Chapter 9

A random number generator selects three numbers from 1 through 10. Find the probability of the event. One number is \(2,4,\) or \(6,\) and the other two numbers are odd.

Finding the Sum of a Finite Geometric Sequence Find the sum. Use a graphing utility to verify your result. $$\sum_{n=1}^{9}(-2)^{n-1}$$

Write the first five terms of the sequence defined recursively. $$a_{0}=1, a_{1}=3, a_{k}=a_{k-2}+a_{k-1}$$

Find the sum of the finite arithmetic sequence. $$2+4+6+8+10+12+14+16+18+20$$

Finding the Sum of a Finite Geometric Sequence Find the sum. Use a graphing utility to verify your result. $$\sum_{i=1}^{2} 64\left(-\frac{1}{2}\right)^{i-1}$$

Find the specified \(n\) th term in the expansion of the binomial. \((x-6 y)^{5}, n=3\)

Write the first five terms of the sequence defined recursively. $$a_{0}=-1, a_{1}=5, a_{k}=a_{k-2}+a_{k-1}$$

Find the sum of the finite arithmetic sequence. $$1+4+7+10+13+16+19$$

Evaluate \(_{n} C_{r}\) using a graphing utility. $$_{10} C_{7}$$

Finding the Sum of a Finite Geometric Sequence Find the sum. Use a graphing utility to verify your result. $$\sum_{i=1}^{6} 32\left(\frac{1}{4}\right)^{i-1}$$

Find the specified \(n\) th term in the expansion of the binomial. \((x-10 z)^{7}, n=4\)

Write the first five terms of the sequence defined recursively. Use the pattern to write the \(n\) th term of the sequence as a function of \(n .\) (Assume \(n\) begins with 1.) $$a_{1}=6, a_{k+1}=a_{k}+2$$

Find the sum of the finite arithmetic sequence. $$-1+(-3)+(-5)+(-7)+(-9)$$

Evaluate \(_{n} C_{r}\) using a graphing utility. $$_{42} C_{5}$$

Finding the Sum of a Finite Geometric Sequence Find the sum. Use a graphing utility to verify your result. $$\sum_{n=0}^{20} 12\left(\frac{6}{5}\right)^{n}$$

Find the specified \(n\) th term in the expansion of the binomial. \((4 x+3 y)^{9}, n=8\)

Write the first five terms of the sequence defined recursively. Use the pattern to write the \(n\) th term of the sequence as a function of \(n .\) (Assume \(n\) begins with 1.) $$a_{1}=25, a_{k+1}=a_{k}-5$$

Find the sum of the finite arithmetic sequence. $$-2+(-5)+(-8)+(-11)+(-14)+(-17)$$

Evaluate \(_{n} C_{r}\) using a graphing utility. $$_{50} C_{6}$$

Finding the Sum of a Finite Geometric Sequence Find the sum. Use a graphing utility to verify your result. $$\sum_{n=0}^{15} 10\left(\frac{7}{6}\right)^{n}$$

Find the specified \(n\) th term in the expansion of the binomial. \((5 a+6 b)^{5}, n=5\)

Write the first five terms of the sequence defined recursively. Use the pattern to write the \(n\) th term of the sequence as a function of \(n .\) (Assume \(n\) begins with 1.) $$a_{1}=81, a_{k+1}=\frac{1}{3} a_{k}$$

Find the sum of the finite arithmetic sequence. Sum of the first 100 positive integers

Use the letters \(\mathbf{A}, \mathbf{B}, \mathbf{C}, \mathbf{D}, \mathbf{E},\) and \(\mathbf{F}\). Write all possible selections of two letters that can be formed from the letters. (The order of the two letters is not important.)

The sample spaces are large and you should use the counting principles discussed in Section 9.5. On a game show, you are given five digits to arrange in the proper order to form the price of a car. If you are correct, you win the car. What is the probability of winning when you (a) randomly guess the position of each digit and (b) know the first digit and randomly guess the others?

Finding the Sum of a Finite Geometric Sequence Find the sum. Use a graphing utility to verify your result. $$\sum_{i=1}^{10} 8\left(-\frac{1}{4}\right)^{i-1}$$

Find the specified \(n\) th term in the expansion of the binomial. \((10 x-3 y)^{12}, n=10\)

Write the first five terms of the sequence defined recursively. Use the pattern to write the \(n\) th term of the sequence as a function of \(n .\) (Assume \(n\) begins with 1.) $$a_{1}=14, a_{k+1}=-2 a_{k}$$

Find the sum of the finite arithmetic sequence. Sum of the first 50 negative integers

Use the letters \(\mathbf{A}, \mathbf{B}, \mathbf{C}, \mathbf{D}, \mathbf{E},\) and \(\mathbf{F}\). Write all possible selections of three letters that can be formed from the letters. (The order of the three letters is not important.)

The sample spaces are large and you should use the counting principles discussed in Section 9.5. The deck for a card game is made up of 108 cards. Twenty-five each are red, yellow, blue, and green, and eight are wild cards. Each player is randomly dealt a seven-card hand. What is the probability that a hand will contain (a) exactly two wild cards, and (b) two wild cards, two red cards, and three blue cards?

Finding the Sum of a Finite Geometric Sequence Find the sum. Use a graphing utility to verify your result. $$\sum_{i=1}^{10} 5\left(-\frac{1}{3}\right)^{i-1}$$

Find the specified \(n\) th term in the expansion of the binomial. \((7 x-2 y)^{15}, n=7\)

Write the first five terms of the sequence (a) using the table feature of a graphing utility and (b) algebraically. (Assume \(n\) begins with 0.) $$a_{n}=\frac{1}{n !}$$

Find the sum of the finite arithmetic sequence. Sum of the integers from -100 to 30

As of May \(2014,\) the U.S. Senate Committee on Indian Affairs had 14 members. Party affiliation is not a factor in selection. How many different committees are possible from the 100 U.S. senators?

The sample spaces are large and you should use the counting principles discussed in Section 9.5. A shipment of 12 microwave ovens contains three defective units. A vending company has ordered four of these units, and because all are packaged identically, the selection will be random. What is the probability that (a) all four units are good, (b) exactly two units are good, and (c) at least two units are good?

Finding the Sum of a Finite Geometric Sequence Find the sum. Use a graphing utility to verify your result. $$\sum_{n=0}^{5} 300(1.06)^{n}$$

Write the first five terms of the sequence (a) using the table feature of a graphing utility and (b) algebraically. (Assume \(n\) begins with 0.) $$a_{n}=\frac{1}{(n+1) !}$$

Find the sum of the finite arithmetic sequence. Sum of the integers from -10 to 50

You can answer any 18 questions from a total of 20 questions on an exam. In how many different ways can you select the questions?

The sample spaces are large and you should use the counting principles discussed in Section 9.5. Two integers from 1 through 40 are chosen by a random number generator. What is the probability that (a) the numbers are both even, (b) one number is even and one is odd, (c) both numbers are less than \(30,\) and (d) the same number is chosen twice?

Finding the Sum of a Finite Geometric Sequence Find the sum. Use a graphing utility to verify your result.$$\sum_{n=0}^{6} 500(1.04)^{n}$$

Find the coefficient \(a\) of the given term in the expansion of the binomial. Binomial \((x+4)^{12}\) Term \(a x^{4}\)

Write the first five terms of the sequence (a) using the table feature of a graphing utility and (b) algebraically. (Assume \(n\) begins with 0.) $$a_{n}=\frac{n^{2}}{(n+1) !}$$

Find the indicated \(n\) th partial sum of the arithmetic sequence. $$8,20,32,44, \ldots ; n=10$$

In how many different ways can a jury of 12 people be randomly selected from a group of 40 people?

Using Summation Notation Use summation notation to write the sum. $$5+15+45+\cdots+3645$$

Find the coefficient \(a\) of the given term in the expansion of the binomial. Binomial =\((x-2 y)^{10}\) Term = \(a x^{8} y^{2}\)

Write the first five terms of the sequence (a) using the table feature of a graphing utility and (b) algebraically. (Assume \(n\) begins with 0.) $$a_{n}=\frac{n^{3}}{(n+2) !}$$