Finite Mathematics, Enhanced 7th Edition (with Enhanced WebAssign with eBook for One Term Math and Science Printed Access Card)

924 Pages·2010·11.38 MB·English

by  Howard L. Rolf

SEVENTH EDITION
Finite
Mathematics
Enhanced Edition
Howard L. Rolf
Baylor University
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Finite Mathematics, Seventh Edition © 2011, 2009 Brooks/Cole, Cengage Learning
Howard L. Rolf
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Contents
1
FUNCTIONS AND LINES 1
1.1 Functions 2
Using Your TI-83/84 11
Using EXCEL 12
1.2 Graphs and Lines 14
Using Your TI-83/84: Graphs of Lines and Evaluating Points
on a Line 34
Using EXCEL 36
1.3 Mathematical Models and Applications of Linear
Functions 38
Using Your TI-83/84: Intersection of Lines 57
Using EXCEL 58
Important Terms in Chapter 1 60
Review Exercises for Chapter 1 61
2
LINEAR SYSTEMS 65
2.1 Systems of Two Equations 66
Using EXCEL 81
2.2 Systems with Three Variables:An Introduction to a Matrix
Representation of a Linear System of Equations 82
Using Your TI-83/84: Solving a System of Equations Using Row
Operations 103
UsingEXCEL:SolvingSystemsofEquationsUsingRow
Operations 105
2.3 Gauss-Jordan Method for General Systems
of Equations 107
Using Your TI-83/84: Obtaining the Reduced Echelon Form
of a Matrix 126
Using EXCEL: General Procedure for Pivoting 128
2.4 Matrix Operations 129
Using Your TI-83/84: Matrix Operations 140
Using EXCEL: Matrix Addition and Scalar Multiplication 140
v
vi Contents
2.5 Multiplication of Matrices 141
Using Your TI-83/84: Matrix Multiplication 158
Using EXCEL 159
2.6 The Inverse of a Matrix 159
Using Your TI-83/84: The Inverse of a Matrix 174
Using EXCEL 175
2.7 Leontief Input–Output Model in Economics 176
Using Your TI-83/84 188
Using EXCEL 189
2.8 Linear Regression 190
Using Your TI-83/84: Regression Lines 199
Using EXCEL: To Draw and Find a Linear Regression Line 200
Important Terms in Chapter 2 202
Review Exercises for Chapter 2 202
3
LINEAR PROGRAMMING 205
3.1 Linear Inequalities in Two Variables 206
3.2 Solutions of Systems of Inequalities:
A Geometric Picture 213
Using Your TI-83/84: Finding Corner Points of a Feasible Region 221
Using EXCEL 223
3.3 Linear Programming:A Geometric Approach 225
Using Your TI-83/84: Evaluate the Objective Function 248
Using EXCEL: Evaluate an Objective Function 250
3.4 Applications 250
Important Terms in Chapter 3 258
Review Exercises for Chapter 3 258
4
LINEAR PROGRAMMING:
THE SIMPLEX METHOD 261
4.1 Setting Up the Simplex Method 262
4.2 The Simplex Method 273
Using Your TI-83/84: A Program for the Simplex Method 293
Using EXCEL 295
4.3 The Standard Minimum Problem:Duality 299
4.4 Mixed Constraints 307
Using EXCEL 329
Contents vii
4.5 Multiple Solutions,Unbounded Solutions,
and No Solutions 330
4.6 What’s Happening in the Simplex Method? (Optional) 339
4.7 Sensitivity Analysis 347
Important Terms in Chapter 4 358
Review Exercises for Chapter 4 358
5
MATHEMATICS OF FINANCE 363
5.1 Simple Interest 364
5.2 Compound Interest 372
Using Your TI-83/84: Making a Table 386
Using EXCEL 387
5.3 Annuities and Sinking Funds 388
Using Your TI-83/84: Growth of Annuities 397
Using EXCEL 398
5.4 Present Value of an Annuity and Amortization 399
Using Your TI-83/84: Monthly Loan Payments 418
Using EXCEL 419
Important Terms in Chapter 5 419
Summary of Formulas in Chapter 5 420
Review Exercises for Chapter 5 420
6
SETS AND COUNTING 423
6.1 Sets 424
6.2 Counting Elements in a Subset
Using a Venn Diagram 432
6.3 Basic Counting Principles 440
6.4 Permutations 452
Using Your TI-83/84: Permutations 462
Using EXCEL: Permutations 462
6.5 Combinations 462
Using Your TI-83/84: Combinations 477
Using EXCEL: Combinations 478
6.6 A Mixture of Counting Problems 478
6.7 Partitions (Optional) 484
Important Terms in Chapter 6 491
Review Exercises for Chapter 6 491
viii Contents
7
PROBABILITY 495
7.1 Introduction to Probability 496
7.2 Equally Likely Events 509
7.3 Compound Events:Union,Intersection,
and Complement 519
7.4 Conditional Probability 532
7.5 Independent Events 547
7.6 Bayes’Rule 564
7.7 Markov Chains 579
Important Terms in Chapter 7 593
Review Exercises for Chapter 7 593
8
STATISTICS 597
8.1 Frequency Distributions 598
Using Your TI-83/84: Histograms 613
Using EXCEL: Histograms and Pie Charts 615
8.2 Measures of Central Tendency 617
Using Your TI-83/84: Calculating the Mean and Median 628
Using EXCEL: Calculate the Mean and Median 629
8.3 Measures of Dispersion:Range,Variance,
and Standard Deviation 630
Using Your TI-83/84 645
Using EXCEL: Measures of Dispersion 647
8.4 Random Variables and Probability Distributions
of Discrete Random Variables 648
8.5 Expected Value of a Random Variable 658
8.6 Bernoulli Experiments and Binomial Distribution 668
Using Your TI-83/84: Binomial Probability Distribution 681
8.7 Normal Distribution 683
Using Your TI-83/84: Area Under the Normal Curve 712
Using EXCEL 713
8.8 Estimating Bounds on a Proportion 713
Important Terms in Chapter 8 727
Review Exercises for Chapter 8 728
Contents ix
9
GAME THEORY 731
9.1 Two-Person Games 732
9.2 Mixed-Strategy Games 740
Important Terms in Chapter 9 750
Review Exercises for Chapter 9 750
10
LOGIC 753
10.1 Statements 754
10.2 Conditional Statements 760
10.3 Equivalent Statements 766
10.4 Valid Arguments 768
Important Terms in Chapter 10 775
Review Exercises for Chapter 10 775
A
REVIEW TOPICS 777
A.1 Properties of Real Numbers 777
A.2 Solving Linear Equations 780
A.3 Coordinate Systems 784
A.4 Linear Inequalities and Interval Notation 787
Important Terms in Appendix A 793
B
USING A TI-83/84 GRAPHING CALCULATOR 795
Notation 795
Arithmetic Operations 795
Graphing 796
Evaluating a Function 797
Finding the Intersection of Two Graphs 797
Constructing a Table 798
Matrices 799
Statistics 801