In Exercise 3e, you graphed an inequality involving lines with the following equations.

$$2x+3y=12$$

$$2x+y=8$$

Use algebra to find the intersection of the two lines. Then check your result by testing the values of $x$ and $y$ in each equation.

While the Petersen family was waiting for their table, 9 people left the restaurant and 15 people entered. Find the sum of -9 and 15 to determine the change in the nu.m ber of people in the restaurant. Use algebra tiles to model the situation.

Use a computer algebra system to (a) find or evaluate the integral and (b) graph two antiderivatives. (c) Describe the relationship between the graphs of the antiderivatives. $\int_{0}^{5} x^{4}\left(25-x^{2}\right)^{3 / 2} d x$

Algebra Two lines are perpendicular. One line has an equation of $r x+3 y=4$ and the other line has an equation of $\frac{2}{5} x+y=6$. Find a linear equation to describe the relationship between $r$ and $s$.

Use a computer algebra system to evaluate the following integral. Find both an exact result and an approximate result for each definite integral. Assume a is a positive real number. $\int_{0}^{\pi / 2} \cos ^{6} x d x$

The $2003 ~Statistical ~Abstract ~of ~the ~United ~States$ reported the percentage of people $18$ years of age and older who smoke. Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of $.30.$

Assume that the study uses your sample size recommendation in part (a) and finds $520$ smokers. What is the point estimate of the proportion of smokers in the population?

Following is the list of letter grades for students in an algebra class:

$$\begin{array}{ccc} \hline A & B & F & A &C & C & A & B & D\\ F & D & A & A & B & C & F & B & D\\ C & A & A & A & F & B & C & A & C\\ \hline \end{array}$$

Construct a relative frequency distribution for these data.

Underline each simple subject once and each simple predicate twice. Label each preposition $prep$., each direct object $d.o$., and each indirect object $i.o$.
Ms. Watkins asked Jenny an algebra question.

Use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. \

$$y=\sqrt{\dfrac{x+1}{x}}$$

Write a double integral that represents the surface area of $z=f(x, y)$ over the region $R$. Use a computer algebra system to evaluate the double integral.

$f(x, y)=4-x^2-y^2$ $R=\{(x, y): 0 \leq x \leq 1,0 \leq y \leq 1\}$

Following is the list of letter grades for students in an algebra class:

$$\begin{array}{ccc} \hline A & B & F & A &C & C & A & B & D\\ F & D & A & A & B & C & F & B & D\\ C & A & A & A & F & B & C & A & C\\ \hline \end{array}$$

Construct a frequency bar graph for these data.

U.S. airlines average about 1.6 fatalities per month. ( Statistical Abstract of the United States: 2010 ). Assume that the probability distribution for x , the number of fatalities per month, can be approximated by a Poisson probability distribution. a. What is the probability that no fatalities will occur during any given month? b. What is the probability that one fatality will occur during any given month? c. Find E(x) and the standard deviation of x .

Algebra In $\triangle P Q R, \angle S Q R \cong \angle S R Q, P Q>P R, \mathrm{~m} \angle P S R=(4 y+9)^{\circ}$ and $\mathrm{m} \angle Q S P=(6 y-24)^{\circ}$. Find the range of values for $y$.

Evaluate the second derivative of the function at the given point. Use a computer algebra system to verify your result.
$h(x)=\dfrac{1}{9}(3 x+1)^3, \quad\left(1, \dfrac{64}{9}\right)$