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.)

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

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.)

Use the Pythagorean Theorem and the square root property to solve this exercise. Express answers in simplified radical form. Then find a decimal approximation to the nearest tenth.

A supporting wire is to be attached to the top of a $70$ -foot antenna. If the wire must be anchored $70$ feet from the base of the antenna, what length of wire is required?

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?

Use the Pythagorean Theorem and the square root property to solve this exercise. Express answers in simplified radical form. Then find a decimal approximation to the nearest tenth.

A supporting wire is to be attached to the top of a $50$ -foot antenna. If the wire must be anchored $50$ feet from the base of the antenna, what length of wire is required?

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?

Jackie is mailing packages to 100 customers. The cost of materials to ship all of the packages is $50.00. The rates for shipping are$15.75 per out-of-state package and $5.50 per in-state package. Write a simplified polynomial to express the total cost to mail the packages if x packages are shipped in state and the rest are shipped out of state.

Hal earns n dollars per hour. Next month he will receive a 2 percent raise in pay per hour The expression n+0.02n is one way to represent Hal's pay per hour after the raise. Write an equivalent simplified expression that will represent his pay per hour after the raise.

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

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

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? $\sim p$

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.

Choose the correct letter. What is the simplified form of $\left(4 j^{2}+6\right)+\left(2 j^{2}-3\right)$? F. $6 j^{2}-3$ G. $6 j^{2}+3$ H. $6 j^{2}+9$ I. $4 j^{4}+3$

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 women, find the probability of selecting a married person.

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?