Use the choices below to fill in each blank. Some choices may be used more than once.

simplified $\text{\ }$ reciprocals $\text{\ }$ equivalent $\text{\ \ }$ denominator

product $\text{\ \ \ \ }$ factors$\text{\ \ \ \ \ \ \ \ }$ fraction$\text{\ \ \ \ \ \ \ }$ numerator

A fraction is said to be ____________ when the numerator and the denominator have no common factors other than $1$.

The below statement corresponds to a numbered sentence in the passage. It contains a blank and is followed by four answer choices. Decide which choice fits best in the blank. The word or phrase that you choose must express roughly the same meaning as the italicized word in the passage. Write the letter of your choice on the answer line.

Martinez learned to make pottery by imitating the $\underline{?}$ of her aunt. _______________ (precepts)

a. guiding principles b. meager examples c. disciples d. representations

Prove that the group of rotations of a tetrahedron is isomorphic to the alternating group $A_4.$

Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises 1-10. Express probabilities as simplified fractions and as decimals rounded to the nearest hundredth. Marital Status of the U.S. Population, Ages 15 or Older, 2010, in Millions

If one person is randomly selected from the population described in the table, find the probability, expressed as a simplified fraction and as a decimal to the nearest hundredth, that the person among those who are divorced, find the probability of selecting a woman.

Here’s another list of false statements from Condensed Knowledge. p: No Africans have Jewish ancestry. q: No religious traditions recognize sexuality as central to their understanding of the sacred. r: All rap is hip-hop. s: Some hip-hop is not rap. Use the representations shown to express each symbolic statement in words. Verbal statements should begin with “all,” “some,” or “no.” What can you conclude about each resulting verbal statement? $\sim q$

In Exercise given below, find the Taylor polynomials (centered at zero) of degrees 2.

$$f(x)=\sqrt{x+1}$$

Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises 1-10. Express probabilities as simplified fractions and as decimals rounded to the nearest hundredth. Marital Status of the U.S. Population, Ages 15 or Older, 2010, in Millions

If one person is randomly selected from the population described in the table, find the probability, expressed as a simplified fraction and as a decimal to the nearest hundredth, that the person among those who are divorced, find the probability of selecting a man.

As described in the chapter, the Federal Reserve in $2008$ faced a decrease in aggregate demand caused by the housing and financial crises and a decrease in short-run aggregate supply caused by rising commodity prices.

Suppose the Fed responds quickly to these shocks and adjusts monetary policy to keep unemployment and output at their natural rates. What action would it take? On the same set of graphs from part (a), show the results. Label the new equilibrium as point $C$.

Have efforts to promote equality for women gone far enough in the United States? A poll on this issue by the cable network MSNBC contacted 1019 adults. A newspaper article about the poll said, "Results have a margin of sampling error of plus or minus 3 percentage points."

The news article said that 65% of men, but only 43% of women, think that efforts to promote equality have gone far enough. Explain why we do not have enough information to give confidence intervals for men and women separately.

This is a simplified inventory problem. Suppose that it costs c dollars to stock an item and that the item sells for s dollars. Suppose that the number of items that will be asked for by customers is a random variable with the frequency function p(k). Find a rule for the number of items that should be stocked in order to maximize the expected income. (Hint: Consider the difference of successive terms.)

Student A and Student B simplified the expression $9 - 4 \cdot 2 .$ Which student is correct? Explain the error.

$$\begin{matrix} \text{Student A} & \text{Student B}\\ \ {9 - 4 \cdot 2} & \ {9 - 4 \cdot 2}\\ \ { = 5 \cdot 2} & \text{ = 9 - 8}\\ \text{ = 10} & \text{ = 1}\\ \end{matrix}$$

An important derivative operation in many applications is called the Laplacian; in Cartesian coordinates, for z=f(x, y), the Laplacian is

$$z _ { x x } + z _ { y y }$$

. Determine the Laplacian in polar coordinates using the following steps. Use the Chain Rule to find

$$z _ { y y } = \frac { \partial } { \partial y } \left( z _ { y } \right)$$

There should be two major terms, which, when expanded and simplified, result in five terms.

A person exerts a $15-\mathrm{N}$ force on a cart attached to a spring and holds the cart steady. The cart is displaced $0.060 \mathrm{m}$ from its equilibrium position. When the person stops holding the cart, the system cart $+$ spring undergoes simple harmonic motion. (a) Determine the spring constant of the spring. (b) Determine the energy of the system. (c) Write an expression $x(t)$ for the motion of the cart. (d) Draw as many graphical representations of the motion as you can.

In Exercise given below, find the Taylor polynomials (centered at zero) of degrees 3.

$$f(x)=\frac{x}{x+1}$$