Finite mathematics with applications: in the management, natural, and social sciences

Cover......Page 1
Title......Page 5
Copyright......Page 6
Contents......Page 9
Preface......Page 11
To the Student......Page 19
Prerequisite Skills Test......Page 21
 1.1 The Real Numbers......Page 23
 1.2 Polynomials......Page 33
 1.3 Factoring......Page 40
 1.4 Rational Expressions......Page 46
 1.5 Exponents and Radicals......Page 53
 1.6 First-Degree Equations......Page 65
 1.7 Quadratic Equations......Page 74
 Summary and Review......Page 82
 CASE STUDY 1 Consumers Often Need to Just Do the Math......Page 85
 2.1 Graphs......Page 87
 2.2 Equations of Lines......Page 97
 2.3 Linear Models......Page 109
 2.4 Linear Inequalities......Page 117
 2.5 Polynomial and Rational Inequalities......Page 123
 Summary and Review......Page 131
 CASE STUDY 2 Using Extrapolation and Interpolation for Prediction......Page 134
 3.1 Functions......Page 137
 3.2 Graphs of Functions......Page 145
 3.3 Applications of Linear Functions......Page 156
 3.4 Quadratic Functions and Applications......Page 167
 3.5 Polynomial Functions......Page 180
 3.6 Rational Functions......Page 190
 Summary and Review......Page 199
 CASE STUDY 3 Architectural Arches......Page 203
 4.1 Exponential Functions......Page 205
 4.2 Applications of Exponential Functions......Page 214
 4.3 Logarithmic Functions......Page 222
 4.4 Logarithmic and Exponential Equations......Page 231
 Summary and Review......Page 240
 CASE STUDY 4 Gapminder.org......Page 243
 5.1 Simple Interest and Discount......Page 247
 5.2 Compound Interest......Page 254
 5.3 Annuities, Future Value, and Sinking Funds......Page 265
 5.4 Annuities, Present Value, and Amortization......Page 274
 Summary and Review......Page 285
 CASE STUDY 5 Continuous Compounding......Page 289
CHAPTER 6Systems of Linear Equationsand Matrices......Page 292
 6.1 Systems of Two Linear Equations in Two Variables......Page 293
 6.2 Larger Systems of Linear Equations......Page 299
 6.3 Applications of Systems of Linear Equations......Page 311
 6.4 Basic Matrix Operations......Page 320
 6.5 Matrix Products and Inverses......Page 327
 6.6 Applications of Matrices......Page 339
 Summary and Review......Page 351
 CASE STUDY 6 Matrix Operations and Airline Route Maps......Page 356
CHAPTER 7 Linear Programming......Page 359
 7.1 Graphing Linear Inequalities in Two Variables......Page 360
 7.2 Linear Programming: The Graphical Method......Page 368
 7.3 Applications of Linear Programming......Page 374
 7.4 The Simplex Method: Maximization......Page 381
 7.5 Maximization Applications......Page 393
 7.6 The Simplex Method: Duality and Minimization......Page 400
 7.7 The Simplex Method: Nonstandard Problems......Page 409
 Summary and Review......Page 421
 CASE STUDY 7 Cooking with Linear Programming......Page 425
 8.1 Sets......Page 427
 8.2 Applications of Venn Diagrams and Contingency Tables......Page 436
 8.3 Introduction to Probability......Page 444
 8.4 Basic Concepts of Probability......Page 454
 8.5 Conditional Probability and Independent Events......Page 463
 8.6 Bayes’ Formula......Page 475
 Summary and Review......Page 480
 CASE STUDY 8 Medical Diagnosis......Page 485
 9.1 Probability Distributions and Expected Value......Page 487
 9.2 The Multiplication Principle, Permutations, and Combinations......Page 497
 9.3 Applications of Counting......Page 509
 9.4 Binomial Probability......Page 515
 9.5 Markov Chains......Page 520
 9.6 Decision Making......Page 531
 Summary and Review......Page 535
 CASE STUDY 9 Quick Draw® from the New York State Lottery......Page 539
 10.1 Frequency Distributions......Page 541
 10.2 Measures of Center......Page 550
 10.3 Measures of Variation......Page 559
 10.4 Normal Distributions and Boxplots......Page 567
 10.5 Normal Approximation to the Binomial Distribution......Page 579
 Summary and Review......Page 585
 CASE STUDY 10 Standard Deviation as a Measure of Risk......Page 588
Appendix A Graphing Calculators......Page 591
 Table 1: Formulas from Geometry......Page 592
 Table 2: Areas under the Normal Curve......Page 593
Appendix C Learning Objectives......Page 595
Appendix D Solutions to Prerequisite Skills Test......Page 600
 Chapter 1......Page 603
 Chapter 2......Page 604
 Chapter 3......Page 607
 Chapter 4......Page 613
 Chapter 5......Page 615
 Chapter 6......Page 616
 Chapter 7......Page 619
 Chapter 8......Page 623
 Chapter 9......Page 624
 Chapter 10......Page 626
 N......Page 631
 X......Page 632
Index of Applications......Page 633
 C......Page 637
 F......Page 638
 I......Page 639
 M......Page 640
 P......Page 641
 R......Page 642
 S......Page 643
 Z......Page 644
Photo Credits......Page 645