A Pathway to Quantitative Literacy 2ND EDITION VIEWING LIFE MATHEMATICALLY DENLEY Annotated Instructor’s Edition - Not for SaleLead Editor: Barbara Miller Editors: Danielle C. Bess, Allison Conger, Jolie Even, Robin Hendrix, S. Rebecca Johnson, Claudia Vance Indexer: Barbara Miller Content Contributors: Karen Crossin, Muff Glover, Lisa Hinton, Silke Hunker, Leonardo Pinheiro, Kara Roché, Joe A. Stickles, Jr. Manager of Math Content Development: Blair Dunivan Creative Services Manager: Trudy Tronco Designers: Lizbeth Mendoza, Patrick Thompson, Joel Travis Cover Design: Lizbeth Mendoza Courseware Developers: Allison Conger, Jolie Even, Adam Flaherty, Kyle Gilstrap Composition and Answer Key Assistance: Quant Systems India Pvt. Ltd. A division of Quant Systems, Inc. 546 Long Point Road Mount Pleasant, SC 29464 Copyright © 2023, 2020, 2016 by Hawkes Learning / Quant Systems, 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 consent of the publisher. Library of Congress Control Number 2022932250 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 ISBN: 978-1-64277-491-7 AIE ISBN: 978-1-64277-497-9Table of Contents iv Preface Ratios, Percentages, Rates, and Proportionality Preface v vi Preface Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .897 Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .901 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .903 Chapter 11 Statistics 11.1 Statistical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .911 11.1 Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .933 11.2 Displaying Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .934 11.2 Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .962 11.3 Describing and Analyzing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .965 Preface vii Statistical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1347 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1350 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1353 Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1361 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1393viii Preface Preface Letter from the Author It is my pleasure to introduce to you the second edition of Viewing Life Mathematically. Building from the first edition, I have endeavored to curate fourteen chapters that not only teach concepts but propel students to be curious about the world around us and how things relate to one another. When I first started writing mathematics textbooks, it was out of a desire to create a text that was both approachable and readable for all students. This mission to create a robust text that is presented with a conversational approach continues to be central to my writing philosophy. While this may be the only college-level mathematics course some students take, it is my hope that this course will not be the end of their mathematical curiosity. Instead, I intend this course to serve as a springboard for students to see the ways in which mathematical thought pertains to their chosen discipline, no matter the field. To this end, I have consciously tried to concentrate the material around pivotal concepts that open doors to future mathematics. Any modern quantitative reasoning text contains far more chapters than could reasonably be taught in any single semester. Consequently, rather than devoting entire chapters to topics such as sports or art, as in the first edition, I have interwoven those topics among the other chapters. In addition, I have expanded topics such as functions and mathematical growth, which are now contained in a new chapter on algebraic methods. Completely new to this second edition is a chapter on data science. The study of data is no longer limited to statistical professionals; it penetrates every profession. As such, I am thrilled to introduce students to the exciting world of a data scientist—wrangling, analyzing, and storytelling. In addition to these changes, this edition contains improved and expanded exercise sets with additional real-world data, new graphics, and updated examples that are of interest to the reader. When appropriate, I’ve also included the use of Excel as a calculation tool in examples. As one of the most sought-after skills for employers, I endeavored to equip students with as much proficiency in Excel as possible. I hope you enjoy this new edition. Best Regards, Kim Denley Preface ix Ǜ Think Back Think Backs are just‑in‑time information located in the margins of the text to remind students of important concepts that they may have forgotten from previous math courses or previous chapters in this course. Ǜ Fun Fact Fun Facts appear in the margin with additional information to pique student interest and make mathematics more relatable. Ǜ Helpful Hint Helpful Hints appear in the margins of the text and provide students with extra insightful pieces of information to help them understand concepts more deeply and avoid common mistakes. Ǜ Math Milestone Math Milestones appear in the margins to give more information about mathematicians and the history of mathematics to help students connect further with the material. CHAPTER 1 Critical Thinking and Problem Solving f SECTIONS 1.1 Thinking Mathematically 1.2 Estimating and Evaluating 1.3 Problem Solving: Processes and Techniques Chapter 1 Exercises Chapter 1 Project Chapter 1 Review Chapter and Section Openers Each chapter begins with a list of sections to prepare students for the topics that will be covered. Objectives are listed at the beginning of each section, helping students to identify the most important concepts in the section and enabling students to focus their time and effort appropriately. JUST TO BE CLEAR… Division: 28 ÷ 7 = 4 Multiplication: 13 ⋅ 7 = 91 Repeated Addition: 13 + 13 + 13 + 13 + 13 + 13 + 13 = 91 Abbott and Costello’s famous skit managed to show by division, multiplication, and repeated addition that 13 ⋅ 7 = 28. So it must be true, right? This makes us laugh because we can all see the errors that he makes right before our eyes. What is not so funny is that we often jump to the same types of misguided conclusions in our everyday lives by using similarly faulty logic. So what was wrong in Costello’s conclusion that 13 ⋅ 7 = 28? The problem is that his conclusion cannot be logically supported by the rules of addition, multiplication, and division. Although this famous error in his conclusion is obvious to us here, what if you are faced with a conclusion and you don’t know if you can trust it? In other words, you are not sure if the conclusion is right or wrong, or if the argument is valid or faulty. As we move through the chapter, not only will we show you ways to identify common errors in logic, like those in the Costello scene, we will also help you better understand how to make strong arguments for yourself. Introduction In their 1941 film In the Navy, Abbott and Costello show by multiplication, division, and repeated addition that 13 ⋅ 7 = 28. What?!? Wait a second… How can that be? Here’s their method of creative math. A. “7 times 3, 21.” B. “7 times 1, 7.” C. “7 and 1 is 8 and then bring this 2 down IT’S 28! 7 ∙ 13 = 28!” 13 7 21 × A.A. 1 7 7 3 21 × B.B. 1 7 3 21 7 82 × + C.C. MultiplicationMultiplication A. “Put down 13 seven times.” B. “Add all the 3s 3, 6, 9, 12, 15, 18, 21.” C. “Add all the 1s 22, 23, 24, 25, 26, 27, 28 YOU GET 28! 13 + 13 + 13 + 13 + 13 + 13 + 13 = 28!” 13 13 13 13 13 13 13 + A.A. 1 1 1 1 1 1 1 3 3 3 3 3 3 3 21 18 15 12 9 6 3 + B.B. 1 1 1 1 1 1 1 3 3 3 3 3 3 3 21 18 15 12 9 6 3 28 + C.C. 22 23 24 25 26 27 28 Repeated Repeated AdditionAddition A. “7 in to 2. . . 7 won’t go into 2, so I gotta take the 2 from here and put it down there. 7 into 8? 1 time.” B. “Now I’m gonna carry the 7 from here and put it under the 8. 7 from 8, 1.” C. “Now I have 21, 7 into 21? 3 times SO 28 ÷ 7 = 13!” DivisionDivision A.A. )78 1 2 2 7 1 3 B.B. )7 1 2 2 8 7 1 3 C.C. 7 21 3 2 8 7 21 0 1 Chapter Introductions An application of the chapter content is introduced on the first page of each chapter to inspire student interest and provide an understanding of how the topics to be studied are useful. Examples Examples are presented in a step-by-step manner that is easy for students to follow. Titles are given to alert students to the concept they will be learning throughout the example. Examples make use of tables, diagrams and graphs, and technology where applicable, giving clarification to the mathematical skill being presented. Margin Boxes Special FeaturesNext >