Finite Mathematics

Front Cover......Page 1
Title Page......Page 2
Copyright......Page 3
Preface......Page 12
Contents......Page 6
1 FUNCTIONS AND LINES......Page 22
1.1 Functions......Page 23
Using Your TI-83/84......Page 32
Using EXCEL......Page 33
1.2 Graphs and Lines......Page 35
Using Your TI-83/84: Graphs of Lines and Evaluating Points on a Line......Page 55
Using EXCEL......Page 57
1.3 Mathematical Models and Applications of Linear Functions......Page 59
Using Your TI-83/84: Intersection of Lines......Page 78
Using EXCEL......Page 79
Important Terms in Chapter 1......Page 81
Review Exercises for Chapter 1......Page 82
2 LINEAR SYSTEMS......Page 86
2.1 Systems of Two Equations......Page 87
Using EXCEL......Page 102
2.2 Systems with Three Variables: An Introduction to a Matrix Representation of a Linear System of Equations......Page 103
Using Your TI-83/84: Solving a System of Equations Using Row Operations......Page 124
Using EXCEL: Solving Systems of Equations Using Row Operations......Page 126
2.3 Gauss-Jordan Method for General Systems of Equations......Page 128
Using Your TI-83/84: Obtaining the Reduced Echelon Form of a Matrix......Page 147
Using EXCEL: General Procedure for Pivoting......Page 149
2.4 Matrix Operations......Page 150
Using EXCEL: Matrix Addition and Scalar Multiplication......Page 161
2.5 Multiplication of Matrices......Page 162
Using Your TI-83/84: Matrix Multiplication......Page 179
2.6 The Inverse of a Matrix......Page 180
Using Your TI-83/84: The Inverse of a Matrix......Page 195
Using EXCEL......Page 196
2.7 Leontief Input–Output Model in Economics......Page 197
Using Your TI-83/84......Page 209
Using EXCEL......Page 210
2.8 Linear Regression......Page 211
Using Your TI-83/84: Regression Lines......Page 220
Using EXCEL: To Draw and Find a Linear Regression Line......Page 221
Review Exercises for Chapter 2......Page 223
3 LINEAR PROGRAMMING......Page 226
3.1 Linear Inequalities in Two Variables......Page 227
3.2 Solutions of Systems of Inequalities: A Geometric Picture......Page 234
Using Your TI-83/84: Finding Corner Points of a Feasible Region......Page 242
Using EXCEL......Page 244
3.3 Linear Programming: A Geometric Approach......Page 246
Using Your TI-83/84: Evaluate the Objective Function......Page 269
3.4 Applications......Page 271
Review Exercises for Chapter 3......Page 279
4 LINEAR PROGRAMMING: THE SIMPLEX METHOD......Page 282
4.1 Setting Up the Simplex Method......Page 283
4.2 The Simplex Method......Page 294
Using Your TI-83/84: A Program for the Simplex Method......Page 314
Using EXCEL......Page 316
4.3 The Standard Minimum Problem: Duality......Page 320
4.4 Mixed Constraints......Page 328
Using EXCEL......Page 350
4.5 Multiple Solutions, Unbounded Solutions, and No Solutions......Page 351
4.6 What’s Happening in the Simplex Method? (Optional)......Page 360
4.7 Sensitivity Analysis......Page 368
Review Exercises for Chapter 4......Page 379
5 MATHEMATICS OF FINANCE......Page 384
5.1 Simple Interest......Page 385
5.2 Compound Interest......Page 393
Using Your TI-83/84: Making a Table......Page 407
Using EXCEL......Page 408
5.3 Annuities and Sinking Funds......Page 409
Using Your TI-83/84: Growth of Annuities......Page 418
Using EXCEL......Page 419
5.4 Present Value of an Annuity and Amortization......Page 420
Using Your TI-83/84: Monthly Loan Payments......Page 439
Important Terms in Chapter 5......Page 440
Review Exercises for Chapter 5......Page 441
6 SETS AND COUNTING......Page 444
6.1 Sets......Page 445
6.2 Counting Elements in a Subset Using a Venn Diagram......Page 453
6.3 Basic Counting Principles......Page 461
6.4 Permutations......Page 473
6.5 Combinations......Page 483
Using Your TI-83/84: Combinations......Page 498
6.6 A Mixture of Counting Problems......Page 499
6.7 Partitions (Optional)......Page 505
Review Exercises for Chapter 6......Page 512
7 PROBABILITY......Page 516
7.1 Introduction to Probability......Page 517
7.2 Equally Likely Events......Page 530
7.3 Compound Events: Union, Intersection, and Complement......Page 540
7.4 Conditional Probability......Page 553
7.5 Independent Events......Page 568
7.6 Bayes’ Rule......Page 585
7.7 Markov Chains......Page 600
Review Exercises for Chapter 7......Page 614
8 STATISTICS......Page 618
8.1 Frequency Distributions......Page 619
Using Your TI-83/84: Histograms......Page 634
Using EXCEL: Histograms and Pie Charts......Page 636
8.2 Measures of Central Tendency......Page 638
Using Your TI-83/84: Calculating the Mean and Median......Page 649
Using EXCEL: Calculate the Mean and Median......Page 650
8.3 Measures of Dispersion: Range,Variance, and Standard Deviation......Page 651
Using Your TI-83/84......Page 666
Using EXCEL: Measures of Dispersion......Page 668
8.4 Random Variables and Probability Distributions of Discrete Random Variables......Page 669
8.5 Expected Value of a Random Variable......Page 679
8.6 Bernoulli Experiments and Binomial Distribution......Page 689
Using Your TI-83/84: Binomial Probability Distribution......Page 702
8.7 Normal Distribution......Page 704
Using Your TI-83/84: Area Under the Normal Curve......Page 733
8.8 Estimating Bounds on a Proportion......Page 734
Important Terms in Chapter 8......Page 748
Review Exercises for Chapter 8......Page 749
9 GAME THEORY......Page 752
9.1 Two-Person Games......Page 753
9.2 Mixed-Strategy Games......Page 761
Review Exercises for Chapter 9......Page 771
10 LOGIC......Page 774
10.1 Statements......Page 775
10.2 Conditional Statements......Page 781
10.3 Equivalent Statements......Page 787
10.4 Valid Arguments......Page 789
Review Exercises for Chapter 10......Page 796
A.1 Properties of Real Numbers......Page 798
A.2 Solving Linear Equations......Page 801
A.3 Coordinate Systems......Page 805
A.4 Linear Inequalities and Interval Notation......Page 808
Important Terms in Appendix A......Page 814
Arithmetic Operations......Page 816
Graphing......Page 817
Finding the Intersection of Two Graphs......Page 818
Constructing a Table......Page 819
Matrices......Page 820
Statistics......Page 822
C: USING EXCEL......Page 826
ANSWERS TO SELECTED ODD-NUMBERED EXERCISES......Page 828
INDEX......Page 886