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SOLUTION MANUAL FOR USING AND UNDERSTANDING MATHEMATICS A QUANTITATIVE REASONING APPROACH 8TH EDITION BY JEFFREY BENNETT, WILLIAM BRIGGS$28.49
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,SOLUTION MANUAL FOR USING AND UNDERSTANDING
MATHEMATICS A QUANTITATIVE REASONING APPROACH
8TH EDITION BY JEFFREY BENNETT, WILLIAM BRIGGS
Table of Contents
Chapter 1: Thinking Critically
Unit 1A: Living in the Media Age ...................................................................................... 1
Unit 1B: Propositions and Truth Values ............................................................................. 4
Unit 1C: Sets and Venn Diagrams .................................................................................... 11
Unit 1D: Analyzing Arguments ........................................................................................ 21
Unit 1E: Critical Thinking in Everyday Life .....................................................................28
Chapter 1 Review Questions ............................................................................................. 32
Chapter 2: Approaches to Problem Solving
Unit 2A: Understand, Solve, and Explain ......................................................................... 35
Unit 2B: Extending Unit Analysis .................................................................................... 43
Unit 2C: Problem-Solving Hints ....................................................................................... 56
Chapter 2 Review Questions ............................................................................................. 61
Chapter 3: Numbers in the Real World
Unit 3A: Uses and Abuses of Percentages ........................................................................ 63
Unit 3B: Putting Numbers in Perspective ......................................................................... 68
Unit 3C: Dealing with Uncertainty ................................................................................... 77
Unit 3D: Index Numbers: The CPI and Beyond ............................................................... 81
Unit 3E: Numerical Surprises: Polygraphs, Mammograms, and More ............................ 86
Chapter 3 Review Questions ............................................................................................. 90
Chapter 4: Managing Money
Unit 4A: Taking Control of Your Finances ...................................................................... 93
Unit 4B: The Power of Compounding .............................................................................. 98
Unit 4C: Savings Plans and Investments ........................................................................ 108
Unit 4D: Loan Payments, Credit Cards, and Mortgages ................................................ 117
Unit 4E: Personal Income Taxes..................................................................................... 130
Unit 4F: Understanding the Federal Budget ................................................................... 138
Chapter 4 Review Questions ........................................................................................... 144
Chapter 5: Statistical Reasoning
Unit 5A: Fundamentals of Statistics ............................................................................... 147
Unit 5B: Should You Believe a Statistical Study?.......................................................... 152
Unit 5C: Statistical Tables and Graphs ........................................................................... 156
Unit 5D: Graphics in the Media ...................................................................................... 164
Unit 5E: Correlation and Causality ................................................................................. 173
Chapter 5 Review Questions ........................................................................................... 178
,Chapter 6: Putting Statistics to Work
Unit 6A: Characterizing Data ......................................................................................... 181
Unit 6B: Measures of Variation ...................................................................................... 187
Unit 6C: The Normal Distribution .................................................................................. 192
Unit 6D: Statistical Inference .......................................................................................... 198
Chapter 6 Review Questions ........................................................................................... 202
Chapter 7: Probability: Living with the Odds
Unit 7A: Fundamentals of Probability ............................................................................ 205
Unit 7B: Combining Probabilities .................................................................................. 210
Unit 7C: The Law of Large Numbers ............................................................................. 215
Unit 7D: Assessing Risk ................................................................................................. 220
Unit 7E: Counting and Probability ................................................................................. 225
Chapter 7 Review Questions ........................................................................................... 230
Chapter 8: Exponential Astonishment
Unit 8A: Growth: Linear vs. Exponential ....................................................................... 233
Unit 8B: Doubling Time and Half-Life .......................................................................... 236
Unit 8C: Real Population Growth ................................................................................... 243
Unit 8D: Logarithmic Scales: Earthquakes, Sounds, and Acids ..................................... 248
Chapter 8 Review Questions ........................................................................................... 252
Chapter 9: Modeling Our World
Unit 9A: Functions: The Building Blocks of Mathematical Models .............................. 255
Unit 9B: Linear Modeling ............................................................................................... 262
Unit 9C: Exponential Modeling ...................................................................................... 269
Chapter 9 Review Questions ........................................................................................... 279
Chapter 10: Modeling with Geometry
Unit 10A: Fundamentals of Geometry ............................................................................ 281
Unit 10B: Problem Solving with Geometry .................................................................... 286
Unit 10C: Fractal Geometry ............................................................................................ 294
Chapter 10 Review Questions ......................................................................................... 299
Chapter 11: Mathematics and the Arts
Unit 11A: Mathematics and Music ................................................................................. 301
Unit 11B: Perspective and Symmetry ............................................................................. 304
Unit 11C: Proportion and the Golden Ratio .................................................................... 308
Chapter 11 Review Questions ......................................................................................... 311
Chapter 12: Mathematics and Politics
Unit 12A: Voting: Does the Majority Always Rule?. ..................................................... 313
Unit 12B: Theory of Voting ............................................................................................ 320
Unit 12C: Apportionment: The House of Representatives and Beyond ......................... 325
Unit 12D: Dividing the Political Pie ............................................................................... 340
Chapter 12 Review Questions ......................................................................................... 345
, UNIT 1A: LIVING IN THE MEDIA AGE 1
UNIT 1A: LIVING IN THE MEDIA AGE
THINK ABOUT IT
Pg. 21. Not guilty does not mean innocent; it means not enough evidence to prove guilt. If defendants were required
to prove innocence, there would be many cases where they would be unable to provide such proof even though
they were, in fact, innocent. This relates to the fallacy of appeal to ignorance in the sense that lack of proof of
guilt does not mean innocence, and lack of proof of innocence does not mean guilt.
Pg. 23. Opinions will vary. One argument is that character questions should be allowed in court if answers to those
questions may show bias or ulterior motives for testimony given by a witness. This would be a good topic for a
discussion either during or outside of class.
QUICK QUIZ
QQ1. a. By the definition used in this book, an argument always contains at least one premise and a conclusion.
QQ2. c. By definition, a fallacy is a deceptive argument.
QQ3. b. An argument must contain a conclusion.
QQ4. a. Circular reasoning is an argument where the premise and the conclusion say essentially the same thing.
QQ5. b. Using the fact that a statement is unproved to imply that it is false is appeal to ignorance.
QQ6. b. “I don’t support the President’s tax plan” is the conclusion because the premise “I don’t trust his motives”
supports that conclusion.
QQ7. b. This is a personal attack because the premise (I don’t trust his motives) attacks the character of the
President, and says nothing about the substance of his tax plan.
QQ8. c. This is limited choice because the argument does not allow for the possibility that you are a fan of, say,
boxing.
QQ9. b. Just because A preceded B does not necessarily imply that A caused B.
QQ10. a. By definition, a straw man is an argument that distorts (or misrepresents) the real issue.
READING QUESTIONS
1. Logic is the study of the methods and principles of reasoning. Arguing logically may or may not change a
person’s position, but it can give either person insight into the other’s thinking.
2. An argument refers to a reasoned or thoughtful process. An argument uses a set of facts or assumptions, called
premises, to support a conclusion.
3. A fallacy is an argument in which the conclusion is not well supported by the premises. The examples of
fallacies given in the text are appeal to popularity, false cause, appeal to ignorance, hasty generalization,
limited choice, appeal to emotion, personal attack, circular reasoning, diversion (red herring), and straw man.
Examples will vary.
4. The five steps (See the information box on page 24 in the text for a summary of each step.) to evaluating media
information are:
1. Consider the source.
2. Check the date.
3. Validate accuracy.
4. Watch for hidden agendas.
5. Don’t miss the big picture.
DOES IT MAKE SENSE?
5. Does not make sense. Raising one’s voice has nothing to do with logical arguments.
6. Does not make sense. Logical arguments always contain at least one premise and a conclusion.
7. Makes sense. A logical person would not put much faith in an argument that uses premises he believes to be
false to support a conclusion.
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