Lial m,greenwell r,ritchey n finite math and calculus with app 9ed 2012

This page intentionally left blank Finite Mathematics and Calculus with Applications NINTH EDITION Margaret L Lial American River College Raymond N Greenwell Hofstra University Nathan P Ritchey Youngstown State University Editor in Chief: Deirdre Lynch Executive Editor: Jennifer Crum Executive Content Editor: Christine O’Brien Senior Project Editor: Rachel S Reeve Editorial Assistant: Joanne Wendelken Senior Managing Editor: Karen Wernholm Senior Production Project Manager: Patty Bergin Associate Director of Design, USHE North and West: Andrea Nix Senior Designer: Heather Scott Digital Assets Manager: Marianne Groth Media Producer: Jean Choe Software Development: Mary Durnwald and Bob Carroll Executive Marketing Manager: Jeff Weidenaar Marketing Coordinator: Caitlin Crain Senior Author Support/Technology Specialist: Joe Vetere Rights and Permissions Advisor: Michael Joyce Image Manager: Rachel Youdelman Senior Manufacturing Buyer: Carol Melville Senior Media Buyer: Ginny Michaud Production Coordination and Composition: Nesbitt Graphics, Inc Illustrations: Nesbitt Graphics, Inc and IllustraTech Cover Design: Heather Scott Cover Image: John Wollwerth/Shutterstock Credits appear on page C-1, which constitutes a continuation of the copyright page Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks Where those designations appear in this book, and Pearson was aware of a trademark claim, the designations have been printed in initial caps or all caps Library of Congress Cataloging-in-Publication Data Lial, Margaret L Finite mathematics and calculus with applications — 9th ed / Margaret L Lial, Raymond N Greenwell, Nathan P Ritchey p.cm Includes bibliographical references and index ISBN-13: 978-0-321-74908-6 ISBN-10: 0-321-74908-1 Mathematics—Textbooks Calculus— Textbooks I Greenwell, Raymond N II Ritchey, Nathan P III Title QA37.3.L54 2013 510 — dc22 2010031432 NOTICE: This work is protected by U.S copyright laws and is provided solely for the use of college instructors in reviewing course materials for classroom use Dissemination or sale of this work, or any part (including on the World Wide Web), will destroy the integrity of the work and is not permitted The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher Printed in the United States of America For information on obtaining permission for use of material in this work, please submit a written request to Pearson Education, Inc., Rights and Contracts Department, 501 Boylston Street, Suite 900, Boston, MA 02116, fax your request to 617-671-3447, or e-mail at http://www.pearsoned.com/legal/permissions.htm 10—QG—15 14 13 12 11 www.pearsonhighered.com ISBN-10: 0-321-74908-1 ISBN-13: 978-0-321-74908-6 Contents Preface ix Dear Student xxii Prerequisite Skills Diagnostic Test CHAPTER R CHAPTER Algebra Reference xxiii R-1 R-2 R.1 Polynomials R.2 Factoring R.3 Rational Expressions R.4 Equations R.5 Inequalities R-16 R.6 Exponents R-21 R.7 Radicals R-5 R-8 R-11 R-25 Linear Functions 1.1 Slopes and Equations of Lines 1.2 Linear Functions and Applications 1.3 The Least Squares Line 17 25 CHAPTER REVIEW 38 EXTENDED APPLICATION Using Extrapolation to Predict Life Expectancy CHAPTER Systems of Linear Equations and Matrices 2.1 Solution of Linear Systems by the Echelon Method 2.2 Solution of Linear Systems by the Gauss-Jordan Method 2.3 Addition and Subtraction of Matrices 2.4 Multiplication of Matrices 2.5 Matrix Inverses 2.6 Input-Output Models 44 45 54 70 77 87 97 CHAPTER REVIEW 104 EXTENDED APPLICATION Contagion CHAPTER 42 110 Linear Programming:The Graphical Method 3.1 Graphing Linear Inequalities 3.2 Solving Linear Programming Problems Graphically 3.3 Applications of Linear Programming 112 113 CHAPTER REVIEW 134 EXTENDED APPLICATION Sensitivity Analysis 120 126 137 iii iv CONTENTS CHAPTER Linear Programming:The Simplex Method 4.1 Slack Variables and the Pivot 4.2 Maximization Problems 4.3 Minimization Problems; Duality 4.4 Nonstandard Problems 142 143 150 161 170 CHAPTER REVIEW 179 EXTENDED APPLICATION Using Integer Programming in the Stock-Cutting Problem CHAPTER Mathematics of Finance 187 5.1 Simple and Compound Interest 5.2 Future Value of an Annuity 5.3 Present Value of an Annuity; Amortization 188 200 209 CHAPTER REVIEW 218 EXTENDED APPLICATION Time, Money, and Polynomials CHAPTER Logic 224 6.1 Statements 6.2 Truth Tables and Equivalent Statements 6.3 The Conditional and Circuits 6.4 More on the Conditional 6.5 Analyzing Arguments and Proofs 6.6 Analyzing Arguments with Quantifiers 225 240 250 257 CHAPTER REVIEW 274 EXTENDED APPLICATION Logic Puzzles CHAPTER Sets and Probability 233 266 279 283 7.1 Sets 7.2 Applications of Venn Diagrams 7.3 Introduction to Probability 7.4 Basic Concepts of Probability 7.5 Conditional Probability; Independent Events 7.6 Bayes’ Theorem 284 292 302 311 322 336 CHAPTER REVIEW 343 EXTENDED APPLICATION Medical Diagnosis 350 222 183 CONTENTS CHAPTER Counting Principles; Further Probability Topics 8.1 The Multiplication Principle; Permutations 8.2 Combinations 8.3 Probability Applications of Counting Principles 8.4 Binomial Probability 8.5 Probability Distributions; Expected Value 353 361 370 381 389 CHAPTER REVIEW 400 EXTENDED APPLICATION Optimal Inventory for a Service Truck CHAPTER Statistics 405 407 9.1 Frequency Distributions; Measures of Central Tendency 9.2 Measures of Variation 9.3 The Normal Distribution 9.4 Normal Approximation to the Binomial Distribution 408 419 428 438 CHAPTER REVIEW 445 EXTENDED APPLICATION Statistics in the Law—The Castaneda Decision CHAPTER Nonlinear Functions 10 10.1 Properties of Functions 453 10.2 Quadratic Functions;Translation and Reflection 10.4 Exponential Functions 487 10.5 Logarithmic Functions 497 465 475 10.6 Applications: Growth and Decay; Mathematics of Finance CHAPTER 10 REVIEW 518 EXTENDED APPLICATION Power Functions 11 The Derivative 11.1 Limits 11.2 Continuity 449 452 10.3 Polynomial and Rational Functions CHAPTER 352 510 526 529 530 548 11.3 Rates of Change 557 11.4 Definition of the Derivative 11.5 Graphical Differentiation 570 588 CHAPTER 11 REVIEW 594 EXTENDED APPLICATION A Model for Drugs Administered Intravenously 601 v vi CONTENTS CHAPTER Calculating the Derivative 604 12 12.1 Techniques for Finding Derivatives 605 12.2 Derivatives of Products and Quotients 12.3 The Chain Rule 619 626 12.4 Derivatives of Exponential Functions 636 12.5 Derivatives of Logarithmic Functions 644 CHAPTER 12 REVIEW 651 EXTENDED APPLICATION Electric Potential and Electric Field CHAPTER 13 Graphs and the Derivative 659 13.1 Increasing and Decreasing Functions 13.2 Relative Extrema 656 660 671 13.3 Higher Derivatives, Concavity, and the Second Derivative Test 13.4 Curve Sketching 682 695 CHAPTER 13 REVIEW 704 A Drug Concentration Model for EXTENDED APPLICATION Orally Administered Medications CHAPTER 14 708 Applications of the Derivative 14.1 Absolute Extrema 711 712 14.2 Applications of Extrema 721 14.3 Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand 14.4 Implicit Differentiation 14.5 Related Rates 730 739 744 14.6 Differentials: Linear Approximation 751 CHAPTER 14 REVIEW 757 EXTENDED APPLICATION A Total Cost Model for a Training Program CHAPTER 15 Integration 15.1 Antiderivatives 15.2 Substitution 761 763 764 776 15.3 Area and the Definite Integral 784 15.4 The Fundamental Theorem of Calculus 15.5 The Area Between Two Curves 15.6 Numerical Integration 796 806 816 CHAPTER 15 REVIEW 824 Estimating Depletion Dates for Minerals EXTENDED APPLICATION 829 CONTENTS CHAPTER 16 Further Techniques and Applications of Integration 16.1 Integration by Parts 834 16.2 Volume and Average Value 16.3 Continuous Money Flow 16.4 Improper Integrals 842 849 856 16.5 Solution of Elementary and Separable Differential Equations 862 CHAPTER 16 REVIEW 875 EXTENDED APPLICATION Estimating Learning Curves in CHAPTER 17 Manufacturing with Integrals 880 Multivariable Calculus 883 17.1 Functions of Several Variables 17.2 Partial Derivatives 884 895 17.3 Maxima and Minima 906 17.4 Lagrange Multipliers 915 17.5 Total Differentials and Approximations 17.6 Double Integrals 923 928 CHAPTER 17 REVIEW 939 Using Multivariable Fitting to Create a EXTENDED APPLICATION Response Surface Design CHAPTER 18 945 Probability and Calculus 949 18.1 Continuous Probability Models 950 18.2 Expected Value and Variance of Continuous Random Variables 18.3 Special Probability Density Functions 961 970 CHAPTER 18 REVIEW 982 EXTENDED APPLICATION Exponential Waiting Times 987 Appendix Solutions to Prerequisite Skills Diagnostic Test A-1 A B Learning Objectives A-4 C MathPrint Operating System for TI-84 and TI-84 Plus Silver Edition D Tables A-12 Formulas from Geometry Area Under a Normal Curve Integrals A-10 833 vii viii CONTENTS Answers to Selected Exercises A-17 Credits C-1 Index of Applications I-1 Index Sources I-7 S-1 Special Topics to Accompany Finite Mathematics and Calculus with Applications The following material is provided free to adopters at www.pearsonhighered.com/mathstatsresources: Digraphs and Networks Graphs and Digraphs Dominance Digraphs Communication Digraphs Networks Review Exercises Index I-11 least squares line on, 28–29 limitations of, 695 limits on, 533, 535, 539–540 linear programming problem solving with, 121 logarithms on, 501, 702 matrix operations on, 73, 81, 90 mean and median on, 414 normal curves on, 431–432, 977 normal distribution and, 432–433 number e on, 490 permutations on, 357 piecewise functions on, 550 plotting data with, 19 probability applications on, 376–377 probability density functions on, 955–956 rational function on, 480 relative extrema on, 675 simplex method on, 148 sinking funds on, 205 tangent lines on, 573–574 trapezoidal rule on, 818 variance and standard deviation on, 421–422 z-scores on, 435 Graphs concavity of, 685–688 curve sketching and, 696–702 explanation of, R-17, of compound interest, 192 of derivatives, 590–591, 659–710 of equations, of exponential functions, 487–488, 520 of increasing and decreasing functions, 661–666 of intervals, R-17 of linear inequalities, R-18, 113–120, 134 of linear programming problems, 112–141 of lines, 10–13 of logarithmic functions, 499, 520, 701–702 of planes, 886–888, 940 of polynomial functions, 477–478, 696–697 of quadratic functions, 465–472, 518 of rational functions, 479–480, 698–701 of system of inequalities, 116–117 translations and reflections of, 471–472 Greatest common factor, R-5 Grouped frequency distributions explanation of, 409 mean of, 412, 445 standard deviation for, 422, 445 Growth, logistic, 868–870 Growth constant, 510, 866 Growth functions exponential, 510 limited, 514 Gunter, Edmund, 500 Half-life, 510 Half-open interval, R-17 Half-plane, 115 Hedonic responses, 945 Heraclitus, 712 Hexagrams, 354 Histograms, 951 Histograms, for probability distributions, 390 Horizontal asymptotes explanation of, 479, 519 method for finding, 541, 695 Horizontal lines equation of, graphs of, 11 slope of, Horizontal reflection, 471 Horizontal translation, 467 Hyperbolic paraboloid, 890 Hyperboloid of two sheets, 890 Hypothetical syllogism See Transitivity Idempotent Laws, 246 Identity Law, 246 Identity matrices, 87 Implicit differentiation, 739–742, 758 Impossible event, 304 Improper integrals applications of, 856–860, 875 explanation of, 857 Inconsistent system, 46 Increasing functions explanation of, 660–667 test for, 662 Indefinite integrals explanation of, 765–766, 769 of exponential functions, 769 power rule to find, 766–767 Independent events explanation of, 328–330, 344 product rule for, 329 Independent variables, 17, 884 Indeterminate form, 538 Index, R-26 Index of diversity, 506 Indicators, 144 Inductive reasoning, 235 Inequalities explanation of, R-17 graphs of, 113–120 linear, R-17, 113 polynomial, R-18–R-19 properties of, R-17 quadratic, R-18 rational, R-19–R-20 symbols for, R-16 systems of, 116–117 with fractions, R-19–R-20 Infinity, limits at, 540–543, 595 Inflection points explanation of, 686 method for finding, 695 Initial conditions, 864 Initial value problems, 864–865 Input-output matrices as open model, 100 closed, 100–102 explanation of, 97 Instantaneous rate of change alternate form of, 561 explanation of, 559–560, 575 formula for, 560, 561 Integer exponents, R-21–R-23 Integer programming, 127, 183–186 Integral calculus, 764 Integral sign, 765, 934 Integrals area between two curves and, 806–813, 824 convergent, 857 definite, 784–791, 798, 824, 838–840, 929–931 divergent, 857 double, 928–937, 941 improper, 856–860, 875 indefinite, 765–766, 769, 929 iterated, 931 learning curves and, 880–882 relationship between sums and, 767 tables of, 840 Integrand, 765, 931 Integration, 763–832 average value and, 846–847 by parts, 834–840, 875 by substitution, 776–784 column, 835–836 continuous money flow and, 850–853 improper integrals and, 856–860 limits of, 788, 936–937 lower limit of, 788 numerical, 816–821 region of, 931 rules of, 767–768 tabular, 835–836 techniques and applications of, 833–866 upper limit of, 788 variable limits of, 934–935 Integration constant, 765, 767–768 Intercepts, Interest compound, 190–193, 194, 488–490 continuously compounded, 490–491 effective rate of, 193–194 exact, 189 explanation of, 488–489 formulas for computing, 194 nominal, 512 ordinary, 189 per period rate of, 191 present value for, 513 rate of, 488 simple, 188, 197, 489, 519 stated, 512 stated rate of, 192 Intermediate Value Theorem, 554 Interpolation, 42 Intersections, 288 Interval notation, R-17 Intervals closed, R-17 half-open, R-17 open, R-17 real number, 951 Intravenous administration of drugs, 601–603 Invalid arguments explanation of, 257 testing for, 258–264, 268–272 Inventory, 405–406, 733 Inverse fallacy of, 259 matrix, 87–97 of statement, 252 Inverse functions, 499 I-12 Index Irrational numbers, 786n Isoprofit lines, 121 Isoquant, 889 Iterated integrals, 931 Jackson, Andrew, 978 Jordan, Wilhelm, 56n Kepler, Johannes, 843 Lagrange, Joseph Louis, 916 Lagrange multipliers applications for, 916–921, 947 explanation of, 915–916, 941 steps for use of, 916–917, 941 Laplace, Pierre Simon, 441 Law of diminishing returns, 690 Leading coefficients, 475 Learning curves, 515, 880–882 Least common denominators, R-10 Least squares line calculation of, 27–30, 39 correlation and, 30–32 explanation of, 25 Least squares method, 20 Leibniz, Gottfried Wilhelm, 531n, 605, 766 Leibniz notation, 605 Leontief, Wassily, 97 Level curves, 888 Level surface, 891 Like terms, R-2 Limited growth functions, 514 Limits, 530–543 at endpoints, 725 at infinity, 540–543 existence of, 535, 595 explanation of, 531–532 from left, 531 from right, 531 methods for determining, 531–535, 539–540 of function, 531–532, 595 of integration, 788, 936–937 on graphing calculators, 533, 535, 539–540 one-sided, 531 rules for, 536 two-sided, 531 Linear approximation, 751–755, 758 Linear cost function, 21, 39 Linear equations explanation of, R-11, solving of, R-11–R-12 systems of See Systems of equations Linear functions, 1–43 break-even analysis and, 21–22 cost analysis and, 20–21, 39 explanation of, 17, 465 least squares method and, 20 marginal cost and, 20 supply and demand and, 17–19 temperature and, 22–23 Linear inequalities application of, 113 explanation of, R-17, 113 method for graphing, 113–120, 134 solving of, R-17 Linear programming application of, 126–134 explanation of, 120 graphical method of, 112–141 simplex method of, 142–186 Linear programming problems duals of, 164–165 graphically solving, 113, 120–126, 134 graphing calculators to solve, 121 maximization and, 120–121, 123–124 minimization and, 121–124, 166 nonstandard, 170–179 with mixed constraints, 170 Linear regression, 20 Linear systems echelon method to solve, 45–54 Gauss-Jordan method to solve, 54–70, 105 transformations of, 47 Lines equation of tangent, 581 equations of, 4–8, 38, 571–572 graphs of, 10–13 horizontal, 7, 11 parallel, 8–9, 38 perpendicular, 9–10, 38 secant, 570–571 slope of, 3–4, 38, 558 tangent, 570–574, 581 vertical, 7–8 Local extrema See Relative extrema Local maximum See Relative maximum Local minimum See Relative minimum Logarithmic equations explanation of, 501 solving of, 501–502 Logarithmic functions, 497–506 continuity and, 552 derivatives of, 644–648, 652 explanation of, 498–499, 519, 652 graphs of, 499, 520, 701–702 Logarithms change-of-base theorem for, 500–501, 520 common, 500 evaluation of, 500–501 explanation of, 497–498, 519 natural, 500 on graphing calculators, 501 properties of, 499–500, 519 Logic, 224–282 symbolic, 225 to simplify circuits, 245 Logic puzzles, 279–282 Logical connectives, 225 Logistic curve, 868, 869–870 Logistic equations, 868 Logistic function, 639 Logistic growth model, 868 Marginal analysis, 611–612, 754–755 Marginal cost average, 623 explanation of, 20, 563, 611 method for finding, 612 Marginal profit, 613–614 Marginal revenue, 613 Marshall, Alfred, 18 Math of finance formulas, 488–490, 519 Mathematical models, 2, 45 Mathematical statements, 230 Matrices, 44–111 addition of, 72–73, 105 applications for, 70–71 augmented, 55 classification of, 70–71 coefficient, 90 column, 71 demand, 98–99 equality of, 71 explanation of, 54 identity, 87 input-output, 97 inverses, 87–97, 105 multiplication of, 77–86 notation, 83 product of, 78–86 product of scalar and, 77–78, 105 product of two, 78, 105 production, 98–99, 101–102, 105 row, 71 size of, 70–71 square, 71 subtraction of, 73, 105 zero, 104 Matrix inverses explanation of, 87–97, 105 finding multiplicative, 87–90 Maturity value, 189–190 Maximization problems, 150–161 elements of, 146 simplex method to solve, 163 solving graphically, 120–121, 123–124 Maximum See also Extrema absolute, 712, 713–715 relative, 671, 674, 906 Maximum form, standard, 143 Maximum sustainable harvest, 725–726 Maximum values, finding, 123–124 Mean See also Expected value deviations from, 419 explanation of, 410, 445 for binomial distributions, 439, 445 for frequency distributions, 410 for grouped data, 412, 445 for squared deviations, 420 population, 412 sample, 412 Median, 412–413, 966–967, 982 Medical diagnosis, 350–351 Midpoint rule, 785 Minimization problems duality, 161–170 explanation of, 161 simplex method to solve, 161–163 solving graphically, 121–124 solving nonstandard problems, 173 Minimum See also Extrema absolute, 712, 713–715 relative, 671, 674, 906 Minimum average cost, 623 Minimum values, 123–124 Mode, 413–414 Modus Ponens, 258, 269 Modus Tollens, 259, 263, 269 Index I-13 Money flow accumulated amount of, 853–855, 875 explanation of, 849–850 present value of, 851–853, 855, 875 total, 850–851, 875 Multiplication of binomials, R-4 of matrices, 77–86 of polynomials, R-3–R-5 of rational expressions, R-8 order of operations, R-2 Multiplication principle, explanation of, 353–355 Multiplication property of equality, R-11 of inequality, R-17 Multiplicative inverse matrices, 87–90 Multipliers, 99 Multivariable fitting, 945–948 Mutually exclusive events, explanation of, 305 Napier, John, 500 Nash, John F JR-, 912 Natural logarithms, 500 Natural numbers, 355 Negation Law, 246 Negations explanation of, 226 of conditional statements, 244–245 of quantifiers, 267–272 of statements, 226 truth tables for, 227 Negative exponents, R-22 Newton, Isaac, 531n, 605 Nominal rate, 192, 512 Nonlinear functions, 452–528 explanations of, 454 exponential functions as, 487–493 illustrations of, 453 limited growth, 514 logarithmic functions as, 497–506 polynomial functions as, 475–478 properties of, 453–461 quadratic functions as, 465–472 rational functions as, 479–481 Nonstandard problems, 170–179, 180 Normal curves area under, 431, 433, 434–435, 445, 974 explanation of, 429, 974 properties of, 430 standard, 430–432 Normal distribution, 428–438 explanation of, 429, 973–979, 983 properties of, 430 standard, 974–975 z-scores and, 433, 445 Notation for derivatives, 605, 683 Leibniz, 605 Numbers counting, 235 critical, 662, 676–677 irrational, 786n natural, 355 real, R-2 Numerators, rationalizing, R-28 Numerical analysis, 821 Numerical integration, 816–821 Objective function, 120, 138 Oblique asymptote, 698 Odd functions, 460 Odds, 313–314, 344 Olson, Ken, 225 Open interval, R-17, 550 Open model, 100 Operations, order of, R-2 Optimal inventory, 405–406 Order of operations, R-2 Ordered pairs, Ordered triples, 885 Ordinary annuities explanation of, 202 future value of, 202–203 Ordinary interest, 189 Origin explanation of, graph of line through, 11–12 Outcomes, 302 Outlier, 32 Parabolas area of segment of, 819 explanation of, 466 Paraboloid, 888, 890 Parallel circuits, 245 Parallel lines, 8–9, 38 Parameter, 49 Parent-progeny function, 725 Parentheses, order of operations, R-2 Partial derivatives evaluation of, 897–898 explanation of, 895–896, 940 rate of change and, 898–900 second-order, 900–901, 940 Particular solutions to differential equations, 864 Pascal, Blaise, 384, 950 Pascal’s triangle, 384–385 Payment period, 202 Pearl, Raymond, 869 Perfect squares, R-7 Permutations distinguishable, 358–359, 377, 400 explanation of, 355–356, 400 formula for, 355 use of, 363–367, 375, 377 Perpendicular lines, 9–10, 38 Piecewise functions, 533, 553 Pivot explanation of, 146–147 method for finding, 147–148, 155–157 Plane explanation of, 886 graph of, 886–888, 940 xy-, 885 Point of diminishing returns, 690 Point-slope form, 6, Polynomial functions continuity and, 551 explanation of, 475, 519 graphs of, 696–697 properties of, 478, 519 Polynomial inequalities, R-18–R-19 Polynomials addition of, R-2–R-3 cubic, 477 explanation of, R-2 factoring of, R-7 graphing of, 477–478 identifying degree of, 478 multiplication of, R-3–R-5 prime, R-7 quartic, 477 subtraction of, R-2–R-3 Popularity Index, 782 Population mean, 412 Population standard deviation, 422 Population variance, 422 Positive root, R-23 Power functions, 476, 526–528 Power rule antiderivative and, 766–767 explanation of, 607–608, 651, 824 Powers, order of operations, R-2 Premises, 257, 262 Present value explanation of, 194, 513 of annuities, 209–211 of compound interest, 194 of continuous money flow, 851–853, 875 Prime polynomials, R-7 Principal, 188, 488 Principal root, R-23 Principle of Duality, 246 Probability background of, 950 basic principle of, 305, 311–321, 344 Bayes’ theorem and, 336–343 binomial, 382–385, 395, 400 combinations and, 361–370 complement rule for, 312–313, 344 conditional, 322–336, 344 counting principles and, 352–406 empirical, 307, 428–429 experiments and, 302–303 explanation of, 305 mutually exclusive events and, 305, 344 normal, 432–433 odds in, 313–314 permutations and, 355–359 product rule of, 325, 344 properties of, 314, 344 union rule for, 311–312, 344 Probability applications of counting principles, 370–381 of tree diagrams, 371–372 Probability density functions discrete probability functions vs., 952 explanation of, 952–957, 982 exponential distribution and, 972–973 normal distribution and, 973–979 special, 970–979 uniform distribution and, 970–972 I-14 Index Probability distributions applications of, 389–391 continuous, 951–952 expected value and, 391–395 expected value of, 961 explanation of, 314, 389 method for finding, 428–429, 439 random variables and, 389 variance of, 961–962 Probability functions discrete, 951 explanation of, 390, 950 of random variable, 951 Probability models, continuous, 949–957 Probability of event, 950n Problem of the points, 950 Producers’ surplus, 812, 825 Product matrices, 78–86, 105 Product rule explanation of, 325–328, 344, 619–621, 622, 651 for independent events, 329 tree diagrams used with, 326 Production function, 888–889, 899–900 Production matrices explanation of, 98–99 method to find, 101 Profit, 21 Proportional, Pry, R- H., 869 Pythagorean theorem, 252, 253 Quadrants, Quadratic equations, R-12 Quadratic formula, R-13, 773, 807 Quadratic functions explanation of, 465, 518 graphs of, 465–472, 518 maximum or minimum of, 469 Quadratic inequalities, R-18 Quantifiers existential, 267 explanation of, 267 negation of, 267–272 universal, 267 Quartic polynomials, 477 Quirin, Jim, 782 Quotient rule, explanation of, 621–622, 651 Radical sign, R-26 Radicals explanation of, R-25–R-29 properties of, R-26 Radicand, R-26 Random samples, 408 Random variables continuous, 951–952, 961–967 explanation of, 389, 950 probability function of, 951 Range domain and, 457–458, 884 explanation of, 419, 454 Rate, 188 Rate per compounding period, 192 Rates of change explanation of, 558 formula for average, 558 formula for instantaneous, 560, 561 of derivatives, 575, 682, 898–900 Rational equations, R-14–R-16 Rational exponents, R-23–R-24 Rational expressions combining of, R-9–R-11 explanation of, R-8 properties of, R-8 reducing of, R-8–R-9 Rational functions continuity and, 551 explanation of, 479, 519 graphs of, 479–480, 698–701 Rational inequality, R-19–R-20 Real number interval, 951 Real numbers, R-2 Real zero, 477 Reasoning by transitivity, 260, 263, 271 deductive, 257 inductive, 235 Reflections of functions, 470–471 Region of feasible solutions, 116–117 Region of integration, 931 Related rates, 744–749, 758 Relative extrema explanation of, 671–672, 940 first derivative test for, 673–674 for realistic problems, 679 methods for finding, 674–679 on graphing calculators, 675 second derivative test for, 689, 704, 909, 940 Relative maximum explanation of, 671, 674, 906 in functions of two variables, 906–912 Relative minimum explanation of, 671, 674, 906 in functions of two variables, 906–912 Removable discontinuity, 550 Residuals, 42 Response surfaces, 945–948 Revenue and elasticity, 736 explanation of, 21 Riemann, Georg, 788n Riemann integral, 788n Riemann sum, 788n Root functions, 551 Roots cube, R-23 positive, R-23 principal, R-23 square, R-23 Rounding of money, 189 Row matrices, 71 Row operations, 55–56, 105 Row vector, 71 Rule of 70, 195–196, 505 Rule of 72, 195–196, 505 Saddle, 890 Saddle points, 907, 909–910 Sample mean, 412 Sample space, 302–303, 322 Sample standard deviation, 422 Sample variance, 422 Scalar, 77, 105 Scatterplots, 12, 29, 32 Secant line, 570–571 Second derivative explanation of, 682 method for finding, 683–684 Second derivative test, 688–689, 688–691, 704 Second-order contacts, 111 Second-order derivatives, 900–901, 940 Sensitivity, 341 Sensitivity analysis, 137–141, 155–156 Separable differential equations, 862, 865, 876 Separation of variables, 865–867 Series, circuit, 245 Set-builder notation, 285 Set operations explanation of, 287–290 for events, 304 Sets complement of, 287 disjoint, 288, 344 elements of, 284 empty, 284 explanation of, 284 intersection of, 288 members of, 284, 344 union of, 289 union rule for, 296, 344 universal, 285 Shadow costs, 167 Shadow profits, 139 Shannon, Claude, 245 Shortage, 19 Simple event, 304 Simple interest applications of, 188–190 explanation of, 188, 489, 519 formulas for, 197 maturity value of, 189 Simplex method, 142–186 explanation of, 143 standard minimization problems and, 161–163 steps in, 153, 179 use of, 143, 153–155 Simplex tableau, 144 Simpson, Thomas, 819 Simpson’s rule, 818–821, 825 Sinking funds, 204–206 Size of matrices, 70–71 Skewed distributions, 429 Slack variables, 143–144 Slope explanation of, of curve, 571 of line, 3–4, 38 of tangent line, 570–573, 662, 687 Slope-intercept form, 4–5, Solid of revolution, 842–845, 875 Solver feature, 155 Spawner-recruit function, 725 Specificity, 341 Spreadsheet exercises, 34–38, 41, 42, 66–68, 84, 86, 95, 102–104, 108, 134, 158, 160, 170, 178, 179, 217, 388, 416, 418, 425, 427, 448, 603, 642, 655, 658, 762, 794, 892, 904, 915, 923 Index I-15 Spreadsheets approximation of area on, 790 binomial probabilities on, 385 combinations on, 363 extrema on, 911–912, 920–921 financial calculations on, 192 Gauss-Jordan method on, 60 least squares line on, 29 matrix inverses on, 90 normal curve values on, 432 normal distribution and, 432 organizing data on, 73 permutations on, 357 sinking funds on, 206 Solver feature in, 155 standard deviation and, 421 trapezoidal rule on, 818 Square matrices, 71 Square root, R-23 Squares difference of two, R-7 perfect, R-7 Standard deviation application of, 422–425 cautions regarding, 422 explanation of, 422, 962, 982 for binomial distributions, 439, 445 for grouped distribution, 422 method for finding, 962 methods for finding, 421–422, 445 normal random variables and, 978 population, 422 sample, 422 variance of, 419 Standard form, R-12 Standard maximization problem duals and, 161 explanation of, 143, 161 Standard maximum form, 143, 179 Standard minimization problem duals and, 161, 166 explanation of, 161 Standard minimum form, 161, 180 Standard normal curves, 430–432 Standard normal distribution, 974-975 Stated interest, 512 Statements biconditional, 242 component, 225 compound, 225 conditional, 240 conjunctions and, 228–229 disjunctions and, 229 equivalent, 237–238, 244, 245, 275 explanation of, 225 logical, 225 mathematical, 230 negation of, 226 symbolic, 226–227 Statistic, 413 Statistical process control, 424–425 Statistics, 407–451 explanation of, 408 frequency distribution and, 408–419 legal applications for, 449–450 measures of variation and, 419–428 normal approximation to binomial distributions and, 438–445 Step functions, 461 Stochastic processes, 328 Stock-cutting problem, 183–186 Subsets, 285–287, 344 Substitution explanation of, 780 integration by, 776–784 method of, 780, 824 Subtraction in order of operations, R-2 of matrices, 73, 105 of polynomials, R-2–R-3 of rational expressions, R-8 Sum, derivative of, 610 Sum or difference rule explanation of, 609, 651, 824 indefinite integrals and, 767 Summation notation, 26, 410 Supply curves, 17–18 Surface explanation of, 887 volume under a, 932 Surplus, 19 Surplus variable, 170 Sylvester, James Joseph, 54n Symbolic logic, 225 Symbolic statements, 226–227, 251–252 Symbols, 226–227 Systems of equations, 44–111 explanation of, 45 inverse matrices and, 90–94 solving for, 47–50 Systems of inequalities applications of, 113, 117–118 graphs of, 113–120 Tabular integration, 835–836 Tangent line equation of, 581 explanation of, 570–574 on graphing calculators, 573–574 slope of, 570–573, 687, 741 Tautology, 244 Technology exercises See Graphing calculator exercises and Spreadsheet exercises Technology notes Graphing calculator, 12, 13, 19, 20, 99, 115, 116, 121, 155, 203, 206, 210, 228, 230, 355, 376, 410, 435, 459, 472, 477, 493, 533, 573, 579, 591, 610, 666, 688, 697, 715, 781, 788, 808, 839, 840, 844, 869, 870, 955, 966, 977 Spreadsheet, 73, 81, 90, 99, 155, 167, 192, 206, 214, 553, 565 Temperature, 22–23 Terms explanation of, R-2 like, R-2 of annuities, 202 unlike, R-2 Third derivative, 683 Time doubling, 497 explanation of, 488 minimizing, 722–723 Time of money earning interest, 188 Total change, 790–791 Total cost model, 761–762 Total differentials for three variables, 925, 941 for two variables, 923–924, 941 Total money flow, 850–851, 875 Traces, 888 Transformations of system, 47 Transitivity, reasoning by, 260, 263, 271 Translations of functions, 470–471 Transportation problems, 54, 173–175 Transpose, 163 Trapezium, 816n Trapezoid, 816n Trapezoidal rule, 785, 816–818, 825 Tree diagrams explanation of, 286 probability applications for, 326, 328, 332, 336–337, 339, 366, 371–372 Trials, 302 Trigrams, 354 Trinomials explanation of, R-6 factoring of, R-6–R-8 Truth tables alternative method for constructing, 236–237 explanation of, 227 for biconditional statements, 254 for conditional statements, 241, 243–244, 253, 258 for conjunction, 228 for disjunction, 229 for equivalent statements, 233–240 for logical operators, 274 for negation, 227 for valid argument, 260 standard method for constructing, 233–235 summary of, 254 testing validity of argument with, 258 Truth values explanation of, 227 of compound statements, 229–230 of conditional statements, 241–243 of conjunctions, 228 of mathematical statements, 230 Turning points, 477 Two-phase method, 172 Unbounded, 117 Uniform distribution, 970–972, 983 Union, of sets, 289 Union rule for disjoint sets, 297 for mutually exclusive events, 311–312 for probability, 311–312 for sets, 296 Unique solution explanation of, 46 systems without, 61–65 Unit elasticity, 734–735 Unit learning curve model, 880 Universal quantifiers, 267 Universal sets, 285 Unlike terms, R-2 I-16 Index Valid arguments explanation of, 257 testing for, 258–264, 268–272 truth tables and, 260 Value average, 846–847, 875 capital, 859–860, 876 expected, 961–967 future, 851 present, 851–853 Variables artificial, 175–176, 180 basic, 146 dependent, 17, 884 explanation of, R-2 functions of several, 884–891 functions of two or more, 884 independent, 17, 884 random, 389, 950, 951, 961–967 separation of, 865–867 slack, 143–144 surplus, 170 three, total differential for, 925, 941 two, total differential for, 923–924, 941 Variance alternative formula for, 964, 982 calculation of, 420, 445 explanation of, 419–420, 961–962, 982 for density function, 961–964, 982 of probability distribution, 961–962 of sample, 420 of standard deviation, 419 population, 422 sample, 422 square root of, 420 Variation measures range as, 419 standard deviation as, 420–425 Vectors column, 71 row, 71 Velocity explanation of, 561, 684–685 integrals and, 772–773 Venn, John, 287 Venn diagrams applications of, 292–302 conditional probability and, 323 explanation of, 287 Verhulst, P.F., 869 Vertex, 466 Vertical asymptotes explanation of, 479, 519 method for finding, 539–540, 695 Vertical line equation of, slope of, 7–8 Vertical line test, 459–460, 518 Vertical reflection, 466 Vertical translation, 466 Volume double integrals and, 932–934, 941 maximizing, 723–724 of box, 919–921 of solid of revolution, 842–845, 875 under a surface, 932 Waiting times, exponential, 987–989 Warehouse problem, 173 Watson, Thomas, 225 Writing exercises, 13–16, 23, 32–39, 41–43, 52, 53, 65, 67–69, 74–76, 83–86, 95, 103, 104, 106, 109, 110, 132–136, 149, 158–161, 168, 169, 177, 178, 180–183, 186, 197–200, 207, 215–217, 219–223, 231, 232, 238, 239, 240, 247–250, 255, 256, 265, 273, 276–278, 290–292, 298–300, 307–310, 316–318, 320, 321, 330–336, 342, 343, 345–347, 349, 350, 359, 361, 367, 369, 370, 378, 381, 386–389, 396, 399, 401, 402, 404, 405, 463–465, 472–474, 481, 483, 485, 486, 494, 495, 497, 506, 507, 515–517, 521, 523–525, 528, 544–546, 555, 556, 566–569, 584–587, 592, 596, 598, 615–619, 624–626, 633–635, 641, 642, 648–650, 652–655, 658, 668–670, 680, 692, 694, 702, 705, 706, 708, 718–720, 728, 730, 737, 738, 744, 758–760, 774, 782, 783, 791, 792, 795, 796, 804, 805, 815, 822, 825–827, 828, 829, 841, 860, 861, 871–875, 876–880, 881, 891, 893, 894, 903, 904, 905, 912, 913, 914, 915, 922, 928, 938, 942–944, 957, 967, 979, 981, 983, 984 equivalent expressions for change in, 578–579 function of, 453 x-axis, x-coordinate, in exponential functions, 493 x-intercept, xy-plane, 885 xy-trace, 888 xz-trace, 888 y-axis, y-coordinate explanation of, in exponential functions, 493 y-intercept, Yield to maturity (YTM), 222 Your Turn exercises, R-3, R-4, R-6, R-7, R-9, R10, R-12, R-14, R-15, R-17, R-18, R-20, R23, R-24, R-26, R-28, 4-6, 8, 9, 17, 19, 21, 22, 29, 31, 48, 50, 52, 57, 60, 63, 72, 73, 79, 81, 90, 91, 94, 99, 101, 115, 117, 124, 127, 129, 145, 148, 154, 155, 164, 166, 173, 175, 189, 190, 191, 193–195, 197, 201, 204–206, 210, 212, 213, 226–228, 230, 234, 238, 242–244, 251, 253, 254, 262, 263, 268–271, 285–289, 293, 294, 296, 297, 303–307, 311–314, 323–327, 329, 330, 337, 339, 353–356, 358, 359, 363, 364–366, 372–375, 377, 383–385, 390, 391, 393–395, 410, 412, 413, 421, 423, 432–434, 440, 442, 458, 459, 468, 469, 476, 488, 489, 491, 498, 500–504, 510, 511, 513, 514, 530, 532–534, 537, 538, 543, 552, 553, 558, 559, 562, 564, 572, 577, 579–581, 589, 590, 608–610, 612, 613, 621–623, 627, 628, 630, 631, 637, 638, 646, 647, 661, 664, 665, 672, 675–678, 683–685, 688, 689, 697, 699, 700, 702, 714, 715, 722, 733–735, 737, 740–742, 745, 747, 748, 753–755, 765, 767–770, 773, 777–780, 790, 791, 797, 799–801, 807–809, 813, 818, 820, 836–840, 844, 847, 850, 853–855, 858, 859, 862, 864, 866, 868, 885, 886, 889, 896, 898, 901, 908, 910, 917, 921, 924–926, 929, 930, 932, 933, 935, 953, 955, 957, 963, 964, 967, 972, 973, 977 yz-trace, 888 z–scores explanation of, 433, 975, 983 importance of, 434–435 normal probability calculations and, 434–435 use of, 434–435, 976–978 Zero-factor property, R-12 Zero matrices, 104 Sources This is a sample of the comprehensive source list available for the tenth edition of Calculus with Applications The complete list is available at the Downloadable Student Resources site, www.pearsonhighered.com/mathstatsresources, as well as to qualified instructors within MyMathLab or through the Pearson Instructor Resource Center, www.pearsonhighered.com/irc Chapter Section 1.1 Example 10 from Morbidity and Mortality Weekly Report, Centers for Disease Control and Prevention, Vol 58, No 44, Nov 13, 2009, p 1227 Example 14 from http://www.trendscollegeboard.com/college_ pricing/1_3_over_ time_current_dollars.html Exercise 62 from Time Almanac 2010, p 150 Exercise 63 from Time Almanac 2010, pp 637–638 Exercise 64 from Alcabes, P., A Munoz, D Vlahov, and G Friedland, “Incubation Period of Human Immunodeficiency Virus,” Epidemiologic Review, Vol 15, No 2, The Johns Hopkins University School of Hygiene and Public Health, 1993, pp 303–318 Exercise 65 from Hockey, Robert V., Physical Fitness: The Pathway to Healthful Living, Times Mirror/ Mosby College Publishing, 1989, pp 85–87 Exercise 66 from Science, Vol 253, No 5017, July 19, 1991, pp 306–308 Exercise 67 from Science, Vol 254, No 5034, Nov 15, 1991, pp 936–938, and http://www.cdc.gov/nchs/data Exercise 68 from World Health Statistics 2010, World Health Organization, pp 56–57 10 Exercise 69 from The New York Times, Sept 11, 2009, p A12 11 Exercise 70 from U S Census Bureau, http://www.census.gov/ population/socdemo/ hh-fam/ms2.pdf 12 Exercise 71 from 2008 Yearbook of Immigration Statistics, Office of Immigration Statistics, Aug 2009, p 13 Exercise 72 from Science News, June 23, 1990, p 391 14 Exercise 73 from Acker, A and C Jaschek, Astronomical Methods and Calculations, John Wiley & Sons, 1986; Karttunen, H (editor), Fundamental Astronomy, Springer-Verlag, 1994 15 Exercise 74 from http://www.stateofthemedia org/2009/narrative_audio_audience.php? media=10&cat=2#1listeningtoradio 16 Exercise 75 from http://www.trendscollegeboard.com/college_ pricing/1_3_ over_time_current_dollars.html Section 1.2 Page 18 from http://www.agmrc.org/media/ cms/oceanspray_4BB99D38246C8.pdf Exercise 46 from Science News, Sept 26, 1992, p 195, Science News, Nov 7, 1992, p 399 Exercise 48 from http://www.calstate.edu/ budget/fybudget/2009-2010/supportbook2/ challenges-off-campus-costs.shtml Section 1.3 Page 25 from U.S Dept of Health and Human Services, National Center for Health Statistics, found in New York Times 2010 Almanac, p 394 Example from Public Education Finances 2007, U.S Census Bureau, July 2009, Table http://www2.census.gov/govs/school/07f33pub pdf; The Nation’s Report Card: Reading 2007, National Center for Education Statistics, U.S Department of Education, Sept 2007, Table 11 http://nces.ed.gov/ nationsreportcard/pdf/main2007/2007496.pdf Exercise from “November 1989 Course 120 Examination Applied Statistical Methods” of the Education and Examination Committee of The Society of Actuaries Reprinted by permission of The Society of Actuaries Exercise 10 from http://www.bea.gov/ national/FA2004/SelectTable.asp Exercise 11 from http://www2.fdic.gov/ hsob/hsobRpt.asp Exercise 12 from http://www.ncta.com/Stats/ CableAvailableHomes.aspx Exercise 13 from http://www.federalreserve gov/releases/g19/Current/ Exercise 14 from http://www.nada.org/NR/ rdonlyres/0FE75B2C-69F0-4039-89FE1366B5B86C97/0/NADAData08_no.pdf Exercise 15 from American Airlines, http:// www.aa.com 10 Exercise 15 from The New York Times, Jan 7, 2000 11 Exercise 16 from www.nctm.org/wlme/ wlme6/five.htm 12 Exercise 17 from Stanford, Craig B., “Chimpanzee Hunting Behavior and Human Evolution,” American Scientist, Vol 83, May–June 1995, pp 256–261, and Goetz, Albert, “Using Open-Ended Problems for Assessment,” Mathematics Teacher, Vol 99, No 1, August 2005, pp 12–17 13 Exercise 18 from Pierce, George W., The Songs of Insects, Cambridge, Mass., Harvard University Press, Copyright © 1948 by the President and Fellows of Harvard College 14 Exercise 19 from Digest of Education Statistics 2006, National Center for Education Statistics, Table 63 15 Exercise 20 from Historical Poverty Tables, U.S Census Bureau 16 Exercise 21 from Lee, Grace, Paul Velleman, and Howard Wainer, “Giving the Finger to Dating Services,” Chance, Vol 21, No 3, 2008, pp 59–61 17 Exercise 23 from data provided by Gary Rockswold, Mankato State University, Minnesota 18 Exercise 25 from Carter, Virgil and Robert E Machol, Operations Research, Vol 19, 1971, pp 541–545 19 Exercise 26 from Whipp, Brian J and Susan Ward, “Will Women Soon Outrun Men?” Nature, Vol 355, Jan 2, 1992, p 25 The data are from Peter Matthews, Track and Field Athletics: The Records, Guinness, 1986, pp 11, 44; from Robert W Schultz and Yuanlong Liu, in Statistics in Sports, edited by Bennett, Jay and Jim Arnold, 1998, p 189; and from The World Almanac and Book of Facts 2006, p 880 20 Exercise 27 from http://www.run100s.com/HR/ Review Exercises Exercises 56 and 57 from TradeStats ExpressTM, http://tse.export.gov Exercise 58 from U.S Census Bureau, Historical Income Tables–Households, Table H-6, 2008 Exercise 59 from Chicago Tribune, Feb 4, 1996, Sec 5, p 4, and NADA Industry Analysis Division, 2006 Exercise 60 from Food and Agriculture Organization Statistical Yearbook, Table D1, Table G5, http://www.fao.org/economic/ess/ publications-studies/statistical-yearbook/ fao-statistical-yearbook-2009/en/ Exercise 62 from http://www.ers.usda.gov/ Data/FoodConsumption/spreadsheets/mtpcc.xls Exercise 63 from http://www.census.gov/ population/socdemo/hh-fam/ms1.xls Exercise 64 from http://www.census.gov/ hhes/www/poverty/histpov/famindex.html Exercise 65 from http://www.census.gov/ popest/states/NST-ann-est.html; http://doa alaska.gov/dop/fileadmin/socc/pdf/bkgrnd_ socc23.pdf Exercise 66 from Moore, Thomas L., “Paradoxes in Film Rating,” Journal of Statistics Education, Vol 14, 2006, http://www amstat.org/publications/jse/v14n1/datasets moore.htm1 Extended Application Page 43 from Health, United States, 2009, National Center for Health Statistics, U.S Department of Health and Human Services, Table 24, http://www.cdc.gov/nchs/data/hus/ hus09.pdf Chapter Section 2.1 Exercise 44 from Goetz, Albert, “Basic Economics: Calculating Against Theatrical Disaster,” The Mathematics Teacher, Vol 89, No 1, Jan 1996, pp 30–32 Exercise 45 from Inouye, David, Billy Barr, Kenneth Armitage, and Brian Inouye, “Climate Change Is Affecting Altitudinal Migrants and Hibernating Species,” Proceedings of the National Academy of Science, Vol 97, No 4, Feb 15, 2000, pp 1630–1633 S-1 S-2 Sources Exercise 46 from National Traffic Safety Institute Student Workbook, 1993, p Exercise 47 from “Kobe’s 81-Point Game Second Only to Wilt,” http://sports.espn.go.com Exercise 48 from Suntex Int Inc., Easton, PA, http://www.24game.com Copied with permission 24® is a registered trademark of Suntex International Inc., all rights reserved Section 2.2 Exercise 46 was provided by Prof Nathan Borchelt, Clayton State University Exercise 55 from L L Bean, http://www llbean.com Exercise 60 from Paredes, Miguel, Mohammad Fatehi, and Richard Hinthorn, “The Transformation of an Inconsistent Linear System into a Consistent System,” The AMATYC Review, Vol 13, No 2, Spring 1992 Exercise 61 from Dorrie, Heinrich, 100 Great Problems of Elementary Mathematics, Their History and Solution, New York: Dover Publications, 1965, pp 3–7 Exercise 62 from The New York Times 2010 Almanac, p 392 Exercise 63 from Bellany, Ian, “Modeling War,” Journal of Peace Research, Vol 36, No 6, 1999, pp 729–739 Exercise 65 from Szydlik, Stephen D., “The Problem with the Snack Food Problem,” The Mathematics Teacher, Vol 103, No 1, Aug 2009, pp 18–28 Exercise 66 from “Kobe’s 81-Point Game Second Only to Wilt,” http://sports.espn.go.com Exercise 68 from Guinard, J., C ZoumasMorse, L Mori, B Uatoni, D Panyam, and A Kilar, “Sugar and Fat Effects on Sensory Properties of Ice Cream,” Journal of Food Science, Vol 62, No 4, Sept./Oct 1997, pp 1087–1094 10 Exercise 69 from Anderson, Marlow and Todd Feil, “Turning Lights Out with Linear Algebra,” Mathematics Magazine, Vol 71, No 4, 1998, pp 300–303 11 Exercise 70 from http://www.baseball-almanac com Section 2.3 Exercise 44 from Traffic Safety Facts Research Note, NHTSA, December 2009 Exercise 45 from The New York Times 2010 Almanac, p 394 Exercise 46 from U.S Census Bureau Educational Attainment, Table A-2, http://www.census.gov/population/ www/socdemo/educ-attn.html Exercise 47 from U.S Census Bureau Educational Attainment, Table A-2, http://www.census.gov/population/ www/socdemo/educ-attn.html Section 2.4 Exercise 52 from David I Schneider, University of Maryland, based on the article “A Dynamic Analysis of Northern Spotted Owl Viability in a Fragmented Forest Landscape,” by Lamberson, R., R McKelvey, B Noon, and C Voss, Conservation Biology, Vol 6, No 4, Dec 1992, pp 505–512 Exercise 53 from http://www.census.gov/ipc/ www/idb/region.php and https://www census.gov/ipc/prod/wp02/tabA-01.xls Section 2.5 Exercise 66 from Isaksen, Daniel, “Linear Algebra on the Gridiron,” The College Mathematics Journal, Vol 26, No 5, Nov 1995, pp 358–360 Section 2.6 Page 102 from http://www.bea.gov/industry/ Exercise 19 from Leontief, Wassily, InputOutput Economics, 2nd ed., Oxford University Press, 1966, pp 20–27 Exercise 20 from Ibid, pp 6–9 Exercise 21 from Ibid, pp 174–177 Exercise 22 from Input-Output Tables of China, 1981, China Statistical Information and Consultancy Service Centre, 1987, pp 17–19 Exercise 23 and 24 from Chase, Robert, Philip Bourque, and Richard Conway Jr., “The 1987 Washington State Input-Output Study,” Report to the Graduate School of Business Administration, University of Washington, Sept 1993 Exercise 25 from an example created by Thayer Watkins, Department of Economics, San Jose State University, www.sjsu.edu/faculty/ watkins/inputoutput.htm Review Exercises Exercise 72 from Lamphear, F Charles and Theodore Roesler, “1970 Nebraska InputOutput Tables,” Nebraska Economic and Business Report No 10, Bureau of Business Research, University of Nebraska-Lincoln, 1971 Exercises 74 and 75 are based on the article “Medical Applications of Linear Equations” by David Jabon, Gail Nord, Bryce W Wilson, and Penny Coffman, The Mathematics Teacher, Vol 89, No 5, May 1996, p 398 Exercise 76 from Benson, Brian, Nicholas Nohtadi, Sarah Rose, and Willem Meeuwisse, “Head and Neck Injuries Among Ice Hockey Players Wearing Full Face Shields vs Half Face Shields,” JAMA, Vol 282, No 24, Dec 22/29, 1999, pp 2328–2332 Exercise 77 from Hibbeler, R., Structural Analysis, Prentice-Hall, 1995 Exercise 79 from Atmospheric Carbon Dioxide Record from Mauna Loa, Scripps Institution of Oceanography http://cdiac.esd ornl.gov/ftp/trends/co2/maunaloa.co2 Exercise 80 from Alberty, Robert, “Chemical Equations Are Actually Matrix Equations,” Journal of Chemical Education, Vol 68, No 12, Dec 1991, p 984 Exercise 82 from http://www.baseballreference.com Extended Application Page 110 from Grossman, Stanley, “First and Second Order Contact to a Contagious Disease.” Finite Mathematics with Applications to Business, Life Sciences, and Social Sciences, WCB/McGraw-Hill, 1993 Chapter Section 3.2 Exercise 17 from Problem from “November 1989 Course 130 Examination Operations Research” of the Education and Examination Committee of The Society of Actuaries Reprinted by permission of The Society of Actuaries Section 3.3 Page 133 from Uniform CPA Examinations and Unofficial Answers, copyright © 1973, 1974, 1975 by the American Institute of Certified Public Accountants, Inc.; reprinted with permission Exercise 25 from Reidhead, Van A., “Linear Programming Models in Archaeology,” Annual Review of Anthropology, Vol 8, 1979, pp 543–578 Review Exercise Exercise 45 from Joy, Leonard, “Barth’s Presentation of Economic Spheres in Darfur,” in Themes in Economic Anthropology, edited by Raymond Firth, Tavistock Publications, 1967, pp 175–189 Chapter Section 4.1 Exercise 29 was provided by Professor Karl K Norton, Husson University Section 4.2 Exercise 31 from Uniform CPA Examination Questions and Unofficial Answers, copyright ©1973, 1974, 1975 by the American Institute of Certified Public Accountants, Inc., is reprinted with permission Exercise 35 from http://www.nutristrategy com/activitylist4.htm Exercise 36 from http://www.nutristrategy com/activitylist4.htm Section 4.3 Exercise 17 from Problem from “November 1989 Course 130 Examination Operations Research” of the Education and Examination Committee of The Society of Actuaries Reprinted by permission of The Society of Actuaries Exercise 27 from http://www.brianmac demon.co.uk/energyexp.htm Sources Section 4.4 Exercise 30 from http://www.nutristrategy com/activitylist4.htm Review Exercise Exercise 47 from http://www.nutristrategy com/activitylist4.htm Extended Application This application based on material from the following online sources: The website of the Optimization Technology Center at Northwestern University at http:// www.ece.nwu.edu/OTC/ There is a link to a thorough explanation of the stock-cutting problem Home page of the Special Interest Group on Cutting and Packing at http://prodlog wiwi.uni-halle.de/sicup/index.html The linear programming FAQ at http://www.faqs.org/faqs/ linear-programming-faq/ Chapter Section 5.1 Exercise 54 from The New York Times, July 20, 1997, Sec 4, p 2 Exercise 54 b from http://money.cnn.com Exercise 54 d from http://www.forbes.com/ lists/2006/10/BH69.html and http://www forbes.com/lists/2010/10/billionaires-2010_ William-Gates-III_BH69.html Exercise 55 from SallieMae: http://www salliemae.com/get_student_loan/find_student _loan/undergrad_student_loan/federal_student _loans/ Exercise 58 from The New York Times, Dec 31, 1995, Sec p Exercise 65 adapted from Problem from “Course 140 Examination, Mathematics of Compound Interest” of the Education and Examination Committee of The Society of Actuaries Reprinted by permission of The Society of Actuaries Exercise 66 from The New York Times, March 30, 1995 Exercise 67 from http://www.ibankmarine.com Exercise 68 from http://us.etrade.com 10 Exercise 69 from https://www.bankrate.com 11 Exercise 77 from The New York Times, March 11, 2007, p 27 12 Exercise 77 b from http://www.american com/archive/2006/december/mitt-romney/ Section 5.2 Exercise 49 from http://articles.moneycentral msn.com/Insurance/InsureYourHealth/High CostOfSmoking.aspx Exercise 65 from The Washington Post, March 10, 1992, p A1 Section 5.3 Exercise 39 from http://www.cars.com/go/ advice/incentives/incentivesAll.jsp, http://www.cars.com/go/buyIndex.jsp Exercise 40 from http://www.cars.com/go/ advice/incentives/incentivesAll.jsp, http://www.cars.com/go/buyIndex.jsp Exercise 41 from Gould, Lois, “Ticket to Trouble,” The New York Times Magazine, April 23, 1995, p 39 Page 216 from http://www.direct.ed.gov/ RepayCalc/dlindex2.html Exercise 47 from The New York Times, Nov 12, 1996, pp A1, A22 Review Exercises Exercise 70 from “Pocket That Pension,” Smart Money, Oct 1994, p 33 Exercise 75 from http://www.bankrate.com Exercise 77 from http://www.cars.com/go/ advice/incentives/incentivesAll.jsp, http://www.cars.com/go/buyIndex.jsp Exercise 78 from http://www.cars.com/go/ advice/incentives/incentivesAll.jsp, http://www.cars.com/go/buyIndex.jsp Exercise 80 from Problem 16 from “Course 140 Examination, Mathematics of Compound Interest” of the Education and Examination Committee of The Society of Actuaries Reprinted by permission of The Society of Actuaries Exercise 81 from The New York Times, Sept 27, 1998, p BU 10 Extended Application Page 218 from COMAP, copyright COMAP “Consortium” 1991 COMAP, Inc 57 Bedford Street #210, Lexington, MA 02420 Chapter Section 6.1 Page 225 from http://research.microsoft.com/ Page 231 from J.K Lasser Institute, Your Income Tax 2010, New York: John Wiley & Sons, pp 10, 562, 487, 435 Page 232 from Goldman, D R., ed., American College of Physicians Complete Home Medical Guide, 2nd ed., New York: DK Publishing, 2003, p 57 Page 232 from Ventura, John, Law for Dummies, Indianapolis, IN: Wiley Publishing, Inc 2005, pp 113, 20, 12, 55, 10 Page 232 from Frost, S E., ed., Masterworks of Philosophy, New York: McGraw-Hill, 1946 Page 232 from TNIV Bible, Zondervan, 2005 Section 6.2 Exercise 40 from J.K Lasser Institute, Your Income Tax 2010, New York: John Wiley & Sons, p 489 Exercise 41 from “AppleCare Protection Plan for iPhone,” Apple Inc., 2009, p 11 Exercise 42 from eBay Exercise 44 from Goldman, David R., ed., American College of Physicians Complete Home Medical Guide, 2nd ed., New York: DK Publishing, 2003, p 223 S-3 Exercise 46 from Ventura, John, Law for Dummies, Indianapolis, IN: Wiley Publishing, Inc 2005, p 21 Exercise 47 from http://www.drmardy.com/ chiasmus/masters/kennedyl.shtml Exercise 49 from Milton Bradley Company, East Longmeadow, MA, 1996 Exercise 50 from Smullyan, Raymond, The Lady or the Tiger? And Other Logic Puzzles, Including a Mathematical Novel That Features Godel’s Great Discovery, New York: Knopf, 1982 Section 6.3 Exercise 89 from J.K Lasser Institute, Your Income Tax 2010, New York: John Wiley & Sons, pp 13, 41, 576 Exercise 90 from “AppleCare Protection Plan for iPhone,” Apple Inc., 2009, p 11 Exercise 92 from Goldman, David R., ed., American College of Physicians Complete Home Medical Guide, 2nd ed., New York: DK Publishing, 2003, p 59 Exercise 93 from Ventura, John, Law for Dummies, Indianapolis, IN: Wiley Publishing, Inc 2005, pp 12, 110, Section 6.4 Exercise 41 from J.K Lasser Institute, Your Income Tax 2010, New York: John Wiley & Sons, p 55, 13, 435 Exercise 42 from J.K Lasser Institute, Your Income Tax 2010, New York: John Wiley & Sons, p 271 Exercise 43 from JP Morgan Chase & Co Exercise 44 from Goldman, David R., ed., American College of Physicians Complete Home Medical Guide, 2nd ed., New York: DK Publishing, 2003, p 72 Exercise 45 from Rosing, Norbert, “Bear Beginnings: New Life on the Ice,” National Geographic, December 2000, p 33 Exercise 46 from Ventura, John, Law for Dummies, Indianapolis, IN: Wiley Publishing, Inc 2005, p 115 Exercise 47 from Ventura, John, Law for Dummies, Indianapolis, IN: Wiley Publishing, Inc 2005, p 55, 190, 114 Exercise 48 from Bartlett, John, Bartlett’s Familiar Quotations, 15th ed., Boston: Little, Brown and Company, 1980 Exercise 49 from Fisher, William E., “An Analysis of the Deutsch Sociocausal Paradigm of Political Integration,” International Organizational, Vol 23, No 2, Spring 1969, pp 254–290 10 Exercise 50 from The New York Times, May 29, 2002, p A1 11 Exercise 51 from Lipset, Seymour Martin, Political Man, 1960, quoted by Hildebrand, David K., James D Laing, and Howard Rosenthal, “Prediction Analysis in Political Research,” The American Political Science Review, Vol 70, No 2, June 1976, pp 509–535 S-4 Sources 12 Exercise 52 from Rosenthal, Howard, “The Electoral Politics of Gaullists in the Fourth French Republic: Ideology or Constituency Interest?” The American Political Science Review, Vol 63, June 1969, pp 476–487 13 Exercise 53 from Bower, Bruce, “Roots of Reason,” Science News, Vol 145, Jan 29, 1994, pp 72–73 14 Exercise 57 from Directions for Scrabble® and Yahtzee®, Milton Bradley Company, East Longmeadow, MA Section 6.5 Page 62 and Exercises 39–44 from The Complete Works of Lewis Carroll, Vintage Books, 1976 Section 6.6 Example from www.fec.gov/pubrec/fe2000/ prespop.htm Exercise 40 from United States v Brown, 381 U.S 437 (1965) Exercise 42 from NIV Bible Review Exercise Exercise 42 from Formal Logic: Its Scope and Limits, 2nd ed., by Richard Jeffrey, New York: McGraw-Hill, 1981 From page 274 from J.K Lasser Institute, Your Income Tax 2010, New York: John Wiley & Sons, pp 561, 450, 399, 435 Exercise 65 from Goldman, David R., ed., American College of Physicians Complete Home Medical Guide, 2nd ed., New York: DK Publishing, 2003, p 55, 32, 45, 48 Exercise 66 from Ventura, John, Law for Dummies, Indianapolis, IN: Wiley Publishing, Inc 2005, p 315, 348, 314 Exercise 67 from Tilly, Charles, “Processes and Mechanisms of Democratization,” Sociological Theory, Vol 18, No 1, March 2000, pp 1–16 Exercise 68 from Estling, Ralph, “It’s a Good Thing Cows Can’t Fly in Mobile,” Skeptical Inquirer, Nov./Dec 2002, pp 57–58 Exercise 68c from Chambers, Timothy, “On Venn Diagrams,” The Mathematics Teacher, Vol 97, No 1, Jan 2004, p Page 278 from Milton Bradley Company Page 278 from The Complete Works of Lewis Carroll, Vintage Books, 1976 Extended Application From page 279 from World-Class Logic Problems, Penny Press, Autumn, 2003 Exercise from World-Class Logic Problems Special, Summer 2003, p Exercise from World-Class Logic Problems Special, October 2003, p 23 Exercise from World-Class Logic Problems Special, Autumn 2003, p 20 Exercise from World-Class Logic Problems Special, Autumn 2003, p 6 Exercise from World-Class Logic Problems Special, Autumn 2003, p Chapter Section 7.1 Page 291 from The Merck Manual of Diagnosis and Therapy, 16th ed., Merck Research Laboratories, 1992, pp 1075 and 1080 Page 292 from The New York Times 2010 Almanac, page 408 Exercise 77 from Stewart, Ian, “Mathematical Recreations: A Strategy for Subsets,” Scientific American, Mar 2000, pp 96–98 Page 292 from The New York Times 2010 Almanac, pp 187–207 Section 7.2 Example from U.S Fish and Wildlife Service, http://ecos.fws.gov Exercise 46 from National Vital Statistics Reports, Vol 57, No 14, April 17, 2009, p.18 Exercise 47 from Benson, Brian, Nicholas Nohtaki, M Sarah Rose, Willem Meeuwisse, “Head and Neck Injuries Among Ice Hockey Players Wearing Full Face Shields vs Half Face Shields,” JAMA, Vol 282, No 24, Dec 22/29, 1999, pp 2328 – 2332 Exercise 48 from usa.gov Page 301 from Population Projections of the United States by Age, Sex, Race, and Hispanic Origin: 1995 to 2050, U.S Bureau of the Census, Feb 1996, pp 16–17 Page 301 from The New York Times 2010 Almanac, p 296 Section 7.3 Example from www.epi.org Example from National Safety Council, Itasca, IL, Injury Facts, 2007 Exercise 50 from http://www.cartalk.com/ content/puzzler/transcripts/200107/ Cartalk.com is a production of Dewey, Cheetham and Howe Contents © 2007, Dewey, Cheetham and Howe Exercise 52 from www.nsf.gov/statistics Exercise 54 from www.bls.gov Exercise 57 from www.cdc.gov Exercise 58 from Population Projections of the United States by Age, Sex, Race, and Hispanic Origin: 1995 to 2050, Bureau of the Census, Feb 1996, p 12 Exercise 59 from Roll Call, March 1, 2010 Exercises 60 and 61 from Busey, John and David Martin, Regimental Strengths and Losses at Gettysburg, Hightstown, N.J., Longstreet House, 1986, p 270 Section 7.4 Example from The New York Times 2010 Almanac, p 365 Exercise 24 from Parade magazine, Nov 6, 1994, p 11 © 1994 Marilyn vos Savant Initially published in Parade magazine All rights reserved Exercise 26 from Staubach, Roger, First Down, Lifetime to Go, Word Incorporated, Dallas, 1976 Exercise 45 from Menand, Louis, “Everybody’s an Expert: Putting Predictions to the Test,” New Yorker, Dec 5, 2005, pp 98–101 Exercise 46 from Problem from the 2005 Sample Exam P of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries Exercise 50 from www.bls.gov Exercise 51 from www.bls.gov Exercise 53: The probabilities of a person being male or female are from The World Almanac and Book of Facts, 1995 The probabilities of a male and female being color-blind are from Parsons’ Diseases of the Eye (18th ed.) by Stephen J H Miller, Churchill Livingstone, 1990, p 269 This reference gives a range of to 4% for the probability of gross color blindness in men; we used the midpoint of this range Exercise 56 from Wright, J R., “An Analysis of Variability in Guinea Pigs,” Genetics, Vol 19, pp 506–536 10 Exercise 57 from Problem from the 2005 Sample Exam P of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries 11 Exercise 58 from Problem from the 2005 Sample Exam P of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries 12 Exercise 59 from Problem 15 from the 2005 Sample Exam P of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries 13 Exercise 60 from Safire, William, “The Henry Poll,” The New York Times, June 25, 2001, p A17 and http://abcnews.go.com 14 Exercise 66 from usa.gov 15 Exercises 67 and 68 from Gibson, J L., “Putting Up with Fellow Russians: An Analysis of Political Tolerance in the Fledgling Russian Democracy,” Political Research Quarterly, Vol 51, No 1, Mar 1998, pp 37–68 16 Exercise 69 from The New York Times, Feb 23, 2006, p D3 17 Exercise 70 from bookofodds.com 18 Exercise 71 from bookofodds.com Section 7.5 Page 325 from Pringle, David, “Who’s the DNA Fingerprinting Pointing At?” New Scientist, Jan 29, 1994, pp 51–52 Exercise 31 from Parade magazine, June 12, 1994, p 18 © 1994 Marilyn vos Savant Initially published in Parade magazine All rights reserved Sources Exercise 32 from Chance News 10.01, Jan 16, 2001 Exercise 35: This problem is based on the “Puzzler of the Week: Prison Marbles” from the week of Sept 7, 1996, on National Public Radio’s Car Talk Exercise 41 from airconsumer.dot.gov Exercise 43 from Chicago Tribune, Dec 18, 1995, Sec 4, p Exercise 63 from American Medical Association, 2010 Page 332 from Benson, Brian, Nicholas Nohtaki, M Sarah Rose, and Willem Meeuwisse, “Head and Neck Injuries Among Ice Hockey Players Wearing Full Face Shields vs Half Face Shields,” JAMA, Vol 282, No 24, Dec 22/29, 1999, pp 2328 –2332 Exercise 69 from Problem 12 from the 2005 Sample Exam P of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries 10 Exercise 70 from Falk, Ruma, Chance News, July 23, 1995 11 Exercise 73 from cdc.gov 12 Exercise 74 from Matthews, Robert A J., Nature, Vol 382, Aug 29, 1996, p 13 Exercise 75 from Science News, Vol 169, April 15, 2006, pp 234–236 14 Exercise 77 from Takis, Sandra L., “Titanic: A Statistical Exploration,” Mathematics Teacher, Vol 92, No 8, Nov 1999, pp 660–664 15 Exercise 87 from Goodman, Terry, “Shooting Free Throws, Probability, and the Golden Ratio,” Mathematics Teacher, Vol 103, No 7, March, 2010, pp 482 – 487 16 Exercise 88 from Goodman, Terry, “Shooting Free Throws, Probability, and the Golden Ratio,” Mathematics Teacher, Vol 103, No 7, March, 2010, pp 482 – 487 17 Exercise 89 from Schielack, Vincent P., Jr., “The Football Coach’s Dilemma: Should We Go for or Points First?” The Mathematics Teacher, Vol 88, No 9, Dec 1995, pp 731–733 Section 7.6 Exercise 18 from Problem from May 2003 Course Examination of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries Exercise 19 from Problem 20 from the 2005 Sample Exam P of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries Exercise 20 from Problem 23 from the 2005 Sample Exam P of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries Exercise 21 from Uniform CPA Examination, Nov 1989 Exercise 23 from Hoffrage, Ulrich, Samuel Lindsey, Ralph Hertwig, and Gerd Gigerenzer, Science, Vol 290, Dec 22, 2000, pp 2261–2262 Exercise 25 from “Mammography facility characteristics associated with interpretive accuracy of screening mammography,” National Cancer Institute, www.cancer.gov Exercise 26 from www.cdc.gov Exercise 27 from Problem 31 from May 2003 Course Examination of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries Exercise 28 from Problem 21 from the 2005 Sample Exam P of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries 10 Exercise 29 from Problem 25 from the 2005 Sample Exam P of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries 11 Exercise 30 from Problem 26 from the 2005 Sample Exam P of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries 12 Exercise 31 from “Binge-Drinking Trends,” Harvard School of Public Health, Vol 50, March 2002, p 209 13 Exercise 32 from Good, I J., “When Batterer Turns Murderer,” Nature, Vol 375, No 15, June 15, 1995, p 541 14 Page 342 from www.uscensus.gov 15 Exercise 36 from “Factors Related to the Likelihood of a Passenger Vehicle Occupant Being Ejected in a Fatal Crash,” National Highway Traffic Safety Administration, U.S Department of Transportation, December, 2009 16 Page 343 from “Cigarette Smoking Among Adults—United States, 2007,” www.cdc.gov 17 Exercise 39 from http://abcnews.go.com/ Technology/WhosCounting/story?id= 1560771 18 Exercise 40 from Shimojo, Shinsuke, and Shin’ichi Ichikawa, “Intuitive Reasoning About Probability: Theoretical and Experimental Analyses of the ‘Problem of Three Prisoners,’” Cognition, Vol 32, 1989, pp 1–24 Review Exercises Exercise 64 from Parade magazine, Sept 9, 1990, p 13 © 1990 Marilyn vos Savant Initially published in Parade magazine All rights reserved Exercise 78 from Problem from the 2005 Sample Exam P of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries Exercise 91 from Problem from May 2003 Course Examination of the Education and Examination Committee of the Society of S-5 Actuaries Reprinted by permission of the Society of Actuaries Exercise 92 from Problem from the 2005 Sample Exam P of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries Exercise 93 from Problem 11 from the 2005 Sample Exam P of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries Exercise 94 from Problem 18 from May 2003 Course Examination of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries Exercise 96 from Young, Victoria, “A Matter of Survival,” The Mathematics Teacher, Vol 95, No 2, Feb 2002, pp 100 –112 Exercise 97 from Problem 13 from the 2005 Sample Exam P of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries Exercise 98 from www.uscensus.gov and “Election Results 2008,” The New York Times, November 5, 2008 10 Exercise 100 from Warner, Stanley, “Randomized Response: A Survey Technique for Eliminating Evasive Answer Bias,” The Journal of the American Statistical Association, Vol 60, No 309, Mar 1965, pp 63–69 11 Exercise 101 from John Allen Paulos, “Coins and Confused Eyewitnesses: Calculating the Probability of Picking the Wrong Guy,” Who’s Counting, Feb 1, 2001 http://more.abcnews go.com/sections/science/ whoscounting_ index/whoscounting_index.html 12 Exercise 102 from Science, Vol 309, July 22, 2005, p 543 13 Exercise 103 from The San Francisco Chronicle, June 8, 1994, p A1 14 Exercise 104 from Carter, Virgil and Robert Machols, “Optimal Strategies on Fourth Down,” Management Science, Vol 24, No 16, Dec 1978 Copyright © 1978 by The Institute of Management Sciences 15 Exercise 107 from http://www.cartalk.com/ content/puzzler/2002.html 16 Exercise 108 from Clancy, Tom, Debt of Honor, New York: G P Putnam’s Sons, 1994, pp 686–687 17 Exercise 109 from Problem from May 2003 Course Examination of the Education and Examination Committee of the Society of Actuaries Reprinted by permission of the Society of Actuaries To view the complete source list, visit the Downloadable Student Resources site, www.pearsonhighered.com/mathstatsresources The complete list is also available to qualified instructors within MyMathLab or through the Pearson Instructor Resource Center, www.pearsonhighered.com/irc KEY DEFINITIONS, THEOREMS, AND FORMULAS 2.2 Row Operations For any augmented matrix of a system of equations, the following operations produce the augmented matrix of an equivalent system: interchanging any two rows; multiplying the elements of a row by any nonzero real number; adding a nonzero multiple of the elements of one row to the corresponding elements of a nonzero multiple of some other row 2.5 Finding a Multiplicative Inverse Matrix To obtain A21 for any n n matrix A for which A21 exists, follow these steps Form the augmented matrix A I , where I is the n n identity matrix Perform row operations on A I to get a matrix of the form I B if this is possible Matrix B is A21 4.2 Simplex Method for Standard Maximization Problems Determine the objective function Write all necessary constraints Convert each constraint into an equation by adding a slack variable in each Set up the initial simplex tableau Locate the most negative indicator If there are two such indicators, choose the one farther to the left Form the necessary quotients to find the pivot Disregard any quotients with or a negative number in the denominator The smallest nonnegative quotient gives the location of the pivot If all quotients must be disregarded, no maximum solution exists If two quotients are both equal and smallest, choose the pivot in the row nearest the top of the matrix Use row operations to change all other numbers in the pivot column to zero by adding a suitable multiple of the pivot row to a positive multiple of each row If the indicators are all positive or 0, this is the final tableau If not, go back to Step and repeat the process until a tableau with no negative indicators is obtained Read the solution from this final tableau 5.1 Compound Amount A P1 1 i 2n r and n mt, m A is the future (maturity) value; P is the principal; r is the annual interest rate; m is the number of compounding periods per year; t is the number of years; n is the number of compounding periods; i is the interest rate per period where i 5.2 Future Value of an Ordinary Annuity 6.1, 6.3 Truth Tables 7.3 Basic Probability Principle S Rc 11 i2 n d i where S is the future value; R is the payment; i is the interest rate per period; n is the number of periods The following truth table defines the logical operators in this chapter p q ,p p ٙ q p ٚ q T T F F T F T F F F T T T F F F T T T F plq piq T F T T T F F T Let S be a sample space of equally likely outcomes, and let event E be a subset of S Then the probability that event E occurs is P 1E2 7.4 Union Rule S Rs ni or n 1E2 n 1S2 For any two events E and F from a sample space S, P 1E < F2 P 1E2 P 1F2 P 1E > F2 7.5 Product Rule If E and F are events, then P 1E > F2 may be found by either of these formulas P 1E > F2 P 1F2 P 1E |F2 7.6 Bayes’ Theorem 8.2 Permutations and Combinations P 1Fi E2 P 1E > F2 P 1E2 P 1F|E2 P 1Fi2 P 1E Fi2 P 1F12 P 1E F12 P 1F22 P 1E F22 ) P 1Fn2 P 1E Fn2 Permutations Different orderings or arrangements of the r objects are different permutations P 1n, r2 n! 1n r2 ! Clue words: arrangement, schedule, order Order matters! 8.4 Binomial Probability or Combinations Each choice or subset of r objects gives one combination Order within the group of r objects does not matter n! C 1n, r2 1n r2 !r! Clue words: group, committee, set, sample Order does not matter! If p is the probability of success in a single trial of a binomial experiment, the probability of x successes and n x failures in n independent repeated trials of the experiment, known as binomial probability, is P 1x successes in n trials2 C 1n, x2 px 112p2 n2x 8.5 Expected Value Suppose the random variable x can take on the n values x1, x2, x3, * , xn Also, suppose the probabilities that these values occur are, respectively, p1, p2, p3, * , pn Then the expected value of the random variable is E x x1p1 x2p2 x3p3 ) xnpn 9.2 Variance and Standard Deviation The variance of a sample of n numbers x1, x2, x3, * , xn, with mean x, is s2 g x 2 nx n21 The standard deviation of a sample of n numbers x1, x2, x3, * , xn, with mean x, is s5 11.4 Derivative g x 22nx Å n21 The derivative of the function f at x, written fr x , is defined as fr x lim hl0 f1 x h 2 f1 x , provided this limit exists h Rules for Derivatives The following rules for derivatives are valid when all the indicated derivatives exist 12.1 Constant Rule If f x k where k is any real number, then fr x 12.1 Power Rule If f x xn for any real number n, then fr x nxn21 12.1 Constant Times a Function Let k be a real number Then the derivative of fr x k g x is fr x k gr x 12.1 Sum or Difference Rule If f x u x v x then fr x ur x vr x 12.2 Product Rule If f x u x v x then fr x u x vr x v x ur x 12.2 Quotient Rule If f x u x / v x , and v x 2 0, then fr x 12.3 v x ur x 2 u x vr x v x 42 Chain Rule If y is a function of u, say y f u , and if u is a function of x, say u g x , then y f u f g x , and dy du dy , dx du dx 12.3 Chain Rule (Alternate Form) If y f g x , then dy / dx fr g x , gr x 12.4 Exponential Function d g1 x a ln a ag1x 2gr x dx d g1 x e eg1x 2gr x dx 12.5 Logarithmic Function gr x d loga|g x | dx ln a g x gr x d ln|g x | dx g1 x 15.2 Substitution Each of the following forms can be integrated using the substitution u f x Form of the Integral 3 f x nfr x dx, 15.4 Fundametal Theorem of Calculus Result n 21 n u du f x n11 un11 1C5 1C n11 n11 fr x 2 dx f1 x u du ln u C ln f x C 3 ef1 x2fr x dx u u fx 1C e du e C e 1 Let f be continuous on the interval [a, b], and let F be any antiderivative of f Then b b f x dx F b 2 F a F x ` a a 17.3 Test for Relative Extrema For a function z f x, y let fxx fyy, and fxy all exist in a circular region contained in the xy-plane with center a, b Further, let fx a, b and fx a, b Define the number D by D fxx a, b fxx a, b 2 fxx a, b Then (a) f a, b is a relative maximum if D Ͼ and fxx a, b Ͻ 0; (b) f a, b is a relative minimum if D Ͼ and fxx a, b Ͼ 0; (c) f a, b is a saddle point (neither a maximum nor a minimum) if D Ͻ 0; (d) if D ϭ 0, the test gives no information ... Reference In the expression an, the power n is the exponent and a is the base This definition can be extended by defining an for zero and negative integer values of n Zero and Negative Exponents... Our main goal is to present finite mathematics and applied calculus in a concise and meaningful way so that students can understand the full picture of the concepts they are learning and apply... instruction for new technology, and new and updated Extended Applications You can view these new features in context in the following Quick Walk-Through of Finite Mathematics and Calculus with Applications,