# Finite Mathematics & Its Applications / Edition 12 by Larry J. Goldstein EBOOK PDF Instant Download

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Finite Mathematics & Its Applications / Edition 12 by Larry J. Goldstein EBOOK PDF Instant Download

Preface
New to This Edition
Trusted Features
Technology and Supplements
Part One
Chapter 1 Linear Equations and Straight Lines
1.1 Coordinate Systems and Graphs
Plotting Points
Solution
Solution of an Equation
Solution
Linear Equations
Intercepts
Exercises 1.1
Technology Exercises
Solutions to Check Your Understanding 1.1
1.2 The Slope of a Straight Line
Definition
Perpendicular and Parallel Lines
Exercises 1.2
Technology Exercises
Solutions to Check Your Understanding 1.2
1.3 The Intersection Point of a Pair of Lines
Finding the Point of Intersection
Solution
Finding the Point of Intersection
Solution
Finding the Point of Intersection
Solution
Solving a System of Equations
Solution
Supply and Demand Curves
Exercises 1.3
Technology Exercises
Solutions to Check Your Understanding 1.3
1.4 The Method of Least Squares
Finding the Sum-of-Squares Error
Solution
Obtaining the Least-Squares Line with a Graphing Calculator
Obtaining a Least-Squares Line with an Excel Spreadsheet
Obtaining a Least-Squares Line with Wolfram|Alpha
The Computational Method for Obtaining a Least-Squares Fit
Exercises 1.4
Solutions to Check Your Understanding 1.4
Summary Chapter 1
Chapter 1 Fundamental Concept Check Exercises
Chapter 1 Review Exercises
Conceptual Exercises
Chapter 2 Matrices
2.1 Systems of Linear Equations with Unique Solutions
Manufacturing
Solution
Demonstrating Elementary Row Operation 2
Solution
Solving a System of Equations by Gauss–Jordan Elimination
Solution
Solving a System of Equations by Gauss–Jordan Elimination
Solution
Solving a System of Equations by Gauss—Jordan Elimination
Solution
Exercises 2.1
Technology Exercises
Solutions to Check Your Understanding 2.1
2.2 General Systems of Linear Equations
Pivoting
Solution
A System of Equations That Has No Solution
Solution
Solving a System of Equations That Has Infinitely Many Solutions
Solution
Solving a System of Equations That Has Infinitely Many Solutions
Solution
Solving a System of Equations That Has Infinitely Many Solutions
Solution
Finding Specific Solutions
Solution
Exercises 2.2
Technology Exercises
Solutions to Check Your Understanding 2.2
2.3 Arithmetic Operations on Matrices
Multiplication of Matrices
Total Revenue as a Matrix Product
Solution
Matrix Multiplication
Solution
Matrix Multiplication
Solution
Investment Earnings
Solution
Manufacturing Revenue
Solution
Identity Matrix
Scalar Multiplication
Scalar Multiplication
Solution
Representing a System of Equations as a Matrix Equation
Solution
Exercises 2.3
Technology Exercises
Solutions to Check Your Understanding 2.3
2.4 The Inverse of a Square Matrix
Using the Formula for the Inverse of a 2×2 Matrix
Solution
Solving Systems of Linear Equations with Inverses
Using a Matrix Inverse to Solve a System of Equations
Solution
Analyzing Marriage Trends
Solution
Using a Matrix Inverse to Solve Systems of Equations
Solution
Exercises 2.4
Technology Exercises
Solutions to Check Your Understanding 2.4
2.5 The Gauss–Jordan Method for Calculating Inverses
Finding the Inverse of a Matrix by the Gauss–Jordan Method
Solution
Demonstrating That a Matrix Does Not Have an Inverse
Solution
Exercises 2.5
Solutions to Check Your Understanding 2.5
2.6 Input–Output Analysis
Determining Industrial Production
Solution
Determining Production for a Conglomerate
Solution
Exercises 2.6
Technology Exercises
Solutions to Check Your Understanding 2.6
Summary Chapter 2
Chapter 2 Fundamental Concept Check Exercises
Chapter 2 Review Exercises
Conceptual Exercises
Chapter 3 Linear Programming, A Geometric Approach
3.1 Linear Inequalities
Graphing Linear Inequalities
Solution of a Linear Inequality
Solution
Graphing a Linear Inequality
Solution
Graphing a Linear Inequality
Solution
Graphing a System of Linear Inequalities
Solution
Feasible Set of a System of Linear Inequalities
Solution
Exercises 3.1
Technology Exercises
Solutions to Check Your Understanding 3.1
3.2 A Linear Programming Problem
Furniture Manufacturing Problem
Furniture Manufacturing Problem—Mathematical Formulation
Exercises 3.2
Solutions to Check Your Understanding 3.2
3.3 Fundamental Theorem of Linear Programming
Solution of the Furniture Manufacturing Problem
Nutrition—People
Solution
Exercises 3.3
Technology Exercises
Solutions to Check Your Understanding 3.3
3.4 Linear Programming
Investment Planning
Solution
Transportation—Shipping
Solution
Verification of the Fundamental Theorem
Range of Optimality
Transportation—Shipping
Solution
Exercises 3.4
Technology Exercises
Solutions to Check Your Understanding 3.4
Summary Chapter 3
Chapter 3 Fundamental Concept Check Exercises
Chapter 3 Review Exercises
Conceptual Exercises
Chapter 3 Project
Chapter 4 The Simplex Method
4.1 Slack Variables and the Simplex Tableau
Furniture Manufacturing Problem
Solution
Solution
Solution
Solution
Exercises 4.1
Solutions to Check Your Understanding 4.1
4.2 The Simplex Method I: Maximum Problems
Mathematical Model for the Furniture Manufacturing Problem
Rationale for Method of Choosing Pivot Element
Solution
Solution
Exercises 4.2
Technology Exercises
Solutions to Check Your Understanding 4.2
4.3 The Simplex Method II: Nonstandard and Minimum Problems
Nonstandard Problems
Solution
Minimum Problems
Solution
Solution
Some Further Comments on the Simplex Method
Exercises 4.3
Technology Exercises
Solutions to Check Your Understanding 4.3
4.4 Sensitivity Analysis and Matrix Formulations of Linear Programming Problems
Sensitivity Analysis of Linear Programming Problems
Solution
Matrix Formulations of Linear Programming Problems
Solution
Solution
Exercises 4.4
Solutions to Check Your Understanding 4.4
4.5 Duality
Problem A
Problem B
Solution
Solution
An Economic Interpretation of the Dual Problem
Solution
A Useful Application of the Dual Problem
Solution
Exercises 4.5
Technology Exercises
Solutions to Check Your Understanding 4.5
Chapter 4 Summary
Chapter 4 Fundamental Concept Check Exercises
Chapter 4 Review Exercises
Part Two
Chapter 5 Sets and Counting
5.1 Sets
Listing the Elements of a Set
Solution
Exercises 5.1
Solutions to Check Your Understanding 5.1
5.2 A Fundamental Principle of Counting
Using the Inclusion–Exclusion Principle
Solution
Venn Diagrams
Verification of De Morgan’s Laws
Exercises 5.2
Solutions to Check Your Understanding 5.2
5.3 Venn Diagrams and Counting
Exercises 5.3
Solutions to Check Your Understanding 5.3
5.4 The Multiplication Principle
Exercises 5.4
Solutions to Check Your Understanding 5.4
5.5 Permutations and Combinations
Verification of the Formulas for P(n,r) and C(n,r)
Exercises 5.5
Technology Exercises
Solutions to Check Your Understanding 5.5
5.6 Further Counting Techniques
Exercises 5.6
Technology Exercises
Solutions to Check Your Understanding 5.6
5.7 The Binomial Theorem
Exercises 5.7
Solutions to Check Your Understanding 5.7
5.8 Multinomial Coefficients and Partitions
Unordered Partitions
Exercises 5.8
Technology Exercises
Solutions to Check Your Understanding 5.8
Chapter 5 Summary
Chapter 5 Fundamental Concept Check Exercises
Chapter 5 Review Exercises
Technology Exercises
Conceptual Exercises
Chapter 6 Probability
6.1 Experiments, Outcomes, Sample Spaces, and Events
Solution
Solution
Solution
Solution
Solution
Solution
Solution
Solution
6.2 Assignment of Probabilities
Solution
Solution
Solution
Solution
Solution
Solution
Solution
Solution
Solution
Odds
Solution
Solution
Solution
Exercises 6.2
Solutions to Check Your Understanding 6.2
6.3 Calculating Probabilities of Events
Experiments with Equally Likely Outcomes
Solution
Solution
Solution
Solution
Solution
The Complement Rule
Solution
Health Statistics
Exercises 6.3
Technology Exercises
Solutions to Check Your Understanding 6.3
6.4 Conditional Probability and Independence
Solution
Solution
6.5 Tree Diagrams
Solution
Solution
Solution
Solution
6.6 Bayes’ Theorem, Natural Frequencies
Solution
Solution
Natural Frequencies
Solution
Exercises 6.6
Solutions to Check Your Understanding 6.6
6.7 Simulation
Solution
Solution
Solution
Solution
Chapter 6 Summary
Chapter 6 Fundamental Concept Check Exercises
Chapter 6 Review Exercises
Conceptual Exercises
Chapter 7 Probability and Statistics
7.1 Visual Representations of Data
Bar and Pie Charts
Solution
Histograms
Solution
Median, Quartiles, and Box Plots
Solution
Solution
Exercises 7.1
Technology Exercises
Solutions to Check Your Understanding 7.1
7.2 Frequency and Probability Distributions
Solution
Solution
Probability Distributions
Solution
Random Variables
Solution
Solution
Solution
Exercises 7.2
Solutions to Check Your Understanding 7.2
7.3 Binomial Trials
Solution
Solution
Solution
Solution
Solution
Summing Binomial Probabilities
Exercises 7.3
Technology Exercises
Solutions to Check Your Understanding 7.3
7.4 The Mean
Solution
Solution
Solution
Expected Value
Solution
Solution
Solution
Solution
Exercises 7.4
Solutions to Check Your Understanding 7.4
7.5 The Variance and Standard Deviation
Solution
Solution
Variance and Standard Deviation of a Binomial Random Variable
Solution
Population Variance and Standard Deviation
Solution
Sample Variance and Standard Deviation
Solution
Chebychev’s Inequality
Solution
Solution
Exercises 7.5
Technology Exercises
Solutions to Check Your Understanding 7.5
7.6 The Normal Distribution
Solution
Solution Using Tables
Solution
Solution
Percentiles
Solution
Solution Using Tables
Solution
Solution
Solution
Solution
Solution
Solution
Exercises 7.6
Technology Exercises
Solutions to Check Your Understanding 7.6
7.7 Normal Approximation to the Binomial Distribution
Solution
Solution
Solution
Solution
Exercises 7.7
Technology Exercises
Solutions to Check Your Understanding 7.7
Chapter 7 Summary
Chapter 7 Fundamental Concept Check Exercises
Chapter 7 Review Exercises
Conceptual Exercises
Part Three
Chapter 8 Markov Processes
8.1 The Transition Matrix
Solution
Solution
Solution
Solution
Interpretation of the Entries of An
Transition Diagrams
Solution
Exercises 8.1
Technology Exercises
Solutions to Check Your Understanding 8.1
8.2 Regular Stochastic Matrices
Solution
Verification
Solution
Solution
Solution
APPENDIX Verification of Method for Obtaining the Stable Distribution
Exercises 8.8
Technology Exercises
Solutions to Check Your Understanding 8.2
8.3 Absorbing Stochastic Matrices
Solution
Solution
Solution
Solution
Solution
Solution
Solution
The Fundamental Matrix
Exercises 8.8
Technology Exercises
Solutions to Check Your Understanding 8.3
Chapter 8 Summary
Chapter 8 Fundamental Concept Check Exercises
Chapter 8 Review Exercises
Conceptual Exercises
Chapter 9 The Theory of Games
9.1 Games and Strategies
Solution
Solution
Strictly Determined Games
Solution
Solution
Exercises 9.1
Solutions to Check Your Understanding 9.1
9.2 Mixed Strategies
Solution
Solution
Solution
Solution
Exercises 9.2
Solutions to Check Your Understanding 9.2
9.3 Determining Optimal Mixed Strategies
Solution
Solution
Verification of the Fundamental Theorem of Game Theory
Exercises 9.3
Technology Exercises
Solutions to Check Your Understanding 9.3
Chapter 9 Summary
Chapter 9 Fundamental Concept Check Exercises
Chapter 9 Review Exercises
Conceptual Exercises
Part Four
Chapter 10 The Mathematics of Finance
10.1 Interest
Compound and Simple Interest
Solution
Solution
Solution
Solution
Solution
Solution
Effective Rate of Interest
Solution
Exercises 10.1
Technology Exercises
Solutions to Check Your Understanding 10.1
10.2 Annuities
Increasing Annuities
Solution
Solution
Solution
Decreasing Annuities
Solution
Solution
Solution
Exercises 10.2
Technology Exercises
Solutions to Check Your Understanding 10.2
10.3 Amortization of Loans
Solution
Solution
Solution
Solution
Solution
Exercises 10.3
Technology Exercises
Solutions to Check Your Understanding 10.3
10.4 Personal Financial Decisions
Individual Retirement Accounts
Solution
Solution
Solution
Verification of the Equivalence Conjecture
Solution
Consumer Loans and the Truth-in-Lending Act
Solution
Solution
Mortgages with Discount Points
Solution
Technology Solution
Solution
Solution
Solution
Solution
Solution
Caps
Solution
Exercises 10.4
Technology Exercises
Solutions to Check Your Understanding 10.4
10.5 A Unifying Equation
Solution
Solution
Solution
Solution
Solution
Solution
Nonfinancial Applications
Solution
Solution
Derivation of the Solution to the Difference Equation for a ? 1
Derivation of the Solution to the Difference Equation for a = 1
Appendix Financial Terms
Saving Accounts
Annuities
Exercises 10.5
Technology Exercises
Solutions to Check Your Understanding 10.5
Chapter 10 Summary
Chapter 10 Fundamental Concept Check Exercises
Chapter 10 Review Exercises
Conceptual Exercises
Chapter 11 Logic
11.1 Introduction to Logic
Statements
Solution
Simple Statements
Solution
Connectives
Solution
Symbolic Form of Compound Statements
Solution
Translating from Symbols to English
Solution
Translating from English to Symbols
Solution
Exercises 11.1
Solutions to Check Your Understanding 11.1
11.2 Truth Tables
Defining Statement Forms
Solution
Constructing a Truth Table
Solution
Constructing a Truth Table
First Solution
Second Solution
Constructing Truth Tables
Solution
Compressing Truth Tables
Solution
11.3 Implication
Hypothesis and Conclusion
Solution
Truth Value of an Implication
Solution
Using a Truth Table for an Implication
Solution
The Conjunction of a Statement and Its Converse
Solution
Implication and Common Language
Order of Precedence
Comparing Truth Tables
Solution
Order of Precedence
Solution
Implications and Computer Languages
Implication and Computing
Solution
Exercises 11.3
Solutions to Check Your Understanding 11.3
11.4 Logical Implication and Equivalence
Solution
Logical Equivalence
Solution
11.5 Valid Argument
Valid Argument
Solution
Multiple-Step Argument
Solution
Verify Validity
Solution
Verify Validity
Solution
Indirect Proof
Using an Indirect Proof
Solution
Invalid Argument
Invalid Argument
Solution
Testing an Argument
First Solution
Second Solution
Exercises 11.5
Solutions to Check Your Understanding 11.5
11.6 Predicate Calculus
Analyzing Predicates
Solution
Truth of a Predicate in a Fixed Universe
Solution
Universal and Existential Quantifiers
Solution
Negation of a Universal Statement
Solution
Negation of an Existential Statement
Solution
Negation of Statements with Quantifiers
Solution
Predicates with Two Variables
Solution
English Translation and Truth Value for Predicates with Two Variables
Solution
Analogy between Sets and Statements
Sets and Statements
Solution
Colloquial Usage
Exercises 11.6
Solutions to Check Your Understanding 11.6
11.7 Logic Circuits
Drawing a Circuit from a Logical Statement
Solution
Finding the Logical Statement from a Circuit
Solution
Simplifying a Circuit
Solution
Circuits with nand, nor, and xor
Exercises 11.7
Technology Exercises
Solutions to Check Your Understanding 11.7
Chapter 11 Summary
Chapter 11 Fundamental Concept Check Exercises
Chapter 11 Review Exercises
Conceptual Exercises
Chapter 12 Difference Equations and Mathematical Models
12.1 Introduction to Difference Equations
Balance Equation
Solution
Balance Equation
Solution
Solving a Difference Equation
Solution
Solving a Difference Equation
Solution
Analyzing a Difference Equation
Solution
Analyzing a Difference Equation
Solution
Population Modeling
Solution
Exercises 12.1
Technology Exercises
Solutions to Check Your Understanding 12.1
12.2 Difference Equations and Interest
Solution
Simple Interest
Solution
Compound Interest
Solution
Solution
Solution
Consumer Loans
Solution
Solution
Verification of Formula (1)
Verification of Formula (2)
Exercises 12.2
Technology Exercises
Solutions to Check Your Understanding 12.2
12.3 Graphing Difference Equations
Constant Graphs
Graphing a Difference Equation
Solution
Vertical Direction of a Difference Equation
Solution
Vertical Direction of a Difference Equation
Solution
Vertical Direction and Long-Run Behavior of a Difference Equation
Solution
Applying Test 2
Solution
Vertical Direction and Long-Run Behavior of a Difference Equation
Solution
Vertical Direction and Long-Run Behavior of a Difference Equation
Solution
Verification of Test 2
Graphing a Difference Equation
Solution
Graphing a Difference Equation
Solution
Using a Mortgage Balance Equation
Solution
Solutions to Check Your Understanding 12.3
Exercises 12.3
Technology Exercises
Solutions to Check Your Understanding 12.3
12.4 Mathematics of Personal Finance
Exercises 12.4
Technology Exercises
Solutions to Check Your Understanding 12.4
12.5 Modeling with Difference Equations
Proportionality
Exercises 12.5
Technology Exercises
Solutions to Check Your Understanding 12.5
Chapter 12 Summary
Chapter 12 Fundamental Concept Check Exercises
Chapter 12 Review Exercises
Appendices
Appendix A Areas Under the Standard Normal Curve
Appendix B Using the TI-84 Plus Graphing Calculator
Lists
Histograms
TVM Solver
Finance Functions
Entering an Address into a Formula by Pointing
Converting Formulas to Values
Summing a Column or Row of Numbers
Using Solver to Solve a System of Linear Equations
Simulating a Random Sample from a Probability Distribution
Creating a Frequency Distribution Table and Histogram for the Preceding Random Sample Generated
Using Goal Seek to Solve an Equation Having One Unknown
Using the Insert Function Dialog Box
Using Excel’s Financial Functions
Appendix D Wolfram|Alpha
Learning Objectives
Chapter 1: Linear Equations and Straight Lines
1.1?Coordinate Systems and Graphs
1.2?The Slope of a Straight Line
1.3?The Intersection Point of a Pair of Lines
1.4?The Method of Least Squares
Chapter 2: Matrices
2.1?Systems of Linear Equations with Unique Solutions
2.2?General Systems of Linear Equations
2.3?Arithmetic Operations on Matrices
2.4?The Inverse of a Square Matrix
2.5?The Gauss-Jordan Method for Calculating Inverses
2.6?Input-Output Analysis
Chapter 3: Linear Programming, A Geometric Approach
3.1?Linear Inequalities
3.2?A Linear Programming Problem
3.3?Fundamental Theorem of Linear Programming
3.4?Linear Programming
Chapter 4: The Simplex Method
4.1?Slack Variables and the Simplex Tableau
4.2 ?The Simplex Method I: Maximum Problems
4.3?The Simplex Method II: Nonstandard and Minimum Problems
4.4?Sensitivity Analysis and Matrix Formulations of Linear Programming Problems
4.5?Duality
Chapter 5: Sets and Counting
5.1?Sets
5.2?A Fundamental Principle of Counting
5.3?Venn Diagrams and Counting
5.4?The Multiplication Principle
5.5?Permutations and Combinations
5.6?Further Counting Techniques
5.7?The Binomial Theorem
5.8?Multinomial Coefficients and Partitions
Chapter 6: Probability
6.1?Experiments, Outcomes, Sample Spaces, and Events
6.2?Assignment of Probabilities
6.3 ?Calculating Probabilities of Events
6.4?Conditional Probability and Independence
6.5?Tree Diagrams
6.6?Bayes’ Theorem, Natural Frequencies
6.7?Simulation
Chapter 7: Probability and Statistics
7.1?Visual Representations of Data
7.2?Frequency and Probability Distributions
7.3?Binomial Trials
7.4?The Mean
7.5?The Variance and Standard Deviation
7.6?The Normal Distribution
7.7?Normal Approximation to the Binomial Distribution
Chapter 8: Markov Processes
8.1?The Transition Matrix
8.2?Regular Stochastic Matrices
8.3?Absorbing Stochastic Matrices
Chapter 9: The Theory of Games
9.1?Games and Strategies
9.2?Mixed Strategies
9.3?Determining Optimal Mixed Strategies
Chapter 10: The Mathematics of Finance
10.1?Interest
10.2?Annuities
10.3?Amortization of Loans
10.4?Personal Financial Decisions
10.5?A Unifying Equation
Chapter 11: Logic
11.1?Introduction to Logic
11.2?Truth Tables
11.3?Implication
11.4?Logical Implication and Equivalence
11.5?Valid Argument
11.6?Predicate Calculus
11.7?Logic Circuits
Chapter 12: Difference Equations and Mathematical Models (Online)
12.1?Introduction to Difference Equations
12.2?Difference Equations and Interest
12.3?Graphing Difference Equations
12.4?Mathematics of Personal Finance
12.5?Modeling with Difference Equations
Chapter 1
Exercises 1.1, page 5
Exercises 1.2, page 15
Exercises 1.3, page 23
Exercises 1.4, page 30
Chapter 1: Review Exercises, page 36
Chapter 2 Exercises 2.1, page 47
Exercises 2.2, page 56
Exercises 2.3, page 68
Exercises 2.4, page 78
Exercises 2.5, page 82
Exercises 2.6, page 88
Chapter 2: Review Exercises, page 93
Chapter 3
Exercises 3.1, page 103
Exercises 3.2, page 109
Exercises 3.3, page 117
Exercises 3.4, page 129
Chapter 3: Review Exercises, page 133
Feasible Sets for Chapter 3
Exercises 3.3
Exercises 3.4
Chapter 3: Review Exercises
Chapter 4
Exercises 4.1, page 142
Exercises 4.2, page 151
Exercises 4.3, page 159
Exercises 4.4, page 167
Exercises 4.5, page 177
Chapter 4: Review Exercises, page 182
Chapter 5
Exercises 5.1, page 189
Exercises 5.2, page 195
Exercises 5.3, page 200
Exercises 5.4, page 206
Exercises 5.5, page 213
Exercises 5.6, page 219
Exercises 5.7, page 225
Exercises 5.8, page 230
Chapter 5: Review Exercises, page 234
Chapter 6
Exercises 6.1, page 244
Exercises 6.2, page 254
Exercises 6.3, page 261
Exercises 6.4, page 271
Exercises 6.5, page 279
Exercises 6.6, page 286
Chapter 6: Review Exercises, page 296
Chapter 7
Exercises 7.1, page 305
Exercises 7.2, page 315
Exercises 7.3, page 322
Exercises 7.4, page 333
Exercises 7.5, page 343
Exercises 7.6, page 357
Exercises 7.7, page 362
Chapter 7: Review Exercises, page 366
Chapter 8
Exercises 8.1, page 378
Exercises 8.2, page 387
Exercises 8.3, page 396
Chapter 8: Review Exercises, page 400
Chapter 9
Exercises 9.1, page 409
Exercises 9.2, page 415
Exercises 9.3, page 424
Chapter 9: Review Exercises, page 427
Chapter 10
Exercises 10.1, page 437
Exercises 10.2, page 446
Exercises 10.3, page 456
Exercises 10.4, page 471
Exercises 10.5, page 482
Chapter 10: Review Exercises, page 487
Chapter 11
Exercises 11.1, page 495
Exercises 11.2, page 502
Exercises 11.3, page 508
Exercises 11.4, page 516
Exercises 11.5, page 523
Exercises 11.6, page 532
Exercises 11.7, page 536
Chapter 11: Review Exercises, page 540
Chapter 12
Exercises 12.1, page D6
Exercises 12.2, page D12
Exercises 12.3, page D20
Exercises 12.4, page D25
Exercises 12.5, page D29
Chapter 12: Answers to Fundamental Concept Check Exercises, page D32
Chapter 12: Review Exercises, page D32
Index of Applications