Chapter 9

Determine the sample space for the experiment. A six-sided die is tossed twice and the results of roll 1 and roll 2 are recorded.

Identifying a Geometric Sequence Determine whether or not the sequence is geometric. If it is, find the common ratio.Identifying a Geometric Sequence Determine whether or not the sequence is geometric. If it is, find the common ratio. $$1,-\frac{1}{2}, \frac{1}{4},-\frac{1}{8}, \dots$$

Find the binomial coefficient. \(\left(\begin{array}{l}12 \\ 0\end{array}\right)\)

Write the first five terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=\left(-\frac{1}{2}\right)^{n}$$

Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic. If it is, find the common difference. (Assume \(n\) begins with 1.) $$a_{n}=8+13 n$$

Determine the sample space for the experiment. A taste tester has to rank three varieties of orange juice, A, \(\mathrm{B},\) and \(\mathrm{C},\) according to preference.

Identifying a Geometric Sequence Determine whether or not the sequence is geometric. If it is, find the common ratio.Identifying a Geometric Sequence Determine whether or not the sequence is geometric. If it is, find the common ratio. $$9,-6,4,-\frac{8}{3}, \dots$$

Find the binomial coefficient. \(\left(\begin{array}{l}20 \\ 20\end{array}\right)\)

Write the first five terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=(-2)^{n}$$

Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic. If it is, find the common difference. (Assume \(n\) begins with 1.) $$a_{n}=150-7 n$$

Determine the sample space for the experiment. Two county supervisors are selected from five supervisors, \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D},\) and \(\mathrm{E},\) to study a recycling plan.

Identifying a Geometric Sequence Determine whether or not the sequence is geometric. If it is, find the common ratio.Identifying a Geometric Sequence Determine whether or not the sequence is geometric. If it is, find the common ratio. $$20,2,0.2,0.02, \ldots$$

Find the binomial coefficient. \(\left(\begin{array}{c}10 \\ 4\end{array}\right)\)

Write the first five terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=\frac{n+1}{n}$$

Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic. If it is, find the common difference. (Assume \(n\) begins with 1.) $$a_{n}=53-4(n+6)$$

Find the probability for the experiment of tossing a coin three times. Use the sample space $$S=\\{H H H, H H T, H T H, H T T, T H H, T H T, T T H, T T T\\}$$ The probability of getting exactly two tails

A customer can choose one of four amplifiers, one of ten stereo receivers, and one of five speaker models for an entertainment system. Determine the number of possible system configurations.

Identifying a Geometric Sequence Determine whether or not the sequence is geometric. If it is, find the common ratio.Identifying a Geometric Sequence Determine whether or not the sequence is geometric. If it is, find the common ratio. $$5,1,0.2,0,04, \dots$$

Find the binomial coefficient. \(\left(\begin{array}{c}10 \\ 6\end{array}\right)\)

Write the first five terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=\frac{n}{n+1}$$

Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic. If it is, find the common difference. (Assume \(n\) begins with 1.) $$a_{n}=1+(n-1) 4$$

Find the probability for the experiment of tossing a coin three times. Use the sample space $$S=\\{H H H, H H T, H T H, H T T, T H H, T H T, T T H, T T T\\}$$ The probability of getting a head on the first toss

A college student is preparing a course schedule for the next semester. The student must select one of two mathematics courses, one of three science courses, and one of five courses from the social sciences and humanities. How many schedules are possible?

Identifying a Geometric Sequence Determine whether or not the sequence is geometric. If it is, find the common ratio.Identifying a Geometric Sequence Determine whether or not the sequence is geometric. If it is, find the common ratio. $$1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \dots$$

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

Write the first five terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=\frac{n}{n^{2}+1}$$

Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic. If it is, find the common difference. (Assume \(n\) begins with 1.) $$a_{n}=2^{n}+n$$

Find the probability for the experiment of tossing a coin three times. Use the sample space $$S=\\{H H H, H H T, H T H, H T T, T H H, T H T, T T H, T T T\\}$$ The probability of getting at least one head

In how many ways can a 10 -question true-false exam be answered? (Assume that no questions are omitted.)

Identifying a Geometric Sequence Determine whether or not the sequence is geometric. If it is, find the common ratio.Identifying a Geometric Sequence Determine whether or not the sequence is geometric. If it is, find the common ratio. $$\frac{1}{5}, \frac{2}{7}, \frac{3}{9}, \frac{4}{11}, \dots$$

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

Write the first five terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=\frac{2 n}{n+1}$$

Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic. If it is, find the common difference. (Assume \(n\) begins with 1.) $$a_{n}=2^{n-1}$$

Find the probability for the experiment of tossing a coin three times. Use the sample space $$S=\\{H H H, H H T, H T H, H T T, T H H, T H T, T T H, T T T\\}$$ The probability of getting at least two heads

In a physiology class, a student must dissect three different specimens. The student can select one of nine earthworms, one of four frogs, and one of seven fetal pigs. In how many ways can the student select the specimens?

Writing the Terms of a Geometric Sequence In Exercises \(17-24,\) write the first five terms of the geometric sequence. $$a_{1}=6, r=3$$

Write the first five terms of the sequence (a) using the table feature of a graphing utility and (b) algebraically. (Assume \(n\) begins with 1.) $$a_{n}=\frac{1+(-1)^{n}}{n}$$

Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic. If it is, find the common difference. (Assume \(n\) begins with 1.) $$a_{n}=3+2(-1)^{n}$$

Find the probability for the experiment of selecting one card at random from a standard deck of 52 playing cards. The card is a face card.

How many three-digit numbers can be formed under each condition? (a) The leading digit cannot be \(0 .\) (b) The leading digit cannot be 0 and no repetition of digits is allowed. (c) The leading digit cannot be 0 and the number must be a multiple of 5.

Writing the Terms of a Geometric Sequence Write the first five terms of the geometric sequence. $$a_{1}=4, r=2$$

Write the first five terms of the sequence (a) using the table feature of a graphing utility and (b) algebraically. (Assume \(n\) begins with 1.) $$a_{n}=\frac{1+(-1)^{n}}{2 n}$$

Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic. If it is, find the common difference. (Assume \(n\) begins with 1.) $$a_{n}=(-1)^{n}$$

Find the probability for the experiment of selecting one card at random from a standard deck of 52 playing cards. The card is a black card.

How many four-digit numbers can be formed under each condition? (a) The leading digit cannot be 0 and the number must be less than 5000. (b) The leading digit cannot be 0 and the number must be even.

Writing the Terms of a Geometric Sequence Write the first five terms of the geometric sequence. $$a_{1}=1, r=\frac{1}{2}$$

Write the first five terms of the sequence (a) using the table feature of a graphing utility and (b) algebraically. (Assume \(n\) begins with 1.) $$a_{n}=1-\frac{1}{2^{n}}$$

Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic. If it is, find the common difference. (Assume \(n\) begins with 1.) $$a_{n}=\frac{(-1)^{2 n}}{4}$$

Find the probability for the experiment of selecting one card at random from a standard deck of 52 playing cards. The card is a red face card.

Writing the Terms of a Geometric Sequence Write the first five terms of the geometric sequence. $$a_{1}=2, r=\frac{1}{3}$$