SOLUTIONS
MANUAL
TAMSEN HERRICK
A SURVEY OF M ATHEMATICS
WITH A PPLICATIONS
NINTH EDITION
By
Allen R. Angel
Christine D. Abbott
Dennis C. Runde
, 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.
,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
Copyright © 2013 Pearson Education, Inc.
, 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
Copyright © 2013 Pearson Education, Inc.
MANUAL
TAMSEN HERRICK
A SURVEY OF M ATHEMATICS
WITH A PPLICATIONS
NINTH EDITION
By
Allen R. Angel
Christine D. Abbott
Dennis C. Runde
, 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.
,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
Copyright © 2013 Pearson Education, Inc.
, 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
Copyright © 2013 Pearson Education, Inc.
