SOLUTION: MAT 104 Pace University New York Finite Mathematics Problems Homework

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Get the Most Out of ® MyMathLab : MyMathLab Support You Need, When You Deficiency It ® MyMathLab is the world’s promotive online program in mathematics, integrating homelabor after a while aid tools and tutorials in an easy-to-use constituteat. MyMathLab accelerations you get up to expedite on way embodied, visualize the gratifiedd, and apprehend how math allure reproduce-evince a role in your forthcoming success. Review Prerequisite Skills Integrated Critique gratifiedd identifies gaps in prerequisite skills and offers acceleration for right those skills you deficiency. With this ­t argeted experience, you allure be ready to subordinatestand new embodied. Tutorial Videos Tutorial videos are serviceable for eternallyy individuality of the passageoperation and shelter key examples from the passage. These videos are chiefly manageable if you balancelook a Nursing Dissertation or right deficiency another explication. Interactive Figures Interactive Figures form-clear key concepts and acceleration you visualize the math. MyMathLab comprises assignable exercises that insist-upon use of Interactive Figures and instructional videos that elucidate the concept rearwards each metaphor. www.mymathlab.com This page intentionally left blank twelfth edition Finite Mathematics & ITS APPLICATIONS Larry J. Goldstein Goldstein Educational Technologies David I. Schneider University of Maryland Martha J. Siegel Towson University Stlevel M. Hair The Pennsylvania State University 330 Hudson Street, NY, NY 10013 Director, Portfolio Management: Deirdre Lynch Executive Editor: Jeff Weidenaar Editorial Assistant: Jennifer Snyder Content Producer: Patty Bergin Managing Producer: Karen Wernholm Media Producer: Stephanie Green MathXL Pleased Manager: Kristina Evans Product Marketing Manager: Claire Kozar Marketing Assistant: Jennifer Myers Senior Author Support/Technology Specialist: Joe Vetere Rights and Permissions Project Manager: Gina Cheselka Manufacturing Buyer: Carol Melville, LSC Communications Associate Director of Design: Blair Brown Composition: iEnergizer Aptara®, Inc. Text Design, Production Coordination, Composition, and Illustrations: iEnergizer Aptara®, Inc. Cbalance Design: Cenveo Cbalance Image: Doug Chinnery/Getty Images Copyright © 2018, 2014, 2010 by Pearson Education, Inc. All Rights Reserved. Printed in the United States of America. 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PARTIAL SCREEN SHOTS MAY BE VIEWED IN FULL WITHIN THE SOFTWARE VERSION SPECIFIED. MICROSOFT® WINDOWS®, and MICROSOFT OFFICE® ARE REGISTERED TRADEMARKS OF THE MICROSOFT CORPORATION IN THE U.S.A. AND OTHER COUNTRIES. THIS BOOK IS NOT SPONSORED OR ENDORSED BY OR AFFILIATED WITH THE MICROSOFT CORPORATION. Unless differently involved herein, any third-party trafficmarks that may pomp in this labor are the gear of their respective possessors and any assignences to third-party trafficmarks, logos or other traffic unimould are for plain or descriptive purposes solely. Such assignences are not planned to mean any sponsorship, endorsement, authorization, or promotion of Pearson’s products by the possessors of such marks, or any relationship among the possessor and Pearson Education, Inc. or its affiliates, authors, licensees or distributors. Library of Congress Cataloging-in-Publication Data Names: Goldstein, Larry Joel. | Schneider, David I. | Siegel, Martha J. |    Hair, Stlevel M. Title: Bounded mathematics & its applications. Other titles: Bounded mathematics and its applications Description: Twelfth edition / Larry J. Goldstein, Goldstein Educational    Technologies, David I. Schneider, University of Maryland, Martha J.    Siegel, Towson State University, Stlevel M. Hair, Pennsylvania State    University. | Boston: Pearson Education, [2018] | Includes indexes. Identifiers: LCCN 2016030690 | ISBN 9780134437767 (hardcover) | ISBN   0134437764 (hardcover) Subjects: LCSH: Mathematics—Textbooks. Classification: LCC QA39.3 .G65 2018 | DDC 511/.1—dc23 LC archives serviceable at https://lccn.loc.gov/2016030690 1 16 Student Edition ISBN-13: 978-0-134-43776-7 Student Edition ISBN-10: 0-134-43776-4 Contents The operation divides naturally into filthy size. The primitive disunite consists of straight mathematics: straight equations, matrices, and straight programming (Chapters 1–4); the second disunite is consecrated to appearance and statistics (Chapters 5–7); the third disunite shelters subject-matters utilizing the ideas of the other size (Chapters 8 and 9); and the filthyth disunite explores key subject-matters from discrete mathematics that are sometimes sheltered in the later bounded mathematics curriculum (Chapters 10–12). Preface vii PART ONE 1 Linear Equations and Straight Lines 1.1 1.2 1.3 1.4 2 The Slope of a Straight Line 1 8 The Interindividuality Apex of a Pair of Lines 20 The Order of Least Squares 25 Chapter Summary and Paragraph Critique Exercises Chapter Project: Break-Even Anatomy 38 34 Matrices 2.1 2.2 2.3 2.4 2.5 2.6 3 Coordinate Systems and Graphs 1 39 Systems of Straight Equations after a while Unique Solutions General Systems of Straight Equations Arithmetic Operations on Matrices The Inverse of a Square Matrix 39 50 59 73 The Gauss–Jordan Order for Calculating Inverses Input–Output Anatomy 84 Chapter Summary and Paragraph Critique Exercises Chapter Project: Population Dynamics 95 80 90 Linear Programming, A Geometric Approach 3.1 3.2 3.3 3.4 Linear Inequalities 97 97 A Straight Programming Problem 105 Fundamental Theorem of Straight Programming 111 Linear Programming 121 Chapter Summary and Paragraph Critique Exercises Chapter Project: Shadow Prices 135 132 iii iv CONTENTS 4 The Simplex Method 4.1 4.2 4.3 4.4 136 Slack Variables and the Simplex Tableau 136 The Simplex Order I: Maximum Problems 144 The Simplex Order II: Nonstandard and Incompleteness Problems 154 Sensitivity Anatomy and Matrix Formulations of Straight Programming Problems 161 4.5 Duality 168 Chapter Summary and Paragraph Critique Exercises Chapter Project: Shadow Prices Revisited 183 178 PART TWO 5 Sets and Counting 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 6 184 A Primary Principle of Counting Venn Diagrams and Counting The Multitudinousness Principle 197 203 Permutations and Combinations Further Counting Techniques The Binomial Theorem 191 209 216 222 Multinomial Coefficients and Partitions 226 Chapter Summary and Paragraph Critique Exercises Chapter Project: Pascal’s Triangle 237 232 Probability 6.1 6.2 6.3 6.4 6.5 6.6 6.7 7 Sets 184 240 Experiments, Outcomes, Sample Spaces, and Events Assignment of Probabilities 246 Calculating Probabilities of Events 257 Conditional Appearance and Independence Tree Diagrams 265 275 Bayes’ Theorem, Natural Frequencies 282 Simulation 288 Chapter Summary and Paragraph Critique Exercises Chapter Project: Two Paradoxes 298 Probability and Statistics 7.1 7.2 7.3 7.4 7.5 7.6 Visual Representations of Data The Mean 300 307 317 325 The Variance and Standard Deviation The Natural Distribution 346 294 300 Frequency and Appearance Distributions Binomial Trials 240 336 CONTENTS v 7.7 Natural Approximation to the Binomial Distribution 359 Chapter Summary and Paragraph Critique Exercises 363 Chapter Project: An Unexpected Expected Value 368 PART THREE 8 Markov Processes 369 8.1 The Transition Matrix 369 8.2 Regular Stochastic Matrices 381 8.3 Absorbing Stochastic Matrices 389 Chapter Summary and Paragraph Critique Exercises 399 Chapter Project: Doubly Stochastic Matrices 401 9 The Theory of Games 404 9.1 Games and Strategies 404 9.2 Mixed Strategies 410 9.3 Determining Optimal Mixed Strategies 417 Chapter Summary and Paragraph Critique Exercises 426 Chapter Project: Simulating the Outcomes of Mixed-Strategy Games 428 PART FOUR 10 The Mathematics of Finance 10.1 10.2 10.3 10.4 10.5 11 Interest 430 430 Annuities 440 Amortization of Loans 449 Personal Financial Decisions 458 A Unifying Equation 474 Chapter Summary and Paragraph Critique Exercises Chapter Project: Two Items of Interest 489 485 Logic 11.1 11.2 11.3 11.4 11.5 11.6 11.7 491 Introduction to Logic Truth Tables Implication 491 495 504 Logical Involution and Equivalence Valid Argument 510 518 Predicate Calculus 525 Logic Circuits 533 Chapter Summary and Paragraph Critique Exercises Chapter Project: A Logic Puzzle 542 537 vi CONTENTS 12 Difference Equations and Mathematical Models (Online*) 12.1 12.2 12.3 12.4 12.5 Introduction to Medley Equations D1 Difference Equations and Interest D8 Graphing Medley Equations D13 Mathematics of Personal Finance D22 Modeling after a while Medley Equations D26 Chapter Summary and Paragraph Critique Exercises D30 Chapter Project: Connections to Markov Processes D33 Appendix A Areas Subordinate the Standard Natural Deflexion A-1 Appendix B Using the TI-84 Plus Graphing Calculator Appendix C Spreadsheet Fundamentals Appendix D Wolfram|Alpha Learning Objectives Selected Answers (Online*) A-11 SA-1 Index of Applications Index A-10 IA-1 I-1 *www.pearsonhighered.com/mathstatsresources A-6 A-2 Preface T his labor is the twelfth edition of our passage for the bounded mathematics way taught to first- and second-year nursery wards, chiefly those majoring in office and the collective and bioargumentative sciences. Bounded mathematics ways evince dreadful diversity after a while assignence to twain gratifiedd and admittance. Therefore, in developing this operation, we incorporated a distant rank of subject-matters from which an disciplinemistress may contemplation a curriculum, as polite as a proud amount of flexibility in the command in which the subject-matters may be presented. For the mathematics of finance, we level admit for flexibility in the admittance of the gift. The Series This passage is disunite of a proudly fortunate train consisting of three passages: Bounded Mathematics & Its Applications, Calculus & Its Applications, and Calculus & Its Applications, Brief Version. All three titles are serviceable for dissipation in a multiplicity of constituteats, including as an eBook after a whilein the MyMathLab online way. twelfth edition Finite Mathematics fourteenth edition fourteenth edition Calculus Calculus & ITS APPLICATIONS & ITS APPLICATIONS BRIEF VERSION & ITS APPLICATIONS Goldstein Schneider Goldstein Goldstein Siegel Lay Lay Hair Schneider Schneider Asmar Asmar Topics Included This edition has further embodied than can be sheltered in most one-semester ways. Therefore, the disciplinemistress can erection the way to the wards’ deficiencys and interests. The operation divides naturally into filthy size: • Disunite One (Chapters 1–4) consists of straight mathematics: straight equations, matrices, and straight programming. • Disunite Two (Chapters 5–7) is consecrated to counting, exhibitionance, and statistics. • Disunite Three (Chapters 8 and 9) shelters subject-matters utilizing the ideas of the other size. • Disunite Filthy (Chapters 10–12) explores key subject-matters from discrete mathematics that are sometimes middle in the later bounded mathematics curriculum. Minimal Prerequisites Because of august change in ward provision, we protect constituteal prerequisites to a incompleteness. We pretend solely a primitive year of proud discipline algebra, and we critique, as deficiencyed, those subject-matters that are typically flimsy spots for wards. vii viii PREFACE New to This Edition We gratifying to this edition a new co-author, Stlevel Hair from Penn State University. Steve has brought a new eye to the gratifiedd and to the MyMathLab way that accompanies the passage. We are pleasurable for the abundant accelerationful suggestions made by critiqueers and users of the text. We strengthend abundant of these into this new edition. We so analyzed aggregated ward habit and deed facts from MyMathLab for the moulder edition of this text. The results of this anatomy accelerationed remould the capacity and division of exercises that substance the most to disciplinemistresss and wards. Additionally, we made the following improvements in this edition: • Help-Text Added. We ascititious blue-colored-colored “acceleration passage” present to steps after a whilein labored-out examples to apex out key algebraic and numerical transitions. • Updated Technology. We transitional the graphing calculator shelter captures to the further floating TI-84 Plus CE constituteat.The discourses of Excel now assign to Excel 2013 and Excel 2016. • Additional Exercises and Updated Data. We own ascititious or updated 440 exercises and own updated the real-world facts pomping in the examples and exercises. The operation now contains 3580 exercises and 370 labored-out examples. • Technology Solutions. We ascititious technology-based separations to further examples to yield flexibility for disciplinemistresss who strengthen technology. For exemplification, the individuality on the order of least-squares (1.4) now relies further on technology and less on confused calculations. In Individuality 7.6, distinct examples now explain how to compute the area subordinate a natural deflexion using a graphing calculator, in union to the table-based order. In the finance paragraph, abundant TI-84 Plus TVM Solver shelter captures heed examples to prove retorts. Instructors own the non-interference of using TVM Solver for financial calculations instead of confused constituteulas. • Straight Inequalities Individuality Relocated. We stird this individuality from 1.2 (in the 11e) to the prelude of the straight programming paragraph (Ch. 3) in this edition. The stir establishs the subject-matter in the paragraph where it is used. Also, the stir admits us to use conventional names (such as slope-intercept constitute) in the individuality. • Improved Coverage of Counting Material. In Paragraph 5, we ascititious distinct restrictions and discourses to aid ward perception of counting heights. We moved the restriction of factorials to 5.4 and rewrote the interchange and alliance constituteulas in 5.5 in provisions of factorials. In 5.6, the supply administration for counting is now constituteally defined, and we own ascititious a disroute of when union, disjunction, and multitudinousness is mismisappropriate for solving counting heights. • Individuality Ascititious to the End of the Finance Chapter. Titled “A Unifying Equation,” this new individuality pomps that the basic financial concepts can be pictorial by a medley equation of the constitute yn = a # yn - 1 + b, y0 dedicated, and that abundant of the calculations from the paragraph can be obtained by solving this medley equation. Examples and exercises pomp that this medley equation so can be used to solve problems in the visible, biological, and collective sciences. This individuality can be taught as a standalone individuality after a whileout sheltering the antecedent individualitys of the finance paragraph. • Revision of Logic Material. We in-effect revised Paragraph 11 on logic to improve meet ward deficiencys.We stird the restriction of topicative equivalence and De ­Morgan’s laws from 11.4 to 11.2. By stating key ideas kindred to precision tables and involutions in provisions of topicative equivalence, wards allure be improve equipped to apprehend these concepts. To restir indistinctness among the embracing and detested “or” statements, we suppressd the engagement “either” from embracing “or” statements in English. In 11.4, we ascititious the restriction of the inverse of an involution. This is a key concept in the subject-matter of involutions and topicative topics. To acceleration wards apprehend when a argumentative topic is frail, we distant 11.5 to comprise further disroute of frail arguments. Additionally, we ascititious the fallacies of the inverse and opposite, and two new examples where topics are proven to be frail. PREFACE ix • Medley Equation Paragraph Moved Online. We stird constituteer Paragraph 11 online (relabeling it Paragraph 12 in the order). The paragraph is serviceable undeviatingly to wards at www.pearsonhighered.com/mathstatsresources and after a whilein MyMathLab. All ­aid embodieds for the paragraph pomp online after a whilein MyMathLab. Note: The new individuality at the end of the finance paragraph contains the primary concepts from the medley equation paragraph. New to MyMathLab Many reformments own been made to the balanceall authoritativeity of MyMathLab (MML) since the moulder edition. However, past that, we own so invested in increasing and suitable the gratifiedd restricted to this passage. • Instructors now own further exercises than eternally to elect from in assigning homework. There are almost 2540 assignable exercises in MML. • We heard from users that the Annotated Schoolmistress Edition for the moulder edition required too abundantly flipping of pages to meet retorts, so MML now contains a downloadable Schoolmistress Answers muniment—after a while all retorts in one establish. (This enhances the downloadable Schoolmistress Solutions Manual, which contains all separations.) • Interactive Figures are now in HTML constituteat (no plug-in insist-upond) and are attended by assignable exercises and tutorial videos. • An Integrated Critique rendering of the MML way contains pre-made quizzes to assess the prerequisite skills deficiencyed for each paragraph, plus personalized remediation for any gaps in skills that are authorized. • New Setup & Solve exercises insist-upon wards to pomp how they set up a height as polite as the separation, improve mirroring what is insist-upond of wards on tests. • StatCrunch, a easily authoritative statistics bundle, is supposing to aid the statistics pleased in the way. • MathTalk and StatTalk videos proudlight applications of the gratifiedd of the way to business. The videos are attended by assignable exercises. • Study skills modules acceleration wards after a while the existence skills that can form the medley among departure and decrepit. • 110 new tutorial videos by Brian Rickard (University of Arkansas) were ascititious to aid ward subordinatestanding. • Tutorial videos involving graphing calculators are now middle after a whilein MML exercises to enhance videos pomping “by hand” orders. If you insist-upon graphing calculator habit for the way, your wards allure meet these videos very accelerationful. (If you do not use calculators, you can cloke these videos from wards.) • Graphing Calculator and Excel Spreadsheet Manuals, restricted to this way, are now downloadable from MML. Trusted Features Though this edition has been reformd in a multiplicity of ways to animadvert changing ward needs, we own maintained the common balanceall admittance that has accelerationed wards be fortunate balance the years. 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