Choose the correct term to complete each sentence. • combination • complement • conditional probability • dependent events • expected value • independent events • mutually exclusive • permutation • probability distribution. The predicted average outcome of many trials in an experiment is called the _____.

True or False. Resource prices provide information to producers that allows them to use resources in a way that maximizes their value.

Determine whether each statement is true or false. If the statement is falsey make the necessary change(s) to produce a true statement. The functions

$$f ( x ) = 3 ^ { - x } \text { and } g ( x ) = - 3 ^ { x }$$

have the same graph.

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. ∫ sin² 2x cos 2x dx = 1/3sin³ 2x + C

Use the data in the accompanying table and express all results in decimal form.

$$\begin{matrix} \text{ } & \text{Driver Killed} & \text{Driver Not Killed}\\ \text{Seatbelt used} & \text{3655} & \text{7005}\\ \text{Seatbelt not used} & \text{4402} & \text{3040}\\ \end{matrix}$$

Fi nd the probability of randomly selecting a driver and getting one who was

not ki lled given that the driver was using a seatbelt.

Simplify each expression. $2 ^ { 4 } \div 8 + 5$

Use prime factorization to subtract these fractions: 1/18 - 1/30

Solve the compound inequality, if possible. Graph the solution set (if one exists) and write it using interval notation.

$$- 6 < f ( x ) \leq 0 \text { where } f ( x ) = 3 x - 9$$

A 4-person leadership committee is randomly chosen from a group of 24 candidates. Ten of the candidates are men, and 14 are women. What is the probability that the committee is all male or all female?

Verify that

$$y _ { 1 } ( x ) = e ^ { x } \cos 2 x , y _ { 2 } = e ^ { x } \sin 2 x , \text { and }y _ { 3 } = e ^ { 3 x }$$

are solutions to the differential equation

$$y ^ { \prime \prime \prime } - 5 y ^ { \prime \prime } + 11 y ^ { \prime } - 15 y = 0$$

and show that

$$\left| \begin{array} { l l l } { y _ { 1 } } & { y _ { 2 } } & { y _ { 3 } } \\ { y _ { 1 } ^ { \prime } } & { y _ { 2 } ^ { \prime } } & { y _ { 3 } ^ { \prime } } \\ { y _ { 1 } ^ { \prime \prime } } & { y _ { 2 } ^ { \prime \prime } } & { y _ { 3 } ^ { \prime \prime } } \end{array} \right|$$

is nonzero on any interval.

Write the integral as a sum of integrals without absolute values and evaluate.

$$\int _ { 0 } ^ { \pi } | \cos x | d x$$

Fill in each blank so that the resulting statement is true. In order to factor

$$7 x ^ { 2 } - 23 x + 6$$

begin by finding two first terms whose product is _____ and two last terms whose product is _____.

Give equations for ellipses and tell how many units up or down and to the right or left each ellipse is to be shifted. Find an equation for the new ellipse, and find the new foci, vertices, and center.

$$\frac { x ^ { 2 } } { 3 } + \frac { y ^ { 2 } } { 2 } = 1 , \quad \text { right } 2 , \text { up } 3$$

use a graphing utility to graph f, g, and y = x in the same viewing window to verify geometrically that is the inverse function of f (Be sure to restrict the domain of f properly.) f(x) = tan x, g(x) = arctan x