Finite Math for Dummies

339 Pages·2018·12.36 MB·English

by  Mary Jane Sterling

Finite Math
by Mary Jane Sterling
Finite Math For Dummies®
Published by: John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, www.wiley.com
Copyright © 2018 by John Wiley & Sons, Inc., Hoboken, New Jersey
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Library of Congress Control Number: 2018934637
ISBN 978-1-119-47636-8 (pbk); ISBN 978-1-119-47643-6 (ebk); ISBN 978-1-119-47644-3 (ebk)
Manufactured in the United States of America
10 9 8 7 6 5 4 3 2 1
Contents at a Glance
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Part 1: Getting Started with Finite Math . . . . . . . . . . . . . . . . . . . . . . 5
CHAPTER 1: Feeling Fine with Finite Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
CHAPTER 2: Lining Up Linear Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
CHAPTER 3: Solving Systems of Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
CHAPTER 4: Taking on Systems of Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Part 2: Making Use of Available Methods . . . . . . . . . . . . . . . . . . . . 63
CHAPTER 5: Making Way for Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
CHAPTER 6: Making Matrices Work for You . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
CHAPTER 7: Getting Lined Up with Linear Programming . . . . . . . . . . . . . . . . . . . . . . 109
CHAPTER 8: Simply the Simplex Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Part 3: Using Finite Math to Tackle World Situations . . . . . 145
CHAPTER 9: Setting Up Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
CHAPTER 10: Processing the Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
CHAPTER 11: Counting on the Mathematics of Finance . . . . . . . . . . . . . . . . . . . . . . . . . 181
CHAPTER 12: Telling the Truth with Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
CHAPTER 13: Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Part 4: Employing the Tools of Finite Math to
Expand and Investigate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
CHAPTER 14: Markov Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
CHAPTER 15: Playing Games with Game Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
CHAPTER 16: Applications of Matrices and Game Theory . . . . . . . . . . . . . . . . . . . . . . . 267
Part 5: The Part of Tens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
CHAPTER 17: Ten Financial Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
CHAPTER 18: Ten Important Graphing Calculator Functions . . . . . . . . . . . . . . . . . . . . 289
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

Table of Contents
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
About This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Foolish Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Icons Used in This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Beyond the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Where to Go from Here . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
PART 1: GETTING STARTED WITH FINITE MATH . . . . . . . . . . . . . 5
CHAPTER 1: Feeling Fine with Finite Math . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Getting in Line with Linear Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Making the Most with Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Staying with the Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Getting Set with Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Posing the Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Figuring in Financial Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
Finding Statistical Satisfaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Considering the Logical Side of Mathematics . . . . . . . . . . . . . . . . . . . . . 15
Unlocking the Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Getting into Gaming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
CHAPTER 2: Lining Up Linear Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Recognizing Equations of Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Identifying slope and its scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Creating different forms of the equation . . . . . . . . . . . . . . . . . . . . . . 21
Writing the equation of a line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Graphing Lines on the Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . . . 22
Graphing a line using two points . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Using the slope and y-intercept to graph a line . . . . . . . . . . . . . . . . 24
Graphing special lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Determining Relationships between Lines . . . . . . . . . . . . . . . . . . . . . . . 27
Parallel and perpendicular lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Intersecting versus coincidental lines . . . . . . . . . . . . . . . . . . . . . . . . . 29
Solving for a Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
CHAPTER 3: Solving Systems of Linear Equations . . . . . . . . . . . . . . . . .33
Solving Systems Using Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Solving a system of two linear equations using elimination . . . . . . 34
Using elimination to solve a system of three linear equations . . . . 36
Table of Contents v
Solving Systems Using Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Solving a system of two linear equations using substitution . . . . . 38
Taking on a system of three linear equations
using substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Dealing with Too Many or No Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Too many solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
No solution at all . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Making Linear Equations Work for You . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Determining the profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Mixing it up with a solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Counting on change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
CHAPTER 4: Taking on Systems of Inequalities . . . . . . . . . . . . . . . . . . . . 49
Ruling with Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Graphing Linear Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Creating graphs of systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Making graphs work for you . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
PART 2: MAKING USE OF AVAILABLE METHODS . . . . . . . . . . . 63
CHAPTER 5: Making Way for Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Squaring Off with Matrix Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Identifying matrices and their components . . . . . . . . . . . . . . . . . . . 66
Equalizing and transposing matrices . . . . . . . . . . . . . . . . . . . . . . . . . 67
Performing matrix operations and processes . . . . . . . . . . . . . . . . . 68
Investigating Row Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Performing the row operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Creating inverses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Applying Matrices and Their Operations . . . . . . . . . . . . . . . . . . . . . . . . . 80
Matrices and motorcycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Taking matrices to the zoo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
CHAPTER 6: Making Matrices Work for You . . . . . . . . . . . . . . . . . . . . . . . . 87
Solving Systems of Equations Using Matrices . . . . . . . . . . . . . . . . . . . . . 88
Solving a linear system in two variables . . . . . . . . . . . . . . . . . . . . . . .89
Forging ahead with four variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Stopping up short . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Multiplying by the inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Discovering Multiple Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Applying Matrices to Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Considering input and output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Distributing temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Taking Advantage of Special Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Inverses of 2 × 2 matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105
Inverses of 3 × 3 matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107
vi Finite Math For Dummies
CHAPTER 7: Getting Lined Up with Linear Programming . . . . . . . 109
Setting Up Linear Programming Problems . . . . . . . . . . . . . . . . . . . . . . 110
Making the problem structure work . . . . . . . . . . . . . . . . . . . . . . . . . 110
Solving a maximization problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Going for a minimum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Going Three-Dimensional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Maximizing in three dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Going for the minimum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
CHAPTER 8: Simply the Simplex Method . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Delineating Simplex Method Steps for Maximization . . . . . . . . . . . . . 126
Setting up for the simplex method . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Solving a maximization application . . . . . . . . . . . . . . . . . . . . . . . . . 131
Making the Most of Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135
Spelling out the format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135
Stepping through minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . .136
Giving minimization meaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
PART 3: USING FINITE MATH TO TACKLE
WORLD SITUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
CHAPTER 9: Setting Up Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Introducing Set Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Describing large and small sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Special types of sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Performing Basic Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .151
Using Venn Diagrams for Better Views . . . . . . . . . . . . . . . . . . . . . . . . . 152
Elements shown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .152
The number of elements shown . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
CHAPTER 10: Processing the Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Introducing Counting Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Multiplication method of counting . . . . . . . . . . . . . . . . . . . . . . . . . .162
Using permutations for counting . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Counting with combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Determining the Probability of an Event . . . . . . . . . . . . . . . . . . . . . . . . 167
Binomial distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Using probability trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Applying Probability Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
Games of chance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
Probability of being chosen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .177
Table of Contents vii
CHAPTER 11: Counting on the Mathematics of Finance . . . . . . . . . . 181
Considering Simple Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Compounding Things with Compound Interest . . . . . . . . . . . . . . . . . . 182
Continuous compounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Effective interest rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Presenting present value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Analyzing Annuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .188
Future value of an annuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .188
Present value of an annuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Sinking funds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Amortization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Creating an amortization schedule . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Accelerating to payoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .193
CHAPTER 12: Telling the Truth with Statistics . . . . . . . . . . . . . . . . . . . . . . 195
Presenting Data Graphically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Barring none with a bar graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Baking up a pie chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
Stem-and-leaf graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Meaning it with the mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Riding down the middle with the median . . . . . . . . . . . . . . . . . . . . 202
Making the most of the mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
Recognizing the geometric mean . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Comparing measures of central tendency . . . . . . . . . . . . . . . . . . . 203
Box-and-whisker plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Variance and Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .208
Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
Standard deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Investigating the Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 210
CHAPTER 13: Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Logically Presenting the Vocabulary . . . . . . . . . . . . . . . . . . . . . . . . . . . .213
Finding the Truth with Truth Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Considering the conjunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Displaying the disjunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
Looking into negativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Conditionally making statements . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Analyzing compound statements . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
Equivalent Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Studying the Conditional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Analyzing Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Applying Logic to Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
viii Finite Math For Dummies