Chapter 12

Use a calculator to evaluate each expression to four decimal places. $$ e^{\frac{1}{2}} $$

What is the value of \(\frac{6 !}{2 !} ?\) A. 3 B. 60 C. 360 D. 720

Solve each equation by factoring. \(3 x^{2}+8 x-3=0\)

fifth term of \((x+y)^{9}\)

What is the mean of the numbers represented by \(x+1\), \(3 x-2,\) and \(2 x-5 ?\) A. \(2 x-2\) B. \(\frac{6 x-7}{3}\) C. \(\frac{x+1}{3}\) D. \(x+4\)

A jar contains 4 red marbles, 3 green marbles, and 2 blue marbles. If a marble is drawn at random, what is the probability that it is not green? F. \(\frac{2}{9}\) G. \(\frac{1}{3}\) H. \(\frac{4}{9}\) J. \(\frac{2}{3}\)

Show that \(C(n-1, r)+C(n-1, r-1)=C(n, r)\)

Solve each matrix equation. \(\left[\begin{array}{ll}{x} & {y}\end{array}\right]=\left[\begin{array}{ll}{y} & {4}\end{array}\right]\)

REVIEW An examination consists of 10 questions. A student must answer only one of the first two questions and only six of the remaining ones. How many choices of questions does the student have? \(\mathrm{F} 112\) \(\mathrm{G} 56\) \(\mathrm{H} 44\) \(\mathrm{J} 30\)

A school has two backup generators having probabilities of 0.9 and 0.95, respectively, of operating in case of power outage. Find the probability that at least one backup generator operates during a power outage. F. 0.855 G. 0.89 H. 0.95 J. 0.995

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. arranging 5 different books on a shelf

Solve each matrix equation. \(\left[\begin{array}{l}{3 y} \\ {2 x}\end{array}\right]=\left[\begin{array}{l}{x+8} \\ {y-x}\end{array}\right]\)

A set of 400 test scores is normally distributed with a mean of 75 and a standard deviation of 8 . What percent of the test scores lie between 67 and 83\(?\)

Determine whether the events are mutually exclusive or inclusive. Then find the probability. A card is drawn from a standard deck of cards. What is the probability that it is a 5 or a spade?

Find each probability if 13 cards are drawn from a standard deck of cards and no replacement occurs. \(P(\text { all hearts })\)

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. arranging the letters of the word arrange

How many diagonals can be drawn in the pentagon? A. 5 B. 10 C. 15 D. 20

Evaluate each expression. \(\frac{5 !}{2 !}\)

A set of 400 test scores is normally distributed with a mean of 75 and a standard deviation of 8 . How many of the test scores are greater than 91\(?\)

Determine whether the events are mutually exclusive or inclusive. Then find the probability. A jar of change contains 5 quarters, 8 dimes, 10 nickels, and 19 pennies. If a coin is pulled from the jar at random, what is the probability that it is a nickel or a dime?

Find each probability if 13 cards are drawn from a standard deck of cards and no replacement occurs. \(P(\text { all red cards })\)

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. picking 3 apples from the last 7 remaining at the grocery store

How many ways can eight runners in an Olympic race finish in first, second, and third places? F 8 G 24 H 56 J 336

Evaluate each expression. \(\frac{6 !}{4 !}\)

A set of 400 test scores is normally distributed with a mean of 75 and a standard deviation of 8 . What is the probability that a randomly-selected score is less than 67\(?\)

Two cards are drawn from a standard deck of cards. Find each probability. P(ace, then king) if replacement occurs

CHALLENGE A textbook gives the following probability equation for events \(A\) and \(B\) that are mutually exclusive or inclusive. \(P(A \text { and } B)=P(A)+P(B)-\) \(P(A \text { or } B)\) Is this correct? Explain.

Find each probability if 13 cards are drawn from a standard deck of cards and no replacement occurs. \(P(\text { all one suit })\)

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. How many ways can 4 different gifts be placed into 4 different gift bags if each bag gets exactly 1 gift?

Darius can do his homework in pencil or pen, using lined or unlined paper, and on one or both sides of each page. How many ways can he do his homework?

Evaluate each expression. \(\frac{7 !}{3 !}\)

A salesperson had sales of \(\$ 11,000, \$ 15,000, \$ 11,000, \$ 16,000, \$ 12,000,\) and \(\$ 12,00\) in the last six months. Which measure of central tendency would he be likely to use to represent these data when he talks with his supervisor? Explain.

Two cards are drawn from a standard deck of cards. Find each probability. P(ace, then king) if no replacement occurs

Find each probability if 13 cards are drawn from a standard deck of cards and no replacement occurs. \(P(\text { no kings })\)

customer in an ice cream shop can order a sundae with a choice of 10 flavors of ice cream, a choice of 4 flavors of sauce, and with or without a cherry on top. How many different sundaes are possible?

Evaluate each expression. \(\frac{6 !}{1 !}\)

Graph each inequality. $$ x \geq-3 $$

Two cards are drawn from a standard deck of cards. Find each probability. P(heart, then club) if no replacement occurs

ACT/SAT In a jar of red and white gumballs, the ratio of white gumballs to red gumballs is \(5 : 4\) . If the jar contains a total of 180 gumballs, how many of them are red? A 45 B 64 C 80 D 100

For Exercises \(46-48\) , use the following information. A bag contains 10 marbles. In this problem, a cycle means that you draw a marble, record its color, and put it back. You go through the cycle 10 times. If you do not record any black marbles, can you conclude that there are no black marbles in the bag?

Find a counterexample for each statement. \(1+2+3+\cdots+n=2 n-1\)

Evaluate each expression. \(\frac{4 !}{2 ! 2 !}\)

Graph each inequality. $$ x+y \leq 4 $$

Two cards are drawn from a standard deck of cards. Find each probability. P(heart, then club) if replacement occurs

Find each product if \(a=\frac{3}{5}, b=\frac{2}{7}, c=\frac{3}{4},\) and \(d=\frac{1}{3}\). \(a b\)

Find a counterexample for each statement. \(5^{n}+1\) is divisible by 6

Evaluate each expression. \(\frac{6 !}{2 ! 4 !}\)

Graph each inequality. $$ y>|5 x| $$

The Energy Booster Company keeps their stock of Health Aid liquid in a tank that is a rectangular prism. Its sides measure \(x-1\) centimeters, \(x+3\) centimeters, and \(x-2\) centimeters. Suppose they would like to bottle their Health Aid in \(x-3\) containers of the same size. How much liquid in cubic centimeters will remain unbottled?

A die is rolled three times. Find each probability. \(P(1, \text { then } 2, \text { then } 3)\)