught that lying or stealing is always unacceptable. Few people are taught that such behavior is acceptable in some circumstances but not in others. Hence, this definitive quality of learned values tends to secure them firmly in our belief systems. This is not to say that values do not change over time. As we grow, we are increasingly confronted with new and often conflicting situations. Often, it is necessary for us to weigh the relative merits of each and choose a course of action. Consider, for example, the worker who has a strong belief in hard work but who is pressured by her colleagues not to outperform the group. What would you do in this situation?
Rokeach has identified two fundamental types of values: instrumental and terminal. 24 Instrumental values represent those values concerning the way we approach end-states. That is, do we believe in ambition, cleanliness, honesty, or obedience? What factors guide your everyday behavior? Terminal values , on the other hand, are those end-state goals that we prize. Included here are such things as a comfortable life, a sense of accomplishment, equality among all people, and so forth. Both sets of values have significant influence on everyday behavior at work.
You can assess your own instrumental and terminal values by completing the self-assessment in the end-of- chapter assignments. Simply rank-order the two lists of values, and then refer to the reference for scoring procedures.
Role of Values and Ethics in Organizations
Personal values represent an important force in organizational behavior for several reasons. In fact, at least three purposes are served by the existence of personal values in organizations: (1) values serve as standards of behavior for determining a correct course of action; (2) values serve as guidelines for decision-making and conflict resolution; and (3) values serve as an influence on employee motivation. Let us consider each of these functions.
Standards of Behavior. First, values help us determine appropriate standards of behavior. They place limits on our behavior both inside and outside the organization. In such situations, we are referring to what is called ethical behavior , or ethics . Employees at all levels of the organization have to make decisions concerning what to them is right or wrong, proper or improper. For example, would you conceal information about a hazardous product made by your company, or would you feel obliged to tell someone? How would you respond to petty theft on the part of a supervisor or coworker in the office? To some extent, ethical behavior is influenced by societal values. Societal norms tell us it is wrong to engage in certain behaviors. In addition, however, individuals must often determine for themselves what is proper and what is not. This is particularly true when people find themselves in “gray zones”—situations where ethical standards are ambiguous or unclear. In many situations, a particular act may not be illegal. Moreover, one’s colleagues and friends may disagree about what is proper. In such circumstances, people have to determine their own standards of behavior.
Expanding Around the Globe
Two Cultures’ Perspectives of Straight Talk
Yukiko Tanabe, a foreign exchange student from Tokyo, Japan, was both eager and anxious about making new friends during her one-year study abroad in the United States. After a month-long intensive course in English over the summer, she began her studies at the University of California. Yukiko was in the same psychology class as Jane McWilliams. Despite Yukiko’s somewhat shy personality, it did not take long before she and Jane were talking before and after class and studying together.
Part of the way through the term, the professor asked for volunteers to be part of an experiment on personalities and problem-solving. The professor also offered extra credit for participation in the experiment and asked interested students to stay after class to discuss the project in more detail.
When class was over, Jane asked Yukiko if she wanted to stay after and learn more about the project and the extra credit. Yukiko hesitated and then said that she was not sure. Jane replied that it would only take a few minutes to listen to the explanation, and so the two young women went up to the front of the class, along with about 20 other students, to hear the details.
The project would simply involve completing a personality questionnaire and then attempting to solve three short case problems. In total, it would take about one hour of time and would be worth 5 percent extra credit. Jane though it was a great idea and asked Yukiko if she wanted to participate. Yukiko replied that she was not sure. Jane responded that they could go together, that it would be fun, and that 5 percent extra credit was a nice bonus. To this Yukiko made no reply, so Jane signed both of them up for the project and suggested that they meet at the quad about 10 minutes before the scheduled beginning of the experiment.
On the day of the experiment, however, Yukiko did not show up. Jane found out later from Yukiko that she did not want to participate in the experiment. “Then why didn’t you just say so?” asked Jane. “Because I did not want to embarrass you in front of all your other friends by saying no,” explained Yukiko.
Source: Personal communication by the author. Names have been disguised.
Guidelines for Decision-Making and Conflict Resolution. In addition, values serve as guidelines for making decisions and for attempting to resolve conflicts. Managers who value personal integrity are less likely to make decisions they know to be injurious to someone else. Relatedly, values can influence how someone approaches a conflict. For example, if your boss asks your opinion about a report she wrote that you don’t like, do you express your opinion candidly or be polite and flatter her?
An interesting development in the area of values and decision-making involves integrity or honesty tests. These tests are designed to measure an individual’s level of integrity or honesty based on the notion that honest or dishonest behavior and decisions flow from a person’s underlying values. Today over 5,000 firms use these tests, some of which use direct questions and some of which use camouflaged questions. Although the reliability of the most common tests seem good, their validity (i.e., the extent to which they can accurately predict dishonest behavior) is more open to question. 25 Nevertheless, because they do not cost much and are less intrusive than drug or polygraph testing, integrity are increasingly used to screen potential employees.
Influence on Motivation. Values affect employee motivation by determining what rewards or outcomes are sought. Employees are often offered overtime work and the opportunity to make more money at the expense of free time and time with their families. Which would you choose? Would you work harder to get a promotion to a perhaps more stressful job or “lay back” and accept a slower and possibly less rewarding career path? Value questions such as these confront employees and managers every day.
Prominent among work-related values is the concept of the work ethic . Simply put, the work ethic refers to the strength of one’s commitment and dedication to hard work, both as an end in itself and as a means to future rewards. Much has been written lately concerning the relative state of the work ethic in North America. It has been repeatedly pointed out that one reason for our trouble in international competition lies in our rather mediocre work ethic. This is not to say that many Americans do not work hard; rather, it is to say that others (most notably those in East Asia) simply work harder.
There are many ways to assess these differences, but perhaps the simplest way is to look at actual hours worked on average in different countries both in Asia and Western Europe. Looking at Table \(\PageIndex{1}\), you may be surprised to discover that although the average American works 1,789 hours (and takes an average of 19.5 vacation days) per year, the average South Korean works 2,070 hours per year (and takes only 4.5 days of vacation)! 26 The typical Japanese worker works 1,742 hours per year and takes 9.6 days of vacation. Meanwhile, Western Europeans work fewer hours and take more vacation days. Thus, although Americans may work longer hours than many Europeans, they fall far behind many in East Asia.
Example: A Country Tries to Reduce Its Workweek
What does a country do when its people are over motivated? Consider the case of Japan. On the basis of Japan’s newfound affluence and success in the international marketplace, many companies—and the government—are beginning to be concerned that perhaps Japanese employees work too hard and should slow down. They may be too motivated for their own good. As a result, the Japanese Department of Labor has initiated a drive to shorten the workweek and encourage more Japanese employees to take longer holidays. The effort is focusing on middle-aged and older employees, because their physical stamina may be less than that of their more junior colleagues. Many companies are following this lead and are beginning to reduce the workweek. This is no easy task in a land where such behavior may be seen by employees as showing disloyalty toward the company. It requires a fundamental change in employee attitudes.
At the same time, among younger employees, cracks are beginning to appear in the fabled Japanese work ethic. Younger workers are beginning to express increased frustration with dull jobs and routine assignments, and job satisfaction appears to be at an all-time low. Young Japanese are beginning to take longer lunch periods and look forward to Friday and the coming weekend. Whether this is attributable to increasing affluence in changing society or simply the emergence of a new generation, things are changing—however slowly-in the East. 27
Exercise \(\PageIndex{1}\)
1. What role do managers undertake to ensure an environment where ethics and values are followed?
23. M. Rokeach, The Nature of Human Values (New York: Free Press, 1973), p. 5.
24. Ibid.
25. Paul R. Sackett, Laura R. Burris, and Christine Callahan. 1989. Integrity Testing for Personnel Selection. Personnel Psychology, 42, 491–529.
26. R. M. Steers, Y. K. Shin, and G. R. Ungson, The Chaebol: Korea’s New Industrial Might (New York: Harper & Row, 1989), p. 96.
27. L. Smith, “Cracks in the Japanese Work Ethic,” Fortune, May 14, 1984, pp. 162–168; K. Van Wolferen, The Enigma of Japanese Power (New York: Knopf, 1989).
Table 2.3 (Attribution: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license)


2.1: Dimensions of Wellness
What is Wellness?
Wellness is being in good physical and mental health. Because mental health and physical health are linked, problems in one area can impact the other. At the same time, improving your physical health can also benefit your mental health, and vice versa. It is important to make healthy choices for both your physical and mental well-being.
Remember that wellness is not just the absence of illness or stress. You can still strive for wellness even if you are experiencing these challenges in your life.
What are the Eight Dimensions of Wellness?
Learning about the Eight Dimensions of Wellness can help you choose how to make wellness a part of your everyday life.
The Eight Dimensions of Wellness are:
- Emotional —Coping effectively with life and expressing emotions in an appropriate manner
- Environmental —Occupying pleasant, healthy, and safe environments that support well-being; positively impacting the quality of our surroundings (including protecting and preserving nature)
- Financial —Achieving satisfaction with current and future financial situations; handling finances wisely
- Intellectual —Recognizing creative abilities and finding ways to expand knowledge and skills; being open-minded
- Occupational —Personal fulfillment and enrichment from one’s work and/or responsibilities
- Physical —Recognizing the need for physical activity, healthy foods, and adequate sleep; avoiding unhealthy habits
- Social —Developing a sense of connection, belonging, and sustained support system; having positive relationships
- Spiritual —Having a sense of purpose and meaning in life; establishing peace, harmony, and balance in our lives
Learn more about the Eight Dimensions of Wellness by watching the video below:
Your Own Views on Health and Wellness
Reflect on the following questions:
- What does health mean to you?
- How important is health to you?
- What are some of your healthy habits?
- Which dimensions of wellness do you need to work on the most?
- Eight Dimensions of Wellness. Authored by : Substance Abuse and Mental Health Services Administration . Provided by : U.S. Department of Health and Human Services. Located at : http://www.samhsa.gov/wellness-initiative/eight-dimensions-wellness . License : Public Domain: No Known Copyright
- Video - The Eight Dimensions of Wellness. Authored by : SAMHSA. Provided by : U.S. Department of Health and Human Services. Located at : https://www.youtube.com/watch?v=tDzQdRvLAfM&feature=youtu.be . License : Public Domain: No Known Copyright