Chapter 11

Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises \(1-10 .\) Express probabilities as simplified fractions and as decimals rounded to the nearest hundredth $$ \begin{array}{llllll} {} & {} & {\text { Never}} \\ {} & {\text {Married}} & {\text { Married }} & {\text { Divorced }} & {\text { Widowed }} & {\text { Total }} \\ \hline \text { Male } & {65} & {40} & {10} & {3} & {118} \\ \hline \text { Female } & {65} & {34} & {14} & {11} & {124} \\ \hline \text { Total } & {130} & {74} & {24} & {14} & {242} \end{array} $$ If one person is randomly selected from the population described in the table, find the probability, expressed as a simplified fraction and as a decimal to the nearest hundredth, that the person $$\text {is divorced.}$$

Write the first five terms of each geometric sequence. $$ a_{1}=5, \quad r=3 $$

Use the formula for \(_{n} P_{r}\) to evaluate each expression. \(_{9} P_{4}\)

Evaluate the given binomial coefficient. $$ \left(\begin{array}{l} {8} \\ {3} \end{array}\right) $$

A statement \(S_{n}\) about the positive integers is given. Write statements \(S_{1}, S_{2},\) and \(S_{3},\) and show that each of these statements is true. \(S_{n}: 1+3+5+\cdots+(2 n-1)=n^{2}\)

write the first four terms of each sequence whose general term is given. $$ a_{n}=3 n+2 $$

Write the first six terms of each arithmetic sequence. $$ a_{1}=200, d=20 $$

Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises \(1-10 .\) Express probabilities as simplified fractions and as decimals rounded to the nearest hundredth $$ \begin{array}{llllll} {} & {} & {\text { Never}} \\ {} & {\text {Married}} & {\text { Married }} & {\text { Divorced }} & {\text { Widowed }} & {\text { Total }} \\ \hline \text { Male } & {65} & {40} & {10} & {3} & {118} \\ \hline \text { Female } & {65} & {34} & {14} & {11} & {124} \\ \hline \text { Total } & {130} & {74} & {24} & {14} & {242} \end{array} $$ If one person is randomly selected from the population described in the table, find the probability, expressed as a simplified fraction and as a decimal to the nearest hundredth, that the person $$\text{has never been married.}$$

Write the first five terms of each geometric sequence. $$ a_{1}=4, \quad r=3 $$

Use the formula for \(_{n} P_{r}\) to evaluate each expression. \(_{7} P_{3}\)

Evaluate the given binomial coefficient. $$ \left(\begin{array}{l} {7} \\ {2} \end{array}\right) $$

A statement \(S_{n}\) about the positive integers is given. Write statements \(S_{1}, S_{2},\) and \(S_{3},\) and show that each of these statements is true. \(S_{n}: 3+4+5+\cdots+(n+2)=\frac{n(n+5)}{2}\)

write the first four terms of each sequence whose general term is given. $$ a_{n}=4 n-1 $$

Write the first six terms of each arithmetic sequence. $$ a_{1}=300, d=50 $$

Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises \(1-10 .\) Express probabilities as simplified fractions and as decimals rounded to the nearest hundredth $$ \begin{array}{llllll} {} & {} & {\text { Never}} \\ {} & {\text {Married}} & {\text { Married }} & {\text { Divorced }} & {\text { Widowed }} & {\text { Total }} \\ \hline \text { Male } & {65} & {40} & {10} & {3} & {118} \\ \hline \text { Female } & {65} & {34} & {14} & {11} & {124} \\ \hline \text { Total } & {130} & {74} & {24} & {14} & {242} \end{array} $$ If one person is randomly selected from the population described in the table, find the probability, expressed as a simplified fraction and as a decimal to the nearest hundredth, that the person $$\text{is female.}$$

Write the first five terms of each geometric sequence. $$ a_{1}=20, \quad r=\frac{1}{2} $$

Use the formula for \(_{n} P_{r}\) to evaluate each expression. \(_{8} P_{5}\)

Evaluate the given binomial coefficient. $$ \left(\begin{array}{c} {12} \\ {1} \end{array}\right) $$

write the first four terms of each sequence whose general term is given. $$ a_{n}=3^{n} $$

Write the first six terms of each arithmetic sequence. $$ a_{1}=-7, d=4 $$

Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises \(1-10 .\) Express probabilities as simplified fractions and as decimals rounded to the nearest hundredth $$ \begin{array}{llllll} {} & {} & {\text { Never}} \\ {} & {\text {Married}} & {\text { Married }} & {\text { Divorced }} & {\text { Widowed }} & {\text { Total }} \\ \hline \text { Male } & {65} & {40} & {10} & {3} & {118} \\ \hline \text { Female } & {65} & {34} & {14} & {11} & {124} \\ \hline \text { Total } & {130} & {74} & {24} & {14} & {242} \end{array} $$ If one person is randomly selected from the population described in the table, find the probability, expressed as a simplified fraction and as a decimal to the nearest hundredth, that the person $$\text{is male.}$$

Write the first five terms of each geometric sequence. $$ a_{1}=24, \quad r=\frac{1}{3} $$

Use the formula for \(_{n} P_{r}\) to evaluate each expression. \(_{10} P_{4}\)

Evaluate the given binomial coefficient. $$ \left(\begin{array}{l} {11} \\ {1} \end{array}\right) $$

write the first four terms of each sequence whose general term is given. $$ a_{n}=\left(\frac{1}{3}\right)^{n} $$

Write the first six terms of each arithmetic sequence. $$ a_{1}=-8, d=5 $$

Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises \(1-10 .\) Express probabilities as simplified fractions and as decimals rounded to the nearest hundredth $$ \begin{array}{llllll} {} & {} & {\text { Never}} \\ {} & {\text {Married}} & {\text { Married }} & {\text { Divorced }} & {\text { Widowed }} & {\text { Total }} \\ \hline \text { Male } & {65} & {40} & {10} & {3} & {118} \\ \hline \text { Female } & {65} & {34} & {14} & {11} & {124} \\ \hline \text { Total } & {130} & {74} & {24} & {14} & {242} \end{array} $$ If one person is randomly selected from the population described in the table, find the probability, expressed as a simplified fraction and as a decimal to the nearest hundredth, that the person $$\text{is a widowed male.}$$

Use the formula for \(_{n} P_{r}\) to evaluate each expression. \(_{6} P_{6}\)

Evaluate the given binomial coefficient. $$ \left(\begin{array}{l} {6} \\ {6} \end{array}\right) $$

write the first four terms of each sequence whose general term is given. $$ a_{n}=(-3)^{n} $$

Write the first six terms of each arithmetic sequence. $$ a_{1}=300, d=-90 $$

A statement \(S_{n}\) about the positive integers is given. Write statements \(S_{k}\) and \(S_{k+1},\) simplifying statement \(S_{k+1}\) completely. \(S_{n}: 4+8+12+\cdots+4 n=2 n(n+1)\)

Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises \(1-10 .\) Express probabilities as simplified fractions and as decimals rounded to the nearest hundredth $$ \begin{array}{llllll} {} & {} & {\text { Never}} \\ {} & {\text {Married}} & {\text { Married }} & {\text { Divorced }} & {\text { Widowed }} & {\text { Total }} \\ \hline \text { Male } & {65} & {40} & {10} & {3} & {118} \\ \hline \text { Female } & {65} & {34} & {14} & {11} & {124} \\ \hline \text { Total } & {130} & {74} & {24} & {14} & {242} \end{array} $$ If one person is randomly selected from the population described in the table, find the probability, expressed as a simplified fraction and as a decimal to the nearest hundredth, that the person $$\text{is a widowed female.}$$

Write the first five terms of each geometric sequence. $$ a_{n}=-3 a_{n-1}, \quad a_{1}=10 $$

Use the formula for \(_{n} P_{r}\) to evaluate each expression. \(_{9} P_{9}\)

Evaluate the given binomial coefficient. $$ \left(\begin{array}{c} {15} \\ {2} \end{array}\right) $$

write the first four terms of each sequence whose general term is given. $$ a_{n}=\left(-\frac{1}{3}\right)^{n} $$

Write the first six terms of each arithmetic sequence. $$ a_{1}=200, d=-60 $$

A statement \(S_{n}\) about the positive integers is given. Write statements \(S_{k}\) and \(S_{k+1},\) simplifying statement \(S_{k+1}\) completely. \(S_{n}: 3+4+5+\cdots+(n+2)=\frac{n(n+5)}{2}\)

Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises \(1-10 .\) Express probabilities as simplified fractions and as decimals rounded to the nearest hundredth $$ \begin{array}{llllll} {} & {} & {\text { Never}} \\ {} & {\text {Married}} & {\text { Married }} & {\text { Divorced }} & {\text { Widowed }} & {\text { Total }} \\ \hline \text { Male } & {65} & {40} & {10} & {3} & {118} \\ \hline \text { Female } & {65} & {34} & {14} & {11} & {124} \\ \hline \text { Total } & {130} & {74} & {24} & {14} & {242} \end{array} $$ If one person is randomly selected from the population described in the table, find the probability, expressed as a simplified fraction and as a decimal to the nearest hundredth, that the person $$\text{Among those who are divorced, find the probability of selecting a woman.}$$

Write the first five terms of each geometric sequence. $$ a_{n}=-5 a_{n-1}, \quad a_{1}=-6 $$

Use the formula for \(_{n} P_{r}\) to evaluate each expression. \(_{8} P_{0}\)

Evaluate the given binomial coefficient. $$ \left(\begin{array}{c} {100} \\ {2} \end{array}\right) $$

write the first four terms of each sequence whose general term is given. $$ a_{n}=(-1)^{n}(n+3) $$

A statement \(S_{n}\) about the positive integers is given. Write statements \(S_{k}\) and \(S_{k+1},\) simplifying statement \(S_{k+1}\) completely. \(S_{n}: 3+7+11+\cdots+(4 n-1)=n(2 n+1)\)

Write the first six terms of each arithmetic sequence. $$ a_{1}=\frac{5}{2}, d=-\frac{1}{2} $$

Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises \(1-10 .\) Express probabilities as simplified fractions and as decimals rounded to the nearest hundredth $$ \begin{array}{llllll} {} & {} & {\text { Never}} \\ {} & {\text {Married}} & {\text { Married }} & {\text { Divorced }} & {\text { Widowed }} & {\text { Total }} \\ \hline \text { Male } & {65} & {40} & {10} & {3} & {118} \\ \hline \text { Female } & {65} & {34} & {14} & {11} & {124} \\ \hline \text { Total } & {130} & {74} & {24} & {14} & {242} \end{array} $$ If one person is randomly selected from the population described in the table, find the probability, expressed as a simplified fraction and as a decimal to the nearest hundredth, that the person $$\text{Among those who are divorced, find the probability of selecting a man.}$$

Write the first five terms of each geometric sequence. $$ a_{n}=-6 a_{n-1}, \quad a_{1}=-2 $$

Use the formula for \(_{n} P_{r}\) to evaluate each expression. \(_{6} P_{0}\)

Evaluate the given binomial coefficient. $$ \left(\begin{array}{c} {100} \\ {98} \end{array}\right) $$