Chapter 9

You are given the probability that an event will not happen. Find the probability that the event will happen. $$P\left(E^{\prime}\right)=\frac{13}{20}$$

Finding a Term of a Geometric Sequence Find a formula for the \(n\)th term of the geometric sequence. Then find the indicated term of the geometric sequence. 9th term: \(7,21,63, \dots\)

Use the Binomial Theorem to expand and simplify the expression. \(\left(5-x^{2}\right)^{5}\)

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$3,7,11,15,19, \ldots$$

Write the first five terms of the arithmetic sequence. Find the common difference and write the \(n\) th term of the sequence as a function of \(n .\) $$a_{1}=6, a_{k+1}=a_{k}+5$$

Evaluate \(_{n} P_{r}\) using a graphing utility. $$_{100} P_{5}$$

You are given the probability that an event will not happen. Find the probability that the event will happen. $$P\left(E^{\prime}\right)=\frac{61}{100}$$

Finding a Term of a Geometric Sequence Find a formula for the \(n\)th term of the geometric sequence. Then find the indicated term of the geometric sequence. 7th term: \(3,36,432, \ldots\)

Use the Binomial Theorem to expand and simplify the expression. \(\left(3-y^{2}\right)^{3}\)

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$7,13,19,25,31, \ldots$$

Write the first five terms of the arithmetic sequence. Find the common difference and write the \(n\) th term of the sequence as a function of \(n .\) $$a_{1}=\frac{3}{5}, a_{k+1}=-\frac{1}{10}+a_{k}$$

From a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer will be filled. In how many ways can the offices be filled?

One card is selected at random from a standard deck of 52 playing cards. Use a formula to find the probability of the union of the two events. The card is a club or a king.

Finding a Term of a Geometric Sequence Find a formula for the \(n\)th term of the geometric sequence. Then find the indicated term of the geometric sequence. 10th term: \(5,30,180, \dots\)

Use the Binomial Theorem to expand and simplify the expression. \(\left(x^{2}+y^{2}\right)^{4}\)

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$9,11,13,15,17, \ldots$$

Write the first five terms of the arithmetic sequence. Find the common difference and write the \(n\) th term of the sequence as a function of \(n .\) $$a_{1}=1.5, a_{k+1}=a_{k}-2.5$$

How many different batting orders can a baseball coach create from a team of 15 players when there are nine positions to fill?

One card is selected at random from a standard deck of 52 playing cards. Use a formula to find the probability of the union of the two events. The card is a face card or a black card.

Use the Binomial Theorem to expand and simplify the expression. \(\left(x^{2}+y^{2}\right)^{6}\)

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$0,3,8,15,24, \ldots$$

The first two terms of the arithmetic sequence are given. Find the missing term. Use the table feature of a graphing utility to verify your results. $$a_{1}=5, \quad a_{2}=11, \quad a_{10}=\square$$

The graphic design department is holding a contest in which it will award scholarships of different values to those who finish in first place, second place, and third place. The department receives 104 entries. How many different orders of the top three places are possible?

One card is selected at random from a standard deck of 52 playing cards. Use a formula to find the probability of the union of the two events. The card is a 5 or a 2

Finding a Term of a Geometric Sequence Find the indicated term of the geometric sequence. $$a_{1}=4, a_{4}=\frac{1}{2}, 10 \text { th term }$$

Use the Binomial Theorem to expand and simplify the expression. \(\left(3 x^{3}-y\right)^{6}\)

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$4,7,12,19,28, \dots$$

The first two terms of the arithmetic sequence are given. Find the missing term. Use the table feature of a graphing utility to verify your results. $$a_{1}=3, a_{2}=13, a_{9}=\square$$

Eight sprinters have qualified for the finals in the 100 -meter dash at the NCAA national track meet. How many different orders of the top three finishes are possible? (Assume there are no ties.)

One card is selected at random from a standard deck of 52 playing cards. Use a formula to find the probability of the union of the two events. The card is a heart or a spade.

Finding a Term of a Geometric Sequence Find the indicated term of the geometric sequence. $$a_{1}=5, a_{3}=\frac{45}{4}, 8 \mathrm{th} \text { term }$$

Use the Binomial Theorem to expand and simplify the expression. \(\left(2 x^{3}-y\right)^{5}\)

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$\frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7}, \dots$$

The first two terms of the arithmetic sequence are given. Find the missing term. Use the table feature of a graphing utility to verify your results. $$a_{1}=4.2, \quad a_{2}=1.8, \quad a_{7}=\square$$

Use the letters \(\mathbf{A}, \mathbf{B}, \mathbf{C},\) and \(\mathbf{D}\). Write all permutations of the letters.

Use the table, which shows the age groups of students in a college sociology class. $$\begin{array}{|c|c|} \hline \text { Age } & \text { Number of students } \\ \hline 18-19 & 11 \\ \hline 20-21 & 18 \\ \hline 22-30 & 2 \\ \hline 31-40 & 1 \\ \hline \end{array}$$ A student from the class is randomly chosen for a project. Find the probability that the student is the given age. 18 or 19 years old

Finding a Term of a Geometric Sequence Find the indicated term of the geometric sequence. $$a_{2}=-18, a_{5}=\frac{2}{3}, 6 \text { th term }$$

Use the Binomial Theorem to expand and simplify the expression. \(\left(\frac{1}{x}+y\right)^{5}\)

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$\frac{2}{1}, \frac{3}{3}, \frac{4}{5}, \frac{5}{7}, \frac{6}{9}, \dots$$

The first two terms of the arithmetic sequence are given. Find the missing term. Use the table feature of a graphing utility to verify your results. $$a_{1}=-0.7, a_{2}=-13.8, a_{8}=\square$$

Use the letters \(\mathbf{A}, \mathbf{B}, \mathbf{C},\) and \(\mathbf{D}\). Write all permutations of the letters when the letters \(\mathrm{B}\) and \(\mathrm{C}\) must remain between the letters \(\mathrm{A}\) and \(\mathrm{D}\).

Use the table, which shows the age groups of students in a college sociology class. $$\begin{array}{|c|c|} \hline \text { Age } & \text { Number of students } \\ \hline 18-19 & 11 \\ \hline 20-21 & 18 \\ \hline 22-30 & 2 \\ \hline 31-40 & 1 \\ \hline \end{array}$$ A student from the class is randomly chosen for a project. Find the probability that the student is the given age. 22 to 30 years old

Finding a Term of a Geometric Sequence Find the indicated term of the geometric sequence. $$a_{2}=-8, a_{5}=\frac{64}{27}, 6 \text { th term }$$

Use the Binomial Theorem to expand and simplify the expression. \(\left(\frac{1}{x}+y\right)^{6}\)

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$\frac{1}{2}, \frac{-1}{4}, \frac{1}{8}, \frac{-1}{16}, \dots$$

Use a graphing utility to graph the first 10 terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=15-\frac{3}{2} n$$

Find the number of distinguishable permutations of the group of letters. \(\mathrm{A}, \mathrm{A}, \mathrm{G}, \mathrm{E}, \mathrm{E}, \mathrm{E}, \mathrm{M}\)

Use the table, which shows the age groups of students in a college sociology class. $$\begin{array}{|c|c|} \hline \text { Age } & \text { Number of students } \\ \hline 18-19 & 11 \\ \hline 20-21 & 18 \\ \hline 22-30 & 2 \\ \hline 31-40 & 1 \\ \hline \end{array}$$ A student from the class is randomly chosen for a project. Find the probability that the student is the given age. 20 to 30 years old

Graphing the Terms of a Sequence Use a graphing utility to graph the first 10 terms of the sequence. $$a_{n}=12(-0.75)^{n-1}$$

Use the Binomial Theorem to expand and simplify the expression. \(\left(\frac{2}{x}-2 y\right)^{4}\)