Mathematical Excursions (MindTap Course List)
4th Edition
ISBN: 9781305965584
Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg
Publisher: Cengage Learning
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Chapter 2.1, Problem 49ES
To determine
(a)
To determine the sets using roster method.
To determine
(b)
To determine the sets using roster method.
To determine
(c)
To determine the sets using roster method.
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Directions: For problems 1 through 3, read each question carefully and be sure to show all work.
1. What is the phase shift for y = 2sin(2x-)?
2. What is the amplitude of y = 7cos(2x+л)?
3. What is the period of y = sin(3x-π)?
Directions: For problems 4 and 5, you were to compare and contrast the two functions in each problem situation. Be sure to
include a discussion of similarities and differences for the periods, amplitudes, y-minimums, y-maximums, and any phase shift
between the two graphs. Write in complete sentences.
4. y 3sin(2x) and y = 3cos(2x)
5. y 4sin(2x) and y = cos(3x- -플)
A graph G of order 12 has vertex set V(G) = {c1, c2, …, c12} for the twelve configurations inFigure 1.4. A “move” on this checkerboard corresponds to moving a single coin to anunoccupied square, where(1) the gold coin can only be moved horizontally or diagonally,(2) the silver coin can only be moved vertically or diagonally.Two vertices ci and cj (i ≠ j) are adjacent if it is possible to move ci to cj by a single move.
(a) What vertices are adjacent to c1 in G?(c) Draw the subgraph of G induced by {c2, c6, c9, c11}.
i) Consider the set S = {−6, −3, 0, 3, 6}. Draw a graph G whose set of verti-
ces be S and such that for i, j ∈ S, ij ∈ E(G) if ij are related to a rule that t'u
you choose to apply to i and j.
(ii) A graph G of order 12 has as a set of vertices c1, c2, . . . , c12 for the do-
ce configurations of figure 1. A movement on said board corresponds to moving a
coin to an unoccupied square using the following two rules:
1. the gold coin can move only horizontally or diagonally,
2. the silver coin can move only vertically or diagonally.
Two vertices ci, cj, i̸ = j are adjacent if it is possible to move ci to cj in a single movement.
a) What vertices are adjacent to c1 in G?
b) Draw the subgraph induced by {c2, c6, c9, c11}
Chapter 2 Solutions
Mathematical Excursions (MindTap Course List)
Ch. 2.1 - Mark, Erica, Larry, and Jennifer have each defined...Ch. 2.1 - In some fuzzy sets, membership values are given by...Ch. 2.1 - The following membership graph provides a...Ch. 2.1 - The membership graphs in the following figure...Ch. 2.1 - The membership graph in Excursion Exercise 2 shows...Ch. 2.1 - Prob. 1ESCh. 2.1 - Prob. 2ESCh. 2.1 - Prob. 3ESCh. 2.1 - Prob. 4ESCh. 2.1 - Prob. 5ES
Ch. 2.1 - Prob. 6ESCh. 2.1 - Prob. 7ESCh. 2.1 - Prob. 8ESCh. 2.1 - Prob. 9ESCh. 2.1 - Prob. 10ESCh. 2.1 - Prob. 11ESCh. 2.1 - Prob. 12ESCh. 2.1 - In Exercises I to 14, use the roster method to...Ch. 2.1 - Prob. 14ESCh. 2.1 - Prob. 15ESCh. 2.1 - In Exercises 15 to 24, write a word description of...Ch. 2.1 - In Exercises 15 to 24, write a word description of...Ch. 2.1 - In Exercises 15 to 24, write a word description of...Ch. 2.1 - Prob. 19ESCh. 2.1 - Prob. 20ESCh. 2.1 - Prob. 21ESCh. 2.1 - Prob. 22ESCh. 2.1 - Prob. 23ESCh. 2.1 - Prob. 24ESCh. 2.1 - In Exercises 25 to 36, determine whether each...Ch. 2.1 - Prob. 26ESCh. 2.1 - Prob. 27ESCh. 2.1 - Prob. 28ESCh. 2.1 - Prob. 29ESCh. 2.1 - In Exercises 25 to 36, determine whether each...Ch. 2.1 - Prob. 31ESCh. 2.1 - Prob. 32ESCh. 2.1 - Prob. 33ESCh. 2.1 - Prob. 34ESCh. 2.1 - Prob. 35ESCh. 2.1 - Prob. 36ESCh. 2.1 - Prob. 37ESCh. 2.1 - Prob. 38ESCh. 2.1 - Prob. 39ESCh. 2.1 - Prob. 40ESCh. 2.1 - In Exercises 37 to 48, use set-builder notation to...Ch. 2.1 - Prob. 42ESCh. 2.1 - Prob. 43ESCh. 2.1 - Prob. 44ESCh. 2.1 - Prob. 45ESCh. 2.1 - Prob. 46ESCh. 2.1 - Prob. 47ESCh. 2.1 - Prob. 48ESCh. 2.1 - Prob. 49ESCh. 2.1 - Prob. 50ESCh. 2.1 - Prob. 51ESCh. 2.1 - Prob. 52ESCh. 2.1 - Prob. 53ESCh. 2.1 - Prob. 54ESCh. 2.1 - Prob. 55ESCh. 2.1 - Prob. 56ESCh. 2.1 - Prob. 57ESCh. 2.1 - Prob. 58ESCh. 2.1 - Prob. 59ESCh. 2.1 - Prob. 60ESCh. 2.1 - Prob. 61ESCh. 2.1 - Prob. 62ESCh. 2.1 - Prob. 63ESCh. 2.1 - In Exercises 63 to 70, state whether each of the...Ch. 2.1 - In Exercises 63 to 70, state whether each of the...Ch. 2.1 - Prob. 66ESCh. 2.1 - Prob. 67ESCh. 2.1 - Prob. 68ESCh. 2.1 - Prob. 69ESCh. 2.1 - Prob. 70ESCh. 2.1 - Prob. 71ESCh. 2.1 - Prob. 72ESCh. 2.1 - Prob. 73ESCh. 2.1 - Prob. 74ESCh. 2.1 - Prob. 75ESCh. 2.1 - Prob. 76ESCh. 2.1 - Prob. 77ESCh. 2.1 - Prob. 78ESCh. 2.1 - Prob. 79ESCh. 2.1 - Prob. 80ESCh. 2.1 - Prob. 81ESCh. 2.1 - Prob. 82ESCh. 2.1 - In Exercises 83 to 86, use the extension of...Ch. 2.1 - Prob. 84ESCh. 2.1 - Prob. 85ESCh. 2.1 - Prob. 86ESCh. 2.1 - Prob. 87ESCh. 2.1 - Prob. 88ESCh. 2.1 - Prob. 89ESCh. 2.1 - Prob. 90ESCh. 2.2 - Let K = {(1, 0.4), (2, 0.6), (3,0.8), (4, 1)) and...Ch. 2.2 - Prob. 2EECh. 2.2 - Prob. 3EECh. 2.2 - Prob. 4EECh. 2.2 - Prob. 5EECh. 2.2 - Prob. 1ESCh. 2.2 - Prob. 2ESCh. 2.2 - Prob. 3ESCh. 2.2 - Prob. 4ESCh. 2.2 - Prob. 5ESCh. 2.2 - Prob. 6ESCh. 2.2 - Prob. 7ESCh. 2.2 - Prob. 8ESCh. 2.2 - Prob. 9ESCh. 2.2 - Prob. 10ESCh. 2.2 - Prob. 11ESCh. 2.2 - Prob. 12ESCh. 2.2 - Prob. 13ESCh. 2.2 - Prob. 14ESCh. 2.2 - Prob. 15ESCh. 2.2 - Prob. 16ESCh. 2.2 - Prob. 17ESCh. 2.2 - Prob. 18ESCh. 2.2 - Prob. 19ESCh. 2.2 - Prob. 20ESCh. 2.2 - Prob. 21ESCh. 2.2 - Prob. 22ESCh. 2.2 - Prob. 23ESCh. 2.2 - Prob. 24ESCh. 2.2 - Prob. 25ESCh. 2.2 - Prob. 26ESCh. 2.2 - Prob. 27ESCh. 2.2 - Prob. 28ESCh. 2.2 - Prob. 29ESCh. 2.2 - Prob. 30ESCh. 2.2 - Prob. 31ESCh. 2.2 - Prob. 32ESCh. 2.2 - Prob. 33ESCh. 2.2 - Prob. 34ESCh. 2.2 - Prob. 35ESCh. 2.2 - Prob. 36ESCh. 2.2 - Prob. 37ESCh. 2.2 - Prob. 38ESCh. 2.2 - Prob. 39ESCh. 2.2 - Prob. 40ESCh. 2.2 - Prob. 41ESCh. 2.2 - Prob. 42ESCh. 2.2 - Prob. 43ESCh. 2.2 - Prob. 44ESCh. 2.2 - Prob. 45ESCh. 2.2 - Prob. 46ESCh. 2.2 - Prob. 47ESCh. 2.2 - Prob. 48ESCh. 2.2 - Prob. 49ESCh. 2.2 - Prob. 50ESCh. 2.2 - Prob. 51ESCh. 2.2 - In Exercises 47 to 54, find the number of subsets...Ch. 2.2 - Prob. 53ESCh. 2.2 - Prob. 54ESCh. 2.2 - Suppose you have a nickel, two dimes, and a...Ch. 2.2 - Prob. 56ESCh. 2.2 - Sandwich Choices A delicatessen makes a...Ch. 2.2 - Upgrade Options A company that builds homes...Ch. 2.2 - Omelet Choices A restaurant provides a brunch...Ch. 2.2 - Truck Options A truck company makes a pickup truck...Ch. 2.2 - Prob. 61ESCh. 2.2 - Prob. 62ESCh. 2.2 - Voting Coalitions Five people, designated A, B, C,...Ch. 2.2 - Prob. 64ESCh. 2.3 - En Excursion Exercise I of Section 2.1, we defined...Ch. 2.3 - En Excursion Exercise I of Section 2.1, we defined...Ch. 2.3 - Prob. 3EECh. 2.3 - En Excursion Exercise I of Section 2.1, we defined...Ch. 2.3 - Prob. 5EECh. 2.3 - Prob. 6EECh. 2.3 - Prob. 7EECh. 2.3 - Prob. 1ESCh. 2.3 - Prob. 2ESCh. 2.3 - Prob. 3ESCh. 2.3 - Prob. 4ESCh. 2.3 - Prob. 5ESCh. 2.3 - Prob. 6ESCh. 2.3 - Prob. 7ESCh. 2.3 - Prob. 8ESCh. 2.3 - Prob. 9ESCh. 2.3 - Prob. 10ESCh. 2.3 - Prob. 11ESCh. 2.3 - Prob. 12ESCh. 2.3 - Prob. 13ESCh. 2.3 - Prob. 14ESCh. 2.3 - Prob. 15ESCh. 2.3 - Prob. 16ESCh. 2.3 - Prob. 17ESCh. 2.3 - Prob. 18ESCh. 2.3 - Prob. 19ESCh. 2.3 - Prob. 20ESCh. 2.3 - Prob. 21ESCh. 2.3 - Prob. 22ESCh. 2.3 - Prob. 23ESCh. 2.3 - Prob. 24ESCh. 2.3 - In Exercises 21 to 28, write a sentence that...Ch. 2.3 - Prob. 26ESCh. 2.3 - Prob. 27ESCh. 2.3 - Prob. 28ESCh. 2.3 - Prob. 29ESCh. 2.3 - Prob. 30ESCh. 2.3 - Prob. 31ESCh. 2.3 - Prob. 32ESCh. 2.3 - Prob. 33ESCh. 2.3 - Prob. 34ESCh. 2.3 - Prob. 35ESCh. 2.3 - Prob. 36ESCh. 2.3 - Prob. 37ESCh. 2.3 - Prob. 38ESCh. 2.3 - Prob. 39ESCh. 2.3 - Prob. 40ESCh. 2.3 - Prob. 41ESCh. 2.3 - Prob. 42ESCh. 2.3 - Prob. 43ESCh. 2.3 - Prob. 44ESCh. 2.3 - Prob. 45ESCh. 2.3 - Prob. 46ESCh. 2.3 - Prob. 47ESCh. 2.3 - Prob. 48ESCh. 2.3 - Prob. 49ESCh. 2.3 - Subtractive Color Mixing Artists who paint with...Ch. 2.3 - Prob. 51ESCh. 2.3 - Subtractive Color Mixing Artists who paint with...Ch. 2.3 - Prob. 53ESCh. 2.3 - Prob. 54ESCh. 2.3 - Prob. 55ESCh. 2.3 - Prob. 56ESCh. 2.3 - Prob. 57ESCh. 2.3 - Prob. 58ESCh. 2.3 - Prob. 59ESCh. 2.3 - Prob. 60ESCh. 2.3 - Prob. 61ESCh. 2.3 - Prob. 62ESCh. 2.3 - A Survey Aspecial interest group plans to conduct...Ch. 2.3 - A Music Survey Theadministrators of an Internet...Ch. 2.3 - Prob. 65ESCh. 2.3 - Prob. 66ESCh. 2.3 - Prob. 67ESCh. 2.3 - Prob. 68ESCh. 2.3 - Prob. 69ESCh. 2.3 - Prob. 70ESCh. 2.3 - Prob. 71ESCh. 2.3 - Prob. 72ESCh. 2.3 - Prob. 73ESCh. 2.3 - Prob. 74ESCh. 2.3 - Prob. 75ESCh. 2.3 - Prob. 76ESCh. 2.3 - Prob. 77ESCh. 2.3 - Prob. 78ESCh. 2.3 - Prob. 79ESCh. 2.3 - In an article in New Scientist magazine, Anthony...Ch. 2.4 - A selection committee consists of Ryan, Susan. and...Ch. 2.4 - A selection committee consists of three people...Ch. 2.4 - Determine the minimal winning coalitions for the...Ch. 2.4 - Prob. 1ESCh. 2.4 - Prob. 2ESCh. 2.4 - In Exercises I to 10, let U = English, French,...Ch. 2.4 - Prob. 4ESCh. 2.4 - Prob. 5ESCh. 2.4 - Prob. 6ESCh. 2.4 - In Exercises I to 10, let U = English, French,...Ch. 2.4 - Prob. 8ESCh. 2.4 - Prob. 9ESCh. 2.4 - Prob. 10ESCh. 2.4 - Prob. 11ESCh. 2.4 - Prob. 12ESCh. 2.4 - Prob. 13ESCh. 2.4 - Prob. 14ESCh. 2.4 - Prob. 15ESCh. 2.4 - Given n(A) = 640, n(B) = 280, and n(A U B) = 765,...Ch. 2.4 - Prob. 17ESCh. 2.4 - In Exercises 17 and 18, use the given information...Ch. 2.4 - In a surveyof 600 investors, it was reported that...Ch. 2.4 - Commuting A survey of 1500 commuters in New York...Ch. 2.4 - A team physician has determined that of all the...Ch. 2.4 - The management of a hotel conducted a survey. ft...Ch. 2.4 - A computer company advertises its computers in PC...Ch. 2.4 - During one month, a blood donation center found...Ch. 2.4 - A special interest group has conducted a survey...Ch. 2.4 - A survey of college students was taken to...Ch. 2.4 - A survey was completed by individuals who were...Ch. 2.4 - Prob. 28ESCh. 2.4 - Prob. 29ESCh. 2.4 - Prob. 30ESCh. 2.4 - Prob. 31ESCh. 2.4 - Prob. 32ESCh. 2.5 - Use two disjoint sets to show that 0+2=0.Ch. 2.5 - Prob. 2EECh. 2.5 - Use sets toshow that 06=0.Ch. 2.5 - Prob. 1ESCh. 2.5 - Establish a one-to-one correspondence between the...Ch. 2.5 - Establish a one-to-one correspondence between D =...Ch. 2.5 - Prob. 4ESCh. 2.5 - Prob. 5ESCh. 2.5 - In Exercises 4 to 10, state the cardinality of...Ch. 2.5 - Prob. 7ESCh. 2.5 - Prob. 8ESCh. 2.5 - Prob. 9ESCh. 2.5 - Prob. 10ESCh. 2.5 - Prob. 11ESCh. 2.5 - In Exercises 11 to 14, determine whether the given...Ch. 2.5 - Prob. 13ESCh. 2.5 - Prob. 14ESCh. 2.5 - Prob. 15ESCh. 2.5 - In Exercises 15 to 18, show that the given set is...Ch. 2.5 - Prob. 17ESCh. 2.5 - Prob. 18ESCh. 2.5 - In Exercises 19 to 26, show that the given set has...Ch. 2.5 - Prob. 20ESCh. 2.5 - Prob. 21ESCh. 2.5 - In Exercises 19 to 26, show that the given set has...Ch. 2.5 - Prob. 23ESCh. 2.5 - In Exercises 19 to 26, show that the given set has...Ch. 2.5 - In Exercises 19 to 26, show that the given set has...Ch. 2.5 - In Exercises 19 to 26, show that the given set has...Ch. 2.5 - Prob. 27ESCh. 2.5 - Prob. 28ESCh. 2.5 - Prob. 29ESCh. 2.5 - The Hubert Hotel is an imaginary hotel created by...Ch. 2 - Prob. 1RECh. 2 - In Exercises 1 to 6, use the roster method to...Ch. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Prob. 31RECh. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - Prob. 35RECh. 2 - Prob. 36RECh. 2 - In Exercises 35 to 38, find the number of subsets...Ch. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - Prob. 40RECh. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Prob. 49RECh. 2 - Prob. 50RECh. 2 - Prob. 51RECh. 2 - Prob. 52RECh. 2 - In a survey at a health club, 208 members...Ch. 2 - A gourmet coffee bar conducted a survey to...Ch. 2 - Prob. 55RECh. 2 - Prob. 56RECh. 2 - Prob. 57RECh. 2 - Prob. 58RECh. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 63RECh. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - Prob. 68RECh. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Prob. 1TCh. 2 - Prob. 2TCh. 2 - Prob. 3TCh. 2 - Prob. 4TCh. 2 - Prob. 5TCh. 2 - Prob. 6TCh. 2 - Prob. 7TCh. 2 - Prob. 8TCh. 2 - Prob. 9TCh. 2 - Prob. 10TCh. 2 - Prob. 11TCh. 2 - Prob. 12TCh. 2 - Prob. 13TCh. 2 - Prob. 14TCh. 2 - Upgrade Options An automobile company makes a...Ch. 2 - Student Demographics A college finds that 841 of...Ch. 2 - The following bar graph shows the monthly...Ch. 2 - A survey of 1000 households was taken to determine...Ch. 2 - Show a method that can be used to establish a...Ch. 2 - Prob. 20T
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