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### Summary

### Summary

Use mathematical analysis in the real world

Finite math takes everything you′ve learned in your previous math courses and brings them together into one course with a focus on organizing and analyzing information, creating mathematical models for approaching business decisions, using statistics principles to understand future states, and applying logic to data organization .

Finite Math For Dummies tracks to a typical college-level course designed for business, computer science, accounting, and other non-math majors, and is the perfect supplement to help you score high!

Organize and analyze information Apply calculation principles to real-world problems Use models for business calculations Supplement your coursework with step-by-step example problemsIf you re not a math person or just want to brush up on your skills to get a better grade, Finite Math For Dummies is your ticket to scoring higher!

### Author Notes

Mary Jane Sterling is the author of Algebra I For Dummies, Algebra Workbook For Dummies, and many other For Dummies books. She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics.

### Table of Contents

Introduction | p. 1 |

About This Book | p. 1 |

Foolish Assumptions | p. 2 |

Icons Used in This Book | p. 2 |

Beyond the Book | p. 3 |

Where to Go from Here | p. 3 |

Part 1 Getting Started with Finite Math | p. 5 |

Chapter 1 Feeling Fine with Finite Math | p. 7 |

Getting in Line with Linear Statements | p. 8 |

Making the Most with Matrices | p. 8 |

Staying with the Program | p. 9 |

Getting Set with Sets | p. 10 |

Posing the Probability | p. 11 |

Figuring in Financial Factors | p. 13 |

Finding Statistical Satisfaction | p. 14 |

Considering the Logical Side of Mathematics | p. 15 |

Unlocking the Chains | p. 16 |

Getting into Gaming | p. 18 |

Chapter 2 Lining Up Linear Functions | p. 19 |

Recognizing Equations of Lines | p. 20 |

Identifying slope and its scope | p. 20 |

Creating different forms of the equation | p. 21 |

Writing the equation of a line | p. 21 |

Graphing Lines on the Coordinate Plane | p. 22 |

Graphing a line using two points | p. 23 |

Using the slope and y-intercept to graph a line | p. 24 |

Graphing special lines | p. 25 |

Determining Relationships between Lines | p. 27 |

Parallel and perpendicular lines | p. 27 |

Intersecting versus coincidental lines | p. 29 |

Solving for a Variable | p. 30 |

Chapter 3 Solving Systems of Linear Equations | p. 33 |

Solving Systems Using Elimination | p. 34 |

Solving a system of two linear equations using elimination | p. 34 |

Using elimination to solve a system of three linear equations | p. 36 |

Solving Systems Using Substitution | p. 38 |

Solving a system of two linear equations using substitution | p. 38 |

Taking on a system of three linear equations using substitution | p. 39 |

Dealing with Too Many or No Solutions | p. 41 |

Too many solutions | p. 41 |

No solution at all | p. 42 |

Making Linear Equations Work for You | p. 43 |

Determining the profit | p. 44 |

Mixing it up with a solution | p. 44 |

Counting on change | p. 46 |

Chapter 4 Taking on Systems of Inequalities | p. 49 |

Ruling with Inequalities | p. 49 |

Graphing Linear Inequalities | p. 51 |

Creating graphs of systems | p. 53 |

Making graphs work for you | p. 56 |

Part 2 Making Use of Available Methods | p. 63 |

Chapter 5 Making Way for Matrices | p. 65 |

Squaring Off with Matrix Basics | p. 65 |

Identifying matrices and their components | p. 66 |

Equalizing and transposing matrices | p. 67 |

Performing matrix operations and processes | p. 68 |

Investigating Row Operations | p. 75 |

Performing the row operations | p. 75 |

Creating inverses | p. 77 |

Applying Matrices and Their Operations | p. 80 |

Matrices and motorcycles | p. 81 |

Taking matrices to the zoo | p. 84 |

Chapter 6 Making Matrices Work for You | p. 87 |

Solving Systems of Equations Using Matrices | p. 88 |

Solving a linear system in two variables | p. 89 |

Forging ahead with four variables | p. 90 |

Stopping up short | p. 92 |

Multiplying by the inverse | p. 94 |

Discovering Multiple Solutions | p. 97 |

Applying Matrices to Tasks | p. 99 |

Considering input and output | p. 99 |

Distributing temperatures | p. 103 |

Taking Advantage of Special Formulas | p. 105 |

Inverses of 2 × 2 matrices | p. 105 |

Inverses of 3 × 3 matrices | p. 107 |

Chapter 7 Getting Lined Up with Linear Programming | p. 109 |

Setting Up Linear Programming Problems | p. 110 |

Making the problem structure work | p. 110 |

Solving a maximization problem | p. 112 |

Going for a minimum | p. 115 |

Going Three-Dimensional | p. 118 |

Maximizing in three dimensions | p. 119 |

Going for the minimum | p. 122 |

Chapter 8 Simply the Simplex Method | p. 125 |

Delineating Simplex Method Steps for Maximization | p. 126 |

Setting up for the simplex method | p. 126 |

Solving a maximization application | p. 131 |

Making the Most of Minimization | p. 135 |

Spelling out the format | p. 135 |

Stepping through minimization | p. 136 |

Giving minimization meaning | p. 140 |

Part 3 Using Finite Math to Tackle World Situations | p. 145 |

Chapter 9 Setting Up Sets | p. 147 |

Introducing Set Notation | p. 147 |

Describing large and small sets | p. 148 |

Special types of sets | p. 149 |

Performing Basic Operations | p. 151 |

Using Venn Diagrams for Better Views | p. 152 |

Elements shown | p. 152 |

The number of elements shown | p. 156 |

Chapter 10 Processing the Probability | p. 161 |

Introducing Counting Methods | p. 161 |

Multiplication method of counting | p. 162 |

Using permutations for counting | p. 163 |

Counting with combinations | p. 165 |

Determining the Probability of an Event | p. 167 |

Binomial distributions | p. 169 |

Using probability trees | p. 171 |

Applying Probability Techniques | p. 174 |

Games of chance | p. 174 |

Probability of being chosen | p. 177 |

Chapter 11 Counting on the Mathematics of Finance | p. 181 |

Considering Simple Interest | p. 181 |

Compounding Things with Compound Interest | p. 182 |

Continuous compounding | p. 184 |

Effective interest rate | p. 185 |

Presenting present value | p. 185 |

Analyzing Annuities | p. 188 |

Future value of an annuity | p. 188 |

Present value of an annuity | p. 189 |

Sinking funds | p. 190 |

Amortization | p. 191 |

Creating an amortization schedule | p. 191 |

Accelerating to payoff | p. 193 |

Chapter 12 Telling the Truth with Statistics | p. 195 |

Presenting Data Graphically | p. 195 |

Barring none with a bar graph | p. 196 |

Histograms | p. 197 |

Baking up a pie chart | p. 198 |

Stem-and-leaf graphs | p. 199 |

Measures of Central Tendency | p. 200 |

Meaning it with the mean | p. 200 |

Riding down the middle with the median | p. 202 |

Making the most of the mode | p. 202 |

Recognizing the geometric mean | p. 203 |

Comparing measures of central tendency | p. 203 |

Box-and-whisker plots | p. 207 |

Variance and Standard Deviation | p. 208 |

Variance | p. 208 |

Standard deviation | p. 209 |

Investigating the Normal Distribution | p. 210 |

Chapter 13 Logic | p. 213 |

Logically Presenting the Vocabulary | p. 213 |

Finding the Truth with Truth Tables | p. 215 |

Considering the conjunction | p. 215 |

Displaying the disjunction | p. 216 |

Looking into negativity | p. 217 |

Conditionally making statements | p. 217 |

Analyzing compound statements | p. 218 |

Equivalent Statements | p. 219 |

Studying the Conditional | p. 221 |

Analyzing Arguments | p. 222 |

Applying Logic to Circuits | p. 225 |

Part 4 Employing the Tools of Finite Math to Expand and Investigate | p. 229 |

Chapter 14 Markov Chains | p. 231 |

Recognizing a Markov Chain | p. 231 |

Coming to Terms with Markov Chains | p. 232 |

Working with Transition Matrices | p. 233 |

Using charts and trees | p. 233 |

Dealing with diagrams | p. 236 |

Probability Vectors | p. 239 |

Absorbing Chains | p. 242 |

Making Long-Term Predictions | p. 244 |

Avoiding ruin | p. 244 |

Alternating even and odd | p. 246 |

Chapter 15 Playing Games with Game Theory | p. 249 |

Playing Fairly | p. 249 |

Playing by the Rules | p. 252 |

Matrix representation | p. 252 |

Vocabulary | p. 252 |

Vocabulary illustrated | p. 253 |

Getting Strategic | p. 255 |

Yielding to Domination | p. 258 |

Determining the Moves | p. 259 |

Finding no saddle point | p. 259 |

Getting down to business | p. 263 |

Chapter 16 Applications of Matrices and Game Theory | p. 267 |

Traffic Flow | p. 267 |

Battle of the Bismarck Sea | p. 270 |

The Game of Chicken | p. 271 |

The Prisoner's Dilemma | p. 272 |

The Traveler's Dilemma | p. 273 |

Blotto's Rules | p. 274 |

Jack Be Nimble | p. 275 |

Nim with two heaps | p. 275 |

Upping the Nim stacks to three | p. 277 |

Part 5 The Part of Tens | p. 279 |

Chapter 17 Ten Financial Formulas | p. 281 |

The Rule of 72 | p. 281 |

Leverage Ratio | p. 282 |

Gains and Losses | p. 282 |

Determining Depreciation | p. 283 |

Total Return on Investments | p. 283 |

Expected Return | p. 284 |

Inflation-Adjusted Return | p. 284 |

Remaining Balance | p. 285 |

Future Value of Annuity Due | p. 286 |

Bond Pricing Formula | p. 286 |

Chapter 18 Ten Important Graphing Calculator Functions | p. 289 |

Graphing Lines for Intersections | p. 289 |

Adjusting the Window | p. 290 |

Entering Matrices | p. 291 |

Adding, Subtracting, and Multiplying Matrices | p. 292 |

Powering Up Matrices | p. 293 |

Finding Matrix Inverses | p. 294 |

Solving Systems of Equations Using Matrices | p. 295 |

Decimals to Fractions | p. 296 |

Counting with Permutations and Combinations | p. 296 |

Making Statistical Statements | p. 298 |

Glossary | p. 301 |

Index | p. 305 |