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mathematics
college algebra
College Algebra 12th edition Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels - Solutions
Fill in the blank(s) to correctly complete each sentence.When a fair coin is tossed, there are ___________possible outcomes, and the probability of each outcome is ________.
Prove each statement for positive integers n and r, with r ≤ n.Explain why the restriction r ≤ n is needed in the formulas for C(n, r) and P(n, r).
Prove the statement for positive integers n and r, with r ≤ n.C(n, n - r) = C(n, r)
Prove the statement for positive integers n and r, with r ≤ n.C(n, n - 1) = n
Prove each statement for positive integers n and r, with r ≤ n.C(0, 0) = 1
Prove each statement for positive integers n and r, with r ≤ n.C(n, 0) = 1
Prove each statement for positive integers n and r, with r ≤ n.C(n, n) = 1
Prove the statement for positive integers n and r, with r ≤ n.P(n, n) = n!
Prove the statement for positive integers n and r, with r ≤ n.P(n, 0) = 1
Prove the statement for positive integers n and r, with r ≤ n.P(n, 1) = n
Prove the statement for positive integers n and r, with r ≤ n.P(n, n - 1) = P(n, n)
In how many different ways can 8 people sit at a round table? Assume that “a different way” means that at least 1 person is sitting next to someone different.
In how many distinguishable ways can 4 keys be put on a circular key ring?
To win the jackpot in a lottery game, a person must pick 4 numbers from 0 to 9 in the correct order. If a number can be repeated, how many ways are there to play the game?
Use any method described in this section to solve each problem.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?
Use any method described in this section to solve each problem.A typical “combination” for a padlock consists of 3 numbers from 0 to 39. Find the number of “combinations” that are possible with this type of lock, if a number may be repeated.
Use any method described in this section to solve each problem.A briefcase has 2 locks. The combination to each lock consists of a 3-digit number, where digits may be repeated. How many combinations are possible? 123
Use any method described in this section to solve each problem.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?
Use any method described in this section to solve the problem.In a club with 8 women and 11 men members, how many 5-member committees can be chosen that satisfy the following conditions?(a) All are women. (b) All are men.(c) There are 3 women and 2 men. (d) There are no more than 3 men.
Use any method described in this section to solve the problem.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 this be done if exactly 2
In a game of musical chairs, 13 children will sit in 12 chairs. (1 will be left out.) How many seating arrangements are possible?
Use any method described in this section to solve each problem.From a pool of 7 secretaries, 3 are selected to be assigned to 3 managers, 1 secretary to each manager. In how many ways can this be done?
Zelma 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?
How many samples of 9 pineapples can be drawn from a crate of 12?
If Dwight has 8 courses to choose from, how many ways can he arrange his schedule if he must pick 4 of them?
Solve the problem involving combinations.Seven workers decide to send a delegation of 2 to their supervisor to discuss their grievances.(a) How many different delegations are possible?(b) If it is decided that a certain employee must be in the delegation, how many different delegations are
Solve the problem involving combinations.A city council is composed of 5 liberals and 4 conservatives. Three members are to be selected randomly as delegates to a convention.(a) How many delegations are possible?(b) How many delegations could have all liberals?(c) How many delegations could have 2
Solve the problem involving combinations.In Exercise 59, if the bag contains 3 yellow, 4 white, and 8 blue marbles, how many samples of 2 can be drawn in which both marbles are blue?Exercise 59If a bag contains 15 marbles, how many samples of 2 marbles can be drawn from it? How many samples of 4
Solve the problem involving combinations.If a bag contains 15 marbles, how many samples of 2 marbles can be drawn from it? How many samples of 4 marbles can be drawn?
Solve the problem involving combinations.Five playing cards having the numbers 2, 3, 4, 5, and 6 are shuffled and 2 cards are then drawn. How many different 2-card hands are possible?
Solve the problem involving combinations.Howard’s Hamburger Heaven sells hamburgers with cheese, relish, lettuce, tomato, mustard, or ketchup.(a) How many different hamburgers can be made that use any 4 of the extras?(b) How many different hamburgers can be made if one of the 4 extras must be
Solve the problem involving combinations.Suppose that in Exercise 55 there are 5 rotten apples in the crate.(a) How many samples of 3 could be drawn in which all 3 are rotten?(b) How many samples of 3 could be drawn in which there are 2 good apples and 1 rotten apple?
Solve the problem involving combinations.How many different samples of 4 apples can be drawn from a crate of 25 apples?
Solve the problem involving combinations.Four financial planners are to be selected from a group of 12 to participate in a special program. In how many ways can this be done? In how many ways can the group that will not participate be selected?
Solve the problem involving combinations.banker’s association has 40 members. If 6 members are selected at random to present a seminar, how many different groups of 6 are possible?
Use the fundamental principle of counting or permutations to solve the problem.In how many ways can 5 players be assigned to the 5 positions on a basketball team, assuming that any player can play any position? In how many ways can 10 players be assigned to the 5 positions?
Use the fundamental principle of counting or permutations to the each problem.Consider the word BRUCE.(a) In how many ways can all the letters of the word BRUCE be arranged?(b) In how many ways can all the first 3 letters of the word BRUCE be arranged?
Use the fundamental principle of counting or permutations to solve the problem.A baseball team has 20 players. How many 9-player batting orders are possible?
Use the fundamental principle of counting or permutations to solve the problem.In a club with 15 members, in how many ways can a slate of 3 officers consisting of president, vice-president, and secretary/treasurer be chosen?
Use the fundamental principle of counting or permutations to solve the problem.If your college offers 400 courses, 20 of which are in mathematics, and your counselor arranges your schedule of 4 courses by random selection, how many schedules are possible that do not include a math course?
Use the fundamental principle of counting or permutations to solve the problem.A business school offers courses in keyboarding, spreadsheets, transcription, business English, technical writing, and accounting. In how many ways can a student arrange a schedule if 3 courses are taken?
Use the fundamental principle of counting or permutations to solve the problem.In how many ways can 7 of 10 rats be arranged in a row for a genetics experiment?
Use the fundamental principle of counting or permutations to solve the problem.In an experiment on social interaction, 9 people will sit in 9 seats in a row. In how many ways can this be done?
Use the fundamental principle of counting or permutations to solve the problem.How many 7-digit telephone numbers are possible if the first digit cannot be 0 and the following conditions apply?(a) Only odd digits may be used.(b) The telephone number must be a multiple of 10 (that is, it must end in
Use the fundamental principle of counting or permutations to solve the problem.For many years, the state of California used 3 letters followed by 3 digits on its automobile license plates.(a) How many different license plates are possible with this arrangement?(b) When the state ran out of new
Use the fundamental principle of counting or permutations to solve the problem.A couple has narrowed down the choice of a name for their new baby to 5 first names and 3 middle names. How many different first- and middle-name combinations are possible?
Use the fundamental principle of counting or permutations to solve the problem.Baby Finley is arranging 7 blocks in a row. How many different arrangements can he make? Finley
Use the fundamental principle of counting or permutations to solve the problem.A menu offers a choice of 3 salads, 8 main dishes, and 5 desserts. How many different 3-course meals (salad, main dish, dessert) are possible?
Use the fundamental principle of counting or permutations to solve the problem.How many different 4-letter radio-station call letters can be made under the following conditions? (Disregard the fact that some may be unacceptable for various reasons.)(a) The first letter must be K or W, and no letter
Use the fundamental principle of counting or permutations to solve the problem.An auto manufacturer produces 7 models, each available in 6 different colors, with 4 different upholstery fabrics, and 5 interior colors. How many varieties of the auto are available?
Use the fundamental principle of counting or permutations to solve the problem.How many different types of homes are available if a builder offers a choice of 5 basic plans, 4 roof styles, and 2 exterior finishes?
What is the difference between a permutation and a combination? Give an example of each.
Decide whether the situation described involves a permutation or a combination of objects.(a) A telephone number (b) A Social Security number(c) A hand of cards in poker (d) A committee of politicians(e) The “combination” on a padlock (f) An automobile license plate(g) A lottery
Use a calculator to evaluate the expression.32C4
Use a calculator to evaluate the expression.15C8
Use a calculator to evaluate the expression.100C5
Use a calculator to evaluate the expression.20C5
Use a calculator to evaluate the expression.32P4
Use a calculator to evaluate the expression.15P8
Use a calculator to evaluate the expression.100P5
Use a calculator to evaluate the expression.20P5
Evaluate the expression.C(16, 3)
Evaluate the expression.C(12, 4)
Evaluate the expression.C(8, 0)
Evaluate the expression.C(6, 0)
Evaluate the expression.C(9, 3)
Evaluate the expression.C(4, 2)
Evaluate the expression.P(6, 1)
Evaluate the expression.P(5, 1)
Evaluate the expression.P(10, 4)
Evaluate the expression.P(9, 2)
Evaluate the expression.P(5, 2)
Evaluate the expression.P(12, 2)
Use the fundamental principle of counting to the each problem.In how many different ways can 4 different boys be selected from a group of 25 boys on a track team to receive 4 different awards?
Use the fundamental principle of counting to the each problem.In how many ways can judges select a 1st-place winner, a 2nd-place winner, and a 3rd-place winner from 16 desserts entered in a cooking contest?
Use the fundamental principle of counting to solve the problem.A telephone messaging system requires a 4-digit security code. How many security codes are possible if numbers may be repeated?
Use the fundamental principle of counting to solve the problem.A college has 7 portraits of past college presidents to arrange in a row on a wall. How many different arrangements are possible?
Use the fundamental principle of counting to solve the problem.A convenience store offers 16 types of soda with 4 options for flavoring and either crushed or cubed ice. Determine the total number of drink options available for selecting 1 soda with 1 flavor and 1 type of ice.
Use the fundamental principle of counting to solve each problem.A conference schedule offers 2 main sessions, 20 break-out sessions, and 4 mini courses. In how many ways can an attendee choose 1 of each to attend?
Use the fundamental principle of counting to the each problem.When saddling her horse, Callie can choose from 2 saddles, 3 blankets, and 2 cinches. Find the number of possible choices for saddling Callie’s horse.
Use the fundamental principle of counting to solve the problem.On a business trip, Terry took 3 pairs of pants, 4 shirts, 1 jacket, and two pairs of shoes. Determine the number of outfits that Terry can choose.
Use the fundamental principle of counting to solve each problem.On a business trip, Terry took 3 pairs of pants, 4 shirts, 1 jacket, and two pairs of shoes. Determine the number of outfits that Terry can choose.
Fill in the blank(s) to correctly complete each sentence.When a fair die is rolled and a fair coin is tossed, there are ________ possible outcomes.
Fill in the blank(s) to correctly complete each sentence.If there are 3 people to choose from, there are ______ ways to choose a pair of them.
Fill in the blank(s) to correctly complete each sentence.There ______ are ways to form a three-digit number consisting of the digits 4, 5, and 9.
Fill in the blank(s) to correctly complete each sentence.If there are 3 ways to choose a salad, 5 ways to choose an entree, and 4 ways to choose a dessert, then there are ______ ways to form a meal consisting of these three choices.
Fill in the blank(s) to correctly complete each sentence.From the two choices permutation and combination, a computer password is an example of a _______ and a hand of cards is an example of a _______ .
Solve the problem.Evaluate each expression. 10 (b) 4 4 |(a) 9!
Solve the problem.Find the fifth term of the binomial expansion of (4x - 1/2 y)5.
Solve the problem.Write the binomial expansion of (x - 3y)5.
Solve the problem.Evaluate each sum that converges. Identify any that diverge. 30 (a) Σ(-3i + 6) (b) Σ (c) i=1 i=1 i=1
Solve the problem.Find the sum of the first ten terms of each series described.(a) arithmetic, a1 = -20, d = 14 (b) geometric, a1 = -20, r = -1/2
Solve the problem.An arithmetic sequence has a1 = -6 and a9 = 18. Find a7.
Write the first five terms of the sequence. State whether the sequence is arithmetic, geometric, or neither.a1 = 5, a2 = 3, an = an-1 + 3an-2, for n ≥ 3
Write the first five terms of the sequence. State whether the sequence is arithmetic, geometric, or neither. -2 an 2)
Write the first five terms of each sequence. State whether the sequence is arithmetic, geometric, or neither.an = -4n + 2
Prove the result of Exercise 37 using mathematical induction.
A pile of n rings, each ring smaller than the one below it, is on a peg. Two other pegs are attached to a board with this peg. In the game called the Tower of Hanoi puzzle, all the rings must be moved to a different peg, with only one ring moved at a time, and with no ring ever placed on top of a
Show that the area of the nth figure in Exercise 34 isExercise 34 vi n- 3 V3 20
Find the perimeter of the nth figure in Exercise 34.Exercise 34.
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