A SURVEY OF MATHEMATICS

SOLUTIONS

MANUAL

TAMSEN HERRICK

A SURVEY OF MATHEMATICS

WITH APPLICATIONS

NINTH EDITION

Allen R. Angel Christine D. Abbott Dennis C. Runde By 1 / 4

Table of Contents

CHAPTER 1 CRITICAL THINKING SKILLS

1.1 Inductive Reasoning 1 1.2 Estimation 3 1.3 Problem Solving 5 Review Exercises 12 Chapter Test 14 Group Projects 16

CHAPTER 2 SETS

2.1 Set Concepts 17 2.2 Subsets 19 2.3 Venn Diagrams and Set Operations 21 2.4 Venn Diagrams With Three Sets and Verification of Equality of Sets 27 2.5 Applications of Sets 37 2.6 Infinite Sets 40 Review Exercises 41 Chapter Test 44 Group Projects 46

CHAPTER 3 LOGIC

3.1 Statements and Logical Connectives 47 3.2 Truth Tables for Negation, Conjunction, and Disjunction 49 3.3 Truth Tables for the Conditional and Biconditional 56 3.4 Equivalent Statements 64 3.5 Symbolic Arguments 73 3.6 Euler Diagrams and Syllogistic Arguments 80 3.7 Switching Circuits 82 Review Exercises 85 Chapter Test 92 Group Projects 94

CHAPTER 4 SYSTEMS OF NUMERATION

4.1 Additive, Multiplicative, and Ciphered Systems of Numeration 95 4.2 Place-Value or Positional-Value Numeration Systems 98 4.3 Other Bases 101 4.4 Computation in Other Bases 108 4.5 Early Computational Methods 111 Review Exercises 115 Chapter Test 119 Group Projects 121

CHAPTER 5 NUMBER THEORY AND THE REAL NUMBER SYSTEM

5.1 Number Theory 123 5.2 The Integers 127 5.3 The Rational Numbers 129 5.4 The Irrational Numbers and the Real Number System 135 5.5 Real Numbers and Their Properties 138 5.6 Rules of Exponents and Scientific Notation 140 5.7 Arithmetic and Geometric Sequences 144 5.8 Fibonacci Sequence 148 Review Exercises 150 Chapter Test 153 Group Projects 153 Copyright © 2013 Pearson Education, Inc. 2 / 4

CHAPTER 6 ALGEBRA, GRAPHS, AND FUNCTIONS

6.1 Order of Operations 155 6.2 Linear Equations in One Variable 157 6.3 Formulas 166 6.4 Applications of Linear Equations in One Variable 176 6.5 Variation 182 6.6 Linear Inequalities 187 6.7 Graphing Linear Equations 193 6.8 Linear Inequalities in Two Variables 203 6.9 Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula 209 6.10 Functions and Their Graphs 215 Review Exercises 226 Chapter Test 238 Group Projects 241

CHAPTER 7 SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES

7.1 Systems of Linear Equations 243 7.2 Solving Systems of Equations by the Substitution and Addition Methods 250 7.3 Matrices 257 7.4 Solving Systems of Equations by Using Matrices 265 7.5 Systems of Linear Inequalities 268 7.6 Linear Programming 271 Review Exercises 275 Chapter Test 280 Group Projects 283

CHAPTER 8 THE METRIC SYSTEM

8.1 Basic Terms and Conversions Within the Metric System 285 8.2 Length, Area, and Volume 286 8.3 Mass and Temperature 288 8.4 Dimensional Analysis and Conversions to and from the Metric System 290 Review Exercises 295 Chapter Test 297 Group Projects 298

CHAPTER 9 GEOMETRY

9.1 Points, Lines, Planes, and Angles 301 9.2 Polygons 305 9.3 Perimeter and Area 310 9.4 Volume and Surface Area 314 9.5 Transformational Geometry, Symmetry, and Tessellations 318 9.6 Topology 322 9.7 Non-Euclidean Geometry and Fractal Geometry 323 Review Exercises 325 Chapter Test 329 Group Projects 330

CHAPTER 10 MATHEMATICAL SYSTEMS

10.1 Groups 331 10.2 Finite Mathematical Systems 332 10.3 Modular Arithmetic 336 Review Exercises 340 Chapter Test 343 Group Projects 345

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CHAPTER 11 CONSUMER MATHEMATICS

11.1 Percent 347 11.2 Personal Loans and Simple Interest 350 11.3 Compound Interest 353 11.4 Installment Buying 356 11.5 Buying a House with a Mortgage 363 11.6 Ordinary Annuities, Sinking Funds, and Retirement Investments 367 Review Exercises 368 Chapter Test 372 Group Projects 373

CHAPTER 12 PROBABILITY

12.1 The Nature of Probability 375 12.2 Theoretical Probability 376 12.3 Odds 379 12.4 Expected Value (Expectation) 382 12.5 Tree Diagrams 386 12.6 Or and And Problems 390 12.7 Conditional Probability 394 12.8 The Counting Principle and Permutations 397 12.9 Combinations 399 12.10 Solving Probability Problems by Using Combinations 402 12.11 Binomial Probability Formula 406 Review Exercises 407 Chapter Test 410 Group Projects 412

CHAPTER 13 STATISTICS

13.1 Sampling Techniques 413 13.2 The Misuses of Statistics 413 13.3 Frequency Distributions and Statistical Graphs 415 13.4 Measures of Central Tendency 423 13.5 Measures of Dispersion 427 13.6 The Normal Curve 433 13.7 Linear Correlation and Regression 439 Review Exercises 450 Chapter Test 455 Group Projects 457

CHAPTER 14 GRAPH THEORY

14.1 Graphs, Paths, and Circuits 459 14.2 Euler Paths and Euler Circuits 462 14.3 Hamilton Paths and Hamilton Circuits 466 14.4 Trees 472 Review Exercises 483 Chapter Test 488 Group Projects 489

CHAPTER 15 VOTING AND APPORTIONMENT

15.1 Voting Systems 491 15.2 Flaws of Voting 496 15.3 Apportionment Methods 500 15.4 Flaws of Apportionment Methods 506 Review Exercises 510 Chapter Test 514

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