Chapter 8

Find the sum of the infinite geometric series. $$ 25-5+1-\frac{1}{5}+\dots+25\left(-\frac{1}{5}\right)^{n-1}+\cdots $$

Find the specified term. The sixth term of \((3 x-2 y)^{6}\)

To win a lottery, a person must pick 3 numbers from 0 to 9 in the correct order. If a number may be repeated, what is the probability of winning this game with one play?

Find a general term \(a_{n}\) for the geometric sequence. $$a_{1}=2, r=\frac{1}{2}$$

In how many ways can 9 players be assigned to the 9 positions on a baseball team, assuming that any player can play any position?

Find the specified term. The seventh term of \((2 a+b)^{9}\)

\(\quad\) To win the jackpot in a lottery, a person must pick 5 numbers from 1 to 55 and then pick the powerball, which has a number from 1 to \(42 .\) If the numbers are picked at random, what is the probability of winning this game with one play?

Find a general term \(a_{n}\) for the geometric sequence. $$a_{1}=0.8, r=-3$$

In a game of musical chairs, 7 children will sit in 6 chairs arranged in a circle. One child will be left out. How many (different) ways can the children sit in the chairs? (For a way to be different, at least one child must be sitting next to someone different.)

Write each national number in the form of an infinite geometric series. $$ \frac{1}{9} $$

Explain how to find the numbers in Pascal's triangle.

\(\quad\) A jar contains 22 red marbles, 18 blue marbles, and 10 green marbles. If a marble is drawn from the jar at random, find the probability that the color is the following. A. Red B. Not red C. Blue or green

Find a general term \(a_{n}\) for the geometric sequence. $$a_{3}=\frac{1}{32}, r=-\frac{1}{4}$$

Write each national number in the form of an infinite geometric series. $$ \frac{9}{11} $$

A jar contains 55 red marbles and 45 blue marbles. If 2 marbles are drawn from the jar at random without replacem A. Both are blue. B. Neither is blue.ent, find the probability that the marbles satisfy the following. C. The first marble is red and the second marble is blue.

Find a general term \(a_{n}\) for the geometric sequence. $$a_{4}=3, r=3$$

A scheduling committee has 1 room in which to offer 5 mathematics courses. In how many ways can the committee arrange the 5 courses over the day?

Write each national number in the form of an infinite geometric series. $$ \frac{14}{33} $$

Conditional Probability and Dependent Events Find the probability of drawing a queen from a standard deck of cards given that one card, a queen, has alrcady been drawn and not replaced.

Find a general term \(a_{n}\) for the geometric sequence. $$a_{3}=2, a_{6}=\frac{1}{4}$$

Write each national number in the form of an infinite geometric series. $$ \frac{1}{7} $$

Conditional Probability and Dependent Events Find the probability of drawing a king from a standard deck of cards given that two cards, both kings, have already been drawn and not replaced.

Find a general term \(a_{n}\) for the geometric sequence. $$a_{2}=6, a_{4}=24, r>0$$

There are 10 basic colors available for a new car, along with 5 basic styles of trim. In how many ways can a person pick the color and trim?

Write each national number in the form of an infinite geometric series. $$\frac{23}{99}$$

\(\mathbf{A}\) card is drawn from a standard deck of 52 cards. Given that the card is a face card, what is the probability that the card is a king? (Hint; A face card is a jack, queen, or king.)

Find a general term \(a_{n}\) for the geometric sequence. $$a_{1}=-5, a_{3}=-125, r<0$$

Write the sum of each geometric series as a rational number. $$0.8+0.08+0.008+0.0008+\cdots$$

Conditional Probability and Dependent Events Three cards are drawn from a deck without replacement. Find the probability that the three cards are an ace, king, and queen in that order.

Find a general term \(a_{n}\) for the geometric sequence. $$a_{1}=10, a_{2}=2$$

Evaluate the expression. \(C(4,3)\)

Write the sum of each geometric series as a rational number. $$0.9+0.09+0.009+0.0009+\cdots$$

Conditional Probability and Dependent Events \(\mathbf{A}\) jar initially contains 10 red marbles and 23 blue marbles. What is the probability of drawing a blue marble, given that 2 red marbles and 4 blue marbles have already been drawn?

Find a general term \(a_{n}\) for the geometric sequence. $$a_{2}=-1, a_{7}=-32$$

Write the sum of each geometric series as a rational number. $$0.45+0.0045+0.000045+\cdots$$

Conditional Probability and Dependent Events The probability that the first serve of a volleyball is out of bounds is \(0.3,\) and the probability that the second serve of a volleyball is in bounds, given that the first serve was out of bounds, is \(0.8 .\) Find the probability that the first serve is out of bounds and the second serve is in bounds.

Find a general term \(a_{n}\) for the geometric sequence. $$a_{2}=\frac{9}{4}, a_{4}=\frac{81}{4}, r<0$$

Evaluate the expression. \(c(7,5)\)

Write the sum of each geometric series as a rational number. $$0.36+0.0036+0.000036+\cdots$$

Conditional Probability and Dependent Events The probability of a day being cloudy is \(30 \%,\) and the probability of it being cloudy and windy is \(12 \% .\) Given that the day is cloudy, what is the probability that it will be windy?

Determine if \(f\) is an arithmetic sequence. $$f(n)=4-3 n^{3}$$

Evaluate the expression. \(C(5,0)\)

Write out the terms of the series and then evaluate it. $$\sum_{k=1}^{4}(k+1)$$

Conditional Probability and Dependent Events The probability of a day being rainy is \(80 \%\), and the probability of it being windy and rainy is \(72 \% .\) Given that the day is rainy, what is the probability that it will be windy?

Determine if \(f\) is an arithmetic sequence. \(f(n)=2(n-1)\)

Evaluate the expression. \(C(10,2)\)

Write out the terms of the series and then evaluate it. $$\sum_{k=1}^{6}(3 k-1)$$

Conditional Probability and Dependent Events Two dice are rolled. If the first die shows a 2, find the probability that the sum of the dice is 7 or more.

Determine if \(f\) is an arithmetic sequence. $$f(n)=4 n-(3-n)$$

Evaluate the expression. \(\left(\begin{array}{l}8 \\ 2\end{array}\right)\)