Chapter 12

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. How many times do you have to repeat the cycle to be certain that there are no black marbles in the bag? Explain your reasoning.

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

Solve each equation or inequality. \(3 e^{x}+1=2\)

Evaluate each expression. \(\frac{8 !}{3 ! 5 !}\)

Evaluate 2\(\sqrt{\frac{p(1-p)}{n}}\) for the given values of \(p\) and \(n\) Round to the nearest thousandth if necessary. $$ p=0.5, n=100 $$

Find each percent. 68% of 200

A die is rolled three times. Find each probability. \(P(\text { no } 4 \mathrm{s})\)

Describe two real-life events that are dependent.

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

Solve each equation or inequality. \(e^{2 x}>5\)

Evaluate each expression. \(\frac{5 !}{5 ! 0 !}\)

Find each percent. 68% of 500

Evaluate 2\(\sqrt{\frac{p(1-p)}{n}}\) for the given values of \(p\) and \(n\) Round to the nearest thousandth if necessary. $$ p=0.5, n=400 $$

A die is rolled three times. Find each probability. \(P(\text { three } 1 \mathrm{s})\)

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

Solve each equation or inequality. \(\ln (x-1)=3\)

Find each percent. 95% of 400

Evaluate 2\(\sqrt{\frac{p(1-p)}{n}}\) for the given values of \(p\) and \(n\) Round to the nearest thousandth if necessary. $$ p=0.25, n=500 $$

A die is rolled three times. Find each probability. \(P(\text { three even numbers) }\)

CHALLENGE If one bulb in a string of holiday lights fails to work, the whole string will not light. If each bulb in a set has a 99.5\(\%\) chance of working, what is the maximum number of lights that can be strung together with at least a 90\(\%\) chance of the whole string lighting?

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

A painter works on a job for 10 days and is then joined by an associate. Together they finish the job in 6 more days. The associate could have done the job in 30 days. How long would it have taken the painter to do the job alone?

Find each percent. 95% of 500

Evaluate 2\(\sqrt{\frac{p(1-p)}{n}}\) for the given values of \(p\) and \(n\) Round to the nearest thousandth if necessary. $$ p=0.75, n=1000 $$

BOOKS Dan has twelve books on his shelf that he has not read yet. There are seven novels and five biographies. He wants to take four books with him on vacation. What is the probability that he randomly selects two novels and two biographies?

Find each percent. 99% of 400

Evaluate 2\(\sqrt{\frac{p(1-p)}{n}}\) for the given values of \(p\) and \(n\) Round to the nearest thousandth if necessary. $$ p=0.3, n=500 $$

Find the sum of each series. $$ 2+4+8+\cdots+128 $$

Evaluate 2\(\sqrt{\frac{p(1-p)}{n}}\) for the given values of \(p\) and \(n\) Round to the nearest thousandth if necessary. $$ p=0.6, n=1000 $$

Find each percent. 99% of 500

Find the sum of each series. $$ \sum_{n=1}^{3}(5 n-2) $$

REVIEW A coin is tossed and a die is rolled. What is the probability of a head and a 3 ? $$ \begin{array}{ll}{\mathbf{F} \frac{1}{4}} & {\mathbf{H} \frac{1}{12}} \\\ {\mathbf{G} \frac{1}{8}} & {\mathbf{J} \frac{1}{24}}\end{array} $$

Evaluate the expression \(\frac{x}{x+y}\) for the given values of \(x\) and \(y\). \(x=3, y=2\)

A gumball machine contains 7 red, 8 orange, 9 purple, 7 white, and 5 yellow gumballs. Tyson buys 3 gumballs. Find each probability, assuming that the machine dispenses the gumballs at random. \(P(3 \text { red })\)

Evaluate the expression \(\frac{x}{x+y}\) for the given values of \(x\) and \(y\). \(x=4, y=4\)

A gumball machine contains 7 red, 8 orange, 9 purple, 7 white, and 5 yellow gumballs. Tyson buys 3 gumballs. Find each probability, assuming that the machine dispenses the gumballs at random. \(P(2 \text { white, } 1 \text { purple })\)

Evaluate the expression \(\frac{x}{x+y}\) for the given values of \(x\) and \(y\). \(x=2, y=8\)

PHOTOGRAPHY A photographer is taking a picture of a bride and groom together with 6 attendants. How many ways can he arrange the 8 people in a row if the bride and groom stand in the middle?

Evaluate the expression \(\frac{x}{x+y}\) for the given values of \(x\) and \(y\). \(x=5, y=10\)

PREREQUISITE SKILL Find the mean, median, mode, and range for each set of data. Round to the nearest hundredth, if necessary. (Pages 759 and 760 ) $$ 298,256,399,388,276 $$

Solve each equation. Check your solutions. $$ \log _{5} 5+\log _{5} x=\log _{5} 30 $$

PREREQUISITE SKILL Find the mean, median, mode, and range for each set of data. Round to the nearest hundredth, if necessary. (Pages 759 and 760 ) $$ 3,75,58,7,34 $$

Solve each equation. Check your solutions. $$ \log _{16} c-2 \log _{16} 3=\log _{16} 4 $$

PREREQUISITE SKILL Find the mean, median, mode, and range for each set of data. Round to the nearest hundredth, if necessary. (Pages 759 and 760 ) $$ 4.8,5.7,2.1,2.1,4.8,2.1 $$

Given a polynomial and one of its factors, find the remaining factors of the polynomial. Some factors may not be binomials. $$ x^{3}-x^{2}-10 x+6 ; x+3 $$

PREREQUISITE SKILL Find the mean, median, mode, and range for each set of data. Round to the nearest hundredth, if necessary. (Pages 759 and 760 ) $$ 80,50,65,55,70,65,75,50 $$

Given a polynomial and one of its factors, find the remaining factors of the polynomial. Some factors may not be binomials. $$ x^{3}-7 x^{2}+12 x ; x-3 $$

PREREQUISITE SKILL Find the mean, median, mode, and range for each set of data. Round to the nearest hundredth, if necessary. (Pages 759 and 760 ) $$ 61,89,93,102,45,89 $$

Find each sum if \(a=\frac{1}{2}, b=\frac{1}{6}, c=\frac{2}{3},\) and \(d=\frac{3}{4}\) $$ a+b $$

PREREQUISITE SKILL Find the mean, median, mode, and range for each set of data. Round to the nearest hundredth, if necessary. (Pages 759 and 760 ) $$ 13.3,15.4,12.5,10.7 $$