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SOLUTIONS MANUAL
TAMSEN HERRICK
A SURVEY
OF MATHEMATICS
WITH APPLICATIONS
TENTH EDITION
Allen R. Angel Christine D.Abbott Dennis C. Runde 1 / 4
Table of Contents
CHAPTER 1 CRITICAL THINKING SKILLS
1.1 Inductive and Deductive Reasoning 1 1.2 Estimation 3 1.3 Problem Solving 5 Review Exercises 11 Chapter Test 14
CHAPTER 2 SETS
2.1 Set Concepts 17 2.2 Subsets 19 2.3 Venn Diagrams an d Set Operations 21 2.4 Venn Diagrams with Three Se ts and Verification of Equality of Sets 27 2.5 Applications of Sets 35 2.6 Infinite Sets 39 Review Exercises 41 Chapter Test 43
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 Con ditional and Biconditional 58 3.4 Equivalent Statements 66 3.5 Symbolic Arguments 74 3.6 Euler Diagrams and Syllogistic Arguments 80 3.7 Switching Circuits 81 Review Exercises 84 Chapter Test 91
CHAPTER 4 SYSTEMS OF NUMERATION
4.1 Additive, Multiplicative, and Ciphered Systems of Numeration 93 4.2 Place-Value or Positional- Value Numeration Systems 96 4.3 Other Bases 99 4.4 Computation in Other Bases 106 4.5 Early Computational Methods 109 Review Exercises 113 Chapter Test 117
CHAPTER 5 NUMBER THEORY AND TH E REAL NUMBER SYSTEM
5.1 Number Theory 121 5.2 The Integers 125 5.3 The Rational Numbers 128 5.4 The Irrational Numbers 133 5.5 Real Numbers and Their Properties 137 5.6 Rules of Exponents a nd Scientific Notation 139 5.7 Arithmetic and Geometric Sequences 143 5.8 Fibonacci Sequence 145 Review Exercises 147 Chapter Test 150 2 / 4
CHAPTER 6 ALGEBRA, GRAPHS, AND FUNCTIONS
6.1 Order of Operations and Solving Equations 153 6.2 Formulas 161 6.3 Applications of Algebra 169 6.4 Variation 175 6.5 Linear Inequalities 179 6.6 Graphing Linear Equations 186 6.7 Solving Systems of Linear Equations 195 6.8 Linear Inequalities and Systems of Linear Inequalities 210 6.9 Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula 221 6.10 Functions and Their Graphs 228 Review Exercises 237 Chapter Test 250
CHAPTER 7 THE METRIC SYSTEM
7.1 Basic Terms and Conversi ons Within the Metric System 255 7.2 Length, Area, and Volume 256 7.3 Mass and Temperature 258 7.4 Dimensional Analysis and Conversions to and from the Metr ic System 260 Review Exercises 265 Chapter Test 267
CHAPTER 8 GEOMETRY
8.1 Points, Lines, Planes, and Angles 269 8.2 Polygons 272 8.3 Perimeter and Area 277 8.4 Volume and Surface Area 282 8.5 Transformational Geometry, Symmetry, and Tessellations 286 8.6 Topology 289 8.7 Non-Euclidean Geometry and Fractal Geometry 290 Review Exercises 291 Chapter Test 295
CHAPTER 9 MATHEMATICAL SYSTEMS
9.1 Groups 297 9.2 Finite Mathematical Systems 298 9.3 Modular Arithmetic 302 9.4 Matrices 306 Review Exercises 314 Chapter Test 316
CHAPTER 10 CONSUMER MATH
10.1 Percent 319 10.2 Personal Loans and Simple Interest 321 10.3 Compound Interest 325 10.4 Installment Buying 328 10.5 Buying a House with a Mortgage 335 10.6 Ordinary Annuities, Sinking Funds, and Retirement Investments 339 Review Exercises 340 Chapter Test 344
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CHAPTER 11 PROBABILITY
11.1 Empirical and Th eoretical Probabilities 347 11.2 Odds 350 11.3 Expected Value (Expectation) 354 11.4 Tree Diagrams 357 11.5 OR and AND Problems 362 11.6 Conditional Probability 366 11.7 The Counting Principle and Permutations 368 11.8 Combinations 371 11.9 Solving Probability Probl ems by Using Combinations 374 11.10 Binomial Probability Formula 377 Review Exercises 378 Chapter Test 382
CHAPTER 12 STATISTICS
12.1 Sampling Techniques and Misuses of Statistics 385 12.2 Frequency Distributi ons and Statistical Graphs 387 12.3 Measures of Central Tendency 395 12.4 Measures of Dispersion 399 12.5 The Normal Curve 404 12.6 Linear Correlation and Regression 410 Review Exercises 422 Chapter Test 427
CHAPTER 13 GRAPH THEORY
13.1 Graphs, Paths, and Circuits 431 13.2 Euler Paths and Euler Circuits 434 13.3 Hamilton Paths and Hamilton Circuits 438 13.4 Trees 444 Review Exercises 452 Chapter Test 457
CHAPTER 14 VOTING AND APPORTIONMENT
14.1 Voting Methods 459 14.2 Flaws of the Voting Methods 465 14.3 Apportionment Methods 468 14.4 Flaws of the Apportionment Methods 474 Review Exercises 478 Chapter Test 484
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