A country’s ? is the average number of children born during each woman’s lifetime.

The number of protons in a neutral atom is balanced by an equal number of _____?

How does the influence of parents over their children change during adolescence?

For the price function defined by

$$p(x)=(182-x / 36)^{1 / 2}$$

find the number of units $x_1$ that makes the total revenue a maximum and state the maximum possible revenue. What is the marginal revenue when the optimum number of units, $x_1$, is sold?

Solve each inequality and graph the solutions. $|x|+17>20$ _____.

Euclid proved that given any finite list of primes, there exists a prime not in the list. Read the following argument and answer the questions that follow. Let 2, 3, 5, 7, ...... , p be a list of all primes less than or equal to a certain prime p. We will show that there exists a prime not on the list. Consider the product $2 \cdot 3 \cdot 5 \cdot 7 \cdot ..... \cdot p$
Every prime in the list divides that product. However, if we add 1 to the product, that is, form the number $n = (2 \cdot3 \cdot 5 \cdot 7 \cdot ..... \cdot p)+ 1$, then none of the primes in the list will divide n. Whether n is prime or composite, some prime q must divide n. Because no prime in the list divides n, q is not one of the primes in the list. Consequently $q>p$. We have shown that there exists a prime greater than p.
a. Explain why no prime in the list will divide n.
b. Explain why some prime must divide n.
c. Does the argument show that there are infinitely many primes? Why or why not?

The grade point averages of the students in your mathematics class are

$$\begin{array}{l}{3.2,3.5,4.0,2.9,2.0,3.3,3.5,2.9,2.5,2.0,} \\ {2.1,3.2,3.6,2.8,2.5,1.9,2.0,2.2,3.9,4.0}\end{array}$$

Use these raw data to construct a frequency table with the following measurement classes: 1.1-2.0, 2.1-3.0, 3.1-4.0, and find the probability distribution using the (rounded) midpoint values as the values of X.

Calculate (a) $P^{2}=P \cdot P$ (b) $P^{4}=P^{2} \cdot P^{2}$ and (c) $P^{8}$. (Round all entries to four decimal places.) (d) Without computing it explicitly, find $P^{1000}$.

$$P=\left[\begin{array}{ll}{0.1} & {0.9} \\ {0} & {1}\end{array}\right]$$

At the corner Shell station, the revenue R varies directly with the number g of gallons of gasoline sold. If the revenue is $47.40 when the number of gallons sold is 12, find a linear equation that relates revenue R to the number g of gallons of gasoline. Then find the revenue R when the number of gallons of gasoline sold is 10.5.

The number of miles a car can travel on one gallon of gas is expressed as "miles per gallon" (mpg). Petro's mother drives an average of 15,000 miles a year. Her car averages 25 mpg. If the average cost of a gallon of gasoline is $2.39, how much will she spend on gasoline?

Solve the equation for the variable.

$$(3 c-2)^3-50=100$$

A toy rocket is launched vertically upward. Using a quadratic equation, we find that the rocket will reach a height of 220 feet at $2.5$ seconds and again at $5.5$ seconds. How can this be?

Total revenue is in dollars and $x$ is the number of units.

If the total revenue function for a product is $R(x)=32 x$, what is the marginal revenue for the product? What does this mean? 3. Suppose that the total revenue function for a commodity is $R=64 x-0.02 x^2$. (a) Find $R(100)$ and tell what it represents.

(b) Find the marginal revenue function.

( c ) Find the marginal revenue at $x=100$ and tell what it predicts about the sale of the next unit and the next $3$ units.

(d) Find $R(101)-R(100)$ and explain what this value represents.

Decide whether the two events listed are independent.

T is the event that Tom Cruise's next movie grosses over $200 million and R is the event that the Republicans have a majority in Congress in the year 2020.