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

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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
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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.
Relevant and Varied Applications
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