Exam 11: Further Topics in Algebra

List the elements in the sample space of the experiment. -A lottery uses balls numbered 1 through 31. List the sample space of the event picking one even-numbered ball.

List the elements in the sample space of the experiment. -A box contains 2 blue cards numbered 1 through 2, and 3 green cards numbered 1 through 3. List the sample space of picking a blue card followed by a green card.

Evaluate the expression. - ${ } _ { 7 } \mathrm { C } _ { 2 }$

Solve the problem. -How many different three-number ʺcombinationsʺ are possible on a combination lock having 23 numbers on its dial without repeating a number?

Find a_n and a₆ for the following arithmetic sequence. - $\mathrm { a } _ { 1 } = - 61 , \mathrm {~d} = - 5$

Use a graphing calculator to evaluate the series. - $\sum _ { k = 3 } ^ { 8 } \left( k ^ { 2 } - 4 k + 3 \right)$

Solve the problem. -A town has a population of 1000 people and is increasing by 9% every year. What will the population be at the end of 9 years?

Evaluate the sum. - $\sum _ { \mathrm { i } = 1 } ^ { 4000 } \mathrm { i }$

Evaluate the sum using the given information. - $x _ { 1 } = - 4 , x _ { 2 } = - 3 , x _ { 3 } = - 1 , x _ { 4 } = - 2$ , and $x _ { 5 } = 0$ $\sum _ { i = 1 } ^ { 5 } \left( - 2 x _ { i } + 1 \right)$

Solve the problem. -A 5-card hand is dealt from a deck of 52 cards. What is the probability that a) none are queens? b) all are queens?

Provide an appropriate response. -The sum of an infinite geometric series exists if:

Find the nth term of the geometric sequence. - $a _ { 1 } = 4 , r = - 3 , n = 9$

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth. - $a _ { 2 } = - 144 , a _ { 6 } = - 9$

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $\mathrm { S } _ { 8 } = - 88 , \text { a8 } = - 18$

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $\mathrm { a } _ { 1 } = 4 - \sqrt { 8 } , \mathrm { a } _ { 2 } = 4 , \mathrm { n } = 4$

Evaluate the series, if it converges. - $- 14 + \frac { 70 } { 3 } - \frac { 350 } { 9 } + \frac { 1750 } { 27 } + \ldots$

It can be shown that $( 1 + x ) ^ { n } = 1 + n x + \frac { n ( n - 1 ) } { 2 ! } x ^ { 2 } + \frac { n ( n - 1 ) ( n - 2 ) } { 3 ! } x ^ { 3 } \ldots$ is true for any real number n (not just positive integer values) and any real number x, where $| x | < 1$ Use this series to approximate the given number to the nearest thousandth. - $4 \cdot 6 + 5 \cdot 7 + 6 \cdot 8 + \ldots + ( n + 3 ) ( n + 5 ) = \frac { n \left( 2 n ^ { 2 } + 27 n + 115 \right) } { 6 }$

Evaluate the expression. -C(8, 0)

Find the common ratio r for the given infinite geometric sequence. - $3,9,27,81,243 , \ldots$

Find the common difference for the arithmetic sequence. - $7,12,17,22 , \ldots$