Chapter 8

Use any or all of the methods described in this section to solve each problem. Pineapple Samples How many samples of 3 pineapples can be drawn from a crate of \(12 ?\)

Find the sum for each series. $$\sum_{i=1}^{50} 2 i^{3}$$

Evaluate each sum. $$\sum_{i=1}^{12}(-5-8 i)$$

Find each sum that converges. $$\sum_{i=1}^{\infty}\left(\frac{1}{5}\right)\left(-\frac{1}{2}\right)^{i-1}$$

Use any or all of the methods described in this section to solve each problem. Soup Ingredients \(\quad\) Madeline Moore specializes in making different vegetable soups with carrots, celery, beans, peas, mushrooms, and potatoes. How many different soups can she make with any 4 ingredients?

Find the sum for each series. $$\sum_{i=1}^{5}(5 i+3)$$

Evaluate each sum. $$\sum_{k=1}^{19}(-3-4 k)$$

Find each sum that converges. $$\sum_{i=1}^{\infty}\left(-\frac{1}{3}\right)\left(\frac{3}{4}\right)^{i-1}$$

Use any or all of the methods described in this section to solve each problem. Assistant/Manager Assignments From a pool of 7 assistants, 3 are selected to be assigned to 3 managers, 1 assistant to each manager. In how many ways can this be done?

Find the sum for each series. $$\sum_{i=1}^{5}(8 i-1)$$

Evaluate each sum. $$\sum_{i=1}^{1000} i$$

Use a graphing calculator to evaluate each sum. Round to the nearest thousandth. $$\sum_{i=1}^{10}-(1.4)^{i}$$

Use any or all of the methods described in this section to solve each problem. Musical Chairs Seatings In a game of musical chairs, 12 children will sit in 11 chairs. One will be left out. How many seatings are possible?

Find the sum for each series. $$\sum_{i=1}^{5}\left(4 i^{2}-2 i+6\right)$$

Evaluate each sum. $$\sum_{k=1}^{2000} k$$

Use a graphing calculator to evaluate each sum. Round to the nearest thousandth. $$\sum_{j=1}^{6}-(3.6)^{j}$$

Use any or all of the methods described in this section to solve each problem. Plant Samples In an experiment on plant hardiness, a researcher gathers 6 wheat plants, 3 barley plants, and 2 rye plants. She wishes to select 4 plants at random. (a) In how many ways can this be done? (b) In how many ways can it be done if exactly 2 wheat plants must be included?

Find the sum for each series. $$\sum_{i=1}^{6}\left(2+i-i^{2}\right)$$

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. In Exercises 69 and 70 , round to the nearest thousandth. $$a_{n}=4.2 n+9.73$$

Use a graphing calculator to evaluate each sum. Round to the nearest thousandth. $$\sum_{j=3}^{8} 2(0.4)^{j}$$

Use any or all of the methods described in this section to solve each problem. Committee Choices In a club with 8 men and 11 women members, how many 5 -member committees can be chosen that have the following? (a) All men (b) All women (c) 3 men and 2 women (d) No more than 3 women

Find the sum for each series. $$\sum_{i=1}^{4}\left(3 i^{3}+2 i-4\right)$$

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. In Exercises 69 and 70 , round to the nearest thousandth. $$a_{n}=8.42 n+36.18$$

Use a graphing calculator to evaluate each sum. Round to the nearest thousandth. $$\sum_{i=4}^{9} 3(0.25)^{i}$$

Use any or all of the methods described in this section to solve each problem. Committee Choices \(\quad\) From 10 names on a ballot, 4 will be elected to a political party committee. In how many ways can the committee of 4 be formed if each person will have a different responsibility?

Find the sum for each series. $$\sum_{i=1}^{6}\left(i^{2}+2 i^{3}\right)$$

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. In Exercises 69 and 70 , round to the nearest thousandth. $$a_{n}=\sqrt{8} n+\sqrt{3}$$

Find the future value of each annuity. Payments of \(\$ 1000\) at the end of each year for 9 years at \(4 \%\) interest compounded annually

Use any or all of the methods described in this section to solve each problem. Garage Door Openers The code for some garage door openers consists of 12 electrical switches that can be set to either 0 or 1 by the owner. With this type of opener, how many codes are possible? (Source: Promax.)

Find the sum for each series. $$\sum_{i=1}^{60}\left(i^{3}-2 i^{2}\right)$$

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. In Exercises 69 and 70 , round to the nearest thousandth. $$a_{n}=-\sqrt[3]{4} n+\sqrt{7}$$

Find the future value of each annuity. Payments of \(\$ 800\) at the end of each year for 12 years at \(3 \%\) interest compounded annually

Use any or all of the methods described in this section to solve each problem. Combination Lock A typical combination for a padlock consists of 3 numbers from 0 to \(39 .\) Count the number of combinations that are possible with this type of lock if a number may be repeated.

Find the sum for each series. $$\sum_{i=1}^{43}\left(15 i^{2}-2\right)$$

Solve each problem. Integer Sum Find the sum of all the integers from 51 to 71

Find the future value of each annuity. Payments of \(\$ 2430\) at the end of each year for 10 years at \(2.5 \%\) interest compounded annually

Use any or all of the methods described in this section to solve each problem. Combination Lock \(\mathrm{A}\) briefcase has 2 locks. The combination to each lock consists of a 3 -digit number, where digits may be repeated. How many different ways are there of choosing the six digits required to open the briefcase?

Find the sum for each series. $$\sum_{i=1}^{77}\left(i^{2}+52 i+672\right)$$

Solve each problem. Integer Sum Find the sum of all the integers from \(-8\) to 30

Find the future value of each annuity. Payments of \(\$ 1500\) at the end of each year for 6 years at \(1.5 \%\) interest compounded annually

Use any or all of the methods described in this section to solve each problem. Lottery To win the jackpot in a lottery game, a person must pick 3 numbers from 0 to 9 in the correct order. If a number can be repeated, how many ways are there to play the game?

Find the sum for each series. $$\sum_{i=1}^{52}\left(i^{2}+27 i+180\right)$$

Solve each problem. Clock Chimes If a clock strikes the proper number of chimes each hour on the hour, how many times will it chime in a month of 30 days?

Solve each problem . (Modeling) Investment for Retirement According to T. Rowe Price Associates, a person who has a moderate investment strategy and \(n\) years until retirement should have accumulated savings of \(a_{n}\) percent of his or her annual salary. The geometric sequence $$ a_{n}=1276(0.916)^{n} $$ gives the appropriate percent for each year \(n\) (a) Find \(a_{1}\) and \(r\) (b) Find and interpret the terms \(a_{10}\) and \(a_{20}\)

Use any or all of the methods described in this section to solve each problem. Keys How many distinguishable ways can 4 keys be put on a circular key ring? (Hint: Consider that clockwise and counterclockwise arrangements are not different.)

Use summation notation to write each series. Start the index at \(i=1\). $$\frac{2}{5(1)}+\frac{2}{5(2)}+\frac{2}{5(3)}+\dots+\frac{2}{5(100)}$$

Solve each problem. Telephone Pole Stack \(\quad\) A stack of telephone poles has 30 in the bottom row, 29 in the next, and so on, with one pole in the top row. How many poles are in the stack?

Use any or all of the methods described in this section to solve each problem. Sitting at a Round Table How many ways can 7 people sit at a round table? Assume that a different way means that at least 1 person is sitting next to someone different.

Use summation notation to write each series. Start the index at \(i=1\). $$\frac{1}{1+1}+\frac{2}{2+1}+\frac{3}{3+1}+\dots+\frac{25}{25+1}$$

Solve each problem. Population Growth Five years ago, the population of a city was \(49,000 .\) Each year, the zoning commission permits an increase of 580 in the population. What will the maximum population be 5 years from now?