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

In the fraction $\frac{3}{11}$ , the number $3$ is called the____________ and the number 11 is called the ____________.

Look up 'Greek Vase Depicting Wedding Preparations' picture on the internet. The scene is from a Greek painting that was created in the 400s b.c. It shows a group of Athenian women preparing a young bride for her wedding. Look at the painting, and then answer the questions that follow.

Compare the representations of the human form in Greek painting and Egyptian painting.

a) How are the two styles similar?

b) How are they different?

c) Why might there be some similarities between these two styles of painting?

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.

This exercise will help you prepare for the material covered in the next section. In this exercise, use properties of exponents to simplify the expression. Be sure that no negative exponents appear in your simplified expression. (If you have forgotten how to simplify an exponential expression.)

$$\left(2^3 x^5\right)\left(2^4 x^{-6}\right)$$

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

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

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

A circle with its center at (2, 4) passes through point (-1, -1). What is the area of the circle in simplified radical form?

$$\begin{array}{ll}{\text{ A. } 34 \pi} & {\text{ B. } \pi \sqrt{34}} \\ {\text{ C. } 2 \pi \sqrt{34}} & {\text{ D. } 68 \pi}\end{array}$$

When simplified, which expressions would be equal to -1? Check all that apply. A. $\csc \theta \sin (-\theta)$ B. $\cos \theta \sec (-\theta)$ C. $\sin ^{2} \theta+\cos ^{2} \theta$ D. $\cot (-\theta) \tan \theta$ E. $\sec ^{2}(-\theta)-\tan ^{2}(-\theta)$

Police officers can use the formula $s=\sqrt{30 f d}$ to determine the speed $s$ that a car was traveling in miles per hour by measuring the distance $d$ in feet of its skid marks. In this formula, $f$ is the coefficient of friction for the type and condition of the road.

What is a simplified formula for the speed if $f=0.8$ for a dry asphalt road?

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

Student A

$$\begin{aligned} &9-4\cdot 2\\ &=5 \cdot 2\\ &=10 \end{aligned}$$

Student B

$$\begin{aligned} &9-4\cdot 2\\ &=9-8\\ &=1 \end{aligned}$$

Jane and Sarah both dive down from the surface of a pool, Jane first dives down 5 feet, and then dives down 3 more feet. Sarah first dives down 3 feet, and then dives down 5 more feet.
a. Multiple Representations Use the number line to model the equation $-5+(-3)=-3+(-5)$ b. Does the order in which you add two integers with the same sign affect the sum? Explain.

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 men, find the probability of selecting a married person.

Look at part d) of Example 4. Suppose that $u=3$ and $v=-2$:

Original expression $\frac{-2uv^2\times8u^2v^2}{(4uv^2)^2}$

Simplified expression $-uv$

a) Which expression would you rather substitute into to evaluate the expression and why?

b) What is the value of the expression after substituting the given value?

In the previous problem, you wrote equations that were models of a real-life situation. Models are usually not perfect representations, but they are useful for describing real-life behavior and for making predictions. You predicted when the two trees would be the same height. a. What are an appropriate domain and range for the two models of tree growth? b. Where can you find they-intercepts of the model on the graph, in the table, and in the equation? In the situation of the story, what does they-intercept represent?

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? $\sim p$