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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
Publisher: Cengage Learning
ISBN: 9781337274203

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Section
BuyFindarrow_forward

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
Publisher: Cengage Learning
ISBN: 9781337274203
Chapter 7.1, Problem 4E
Textbook Problem
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In Exercises 1–16, list the elements in the given set.

The set N of all negative integers greater than –3

To determine

The elements in the set N consisting of all negative integers greater than 3.

Explanation of Solution

Consider the set N consists of all negative integers greater than 3.

A set is a collection of items, referred as elements of the set.

All negative integers greater than 3 are 2 and 1

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Chapter 7 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)
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Ch. 7.1 - In Exercises 116, list the elements in the given...Ch. 7.1 - In Exercises 116, list the elements in the given...Ch. 7.1 - In Exercises 116, list the elements in the given...Ch. 7.1 - In Exercises 116, list the elements in the given...Ch. 7.1 - In Exercises 116, list the elements in the given...Ch. 7.1 - In Exercises 116, list the elements in the given...Ch. 7.1 - In Exercises 1720, draw a Venn diagram that...Ch. 7.1 - In Exercises 1720, draw a Venn diagram that...Ch. 7.1 - In Exercises 1720, draw a Venn diagram that...Ch. 7.1 - In Exercises 1720, draw a Venn diagram that...Ch. 7.1 - Let A={June,Janet,Jill,Justin,Jeffrey,Jello},...Ch. 7.1 - Let A={June,Janet,Jill,Justin,Jeffrey,Jello},...Ch. 7.1 - Let A={June,Janet,Jill,Justin,Jeffrey,Jello},...Ch. 7.1 - Let A={June,Janet,Jill,Justin,Jeffrey,Jello},...Ch. 7.1 - Let A={June,Janet,Jill,Justin,Jeffrey,Jello},...Ch. 7.1 - Let A={June,Janet,Jill,Justin,Jeffrey,Jello},...Ch. 7.1 - Let A={June,Janet,Jill,Justin,Jeffrey,Jello},...Ch. 7.1 - Let A={June,Janet,Jill,Justin,Jeffrey,Jello},...Ch. 7.1 - Let A={June,Janet,Jill,Justin,Jeffrey,Jello},...Ch. 7.1 - Let A={June,Janet,Jill,Justin,Jeffrey,Jello},...Ch. 7.1 - Let A={June,Janet,Jill,Justin,Jeffrey,Jello},...Ch. 7.1 - Let A={June,Janet,Jill,Justin,Jeffrey,Jello},...Ch. 7.1 - Let A={June,Janet,Jill,Justin,Jeffrey,Jello},...Ch. 7.1 - Let A={June,Janet,Jill,Justin,Jeffrey,Jello},...Ch. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - Let A={H, T} be the set of outcomes when a coin is...Ch. 7.1 - Let A={H, T} be the set of outcomes when a coin is...Ch. 7.1 - Let A={H, T} be the set of outcomes when a coin is...Ch. 7.1 - Let A={H, T} be the set of outcomes when a coin is...Ch. 7.1 - Let S be the set of outcomes when two...Ch. 7.1 - Let S be the set of outcomes when two...Ch. 7.1 - Let S be the set of outcomes when two...Ch. 7.1 - Let S be the set of outcomes when two...Ch. 7.1 - Let S be the set of outcomes when two...Ch. 7.1 - Let S be the set of outcomes when two...Ch. 7.1 - In Exercises 5360, use Venn diagrams to illustrate...Ch. 7.1 - In Exercises 5360, use Venn diagrams to illustrate...Ch. 7.1 - In Exercises 5360, use Venn diagrams to illustrate...Ch. 7.1 - In Exercises 5360, use Venn diagrams to illustrate...Ch. 7.1 - In Exercises 5360, use Venn diagrams to illustrate...Ch. 7.1 - In Exercises 5360, use Venn diagrams to illustrate...Ch. 7.1 - In Exercises 5360, use Venn diagrams to illustrate...Ch. 7.1 - In Exercises 5360, use Venn diagrams to illustrate...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - You sell iPads and jPads. Let I be the set of all...Ch. 7.1 - You sell two models of music players: the yoVaina...Ch. 7.1 - You are searching online for techno music that is...Ch. 7.1 - You would like to see either a World War II movie,...Ch. 7.1 - Explain, illustrating by means of an example, why...Ch. 7.1 - Explain, making reference to operations on sets,...Ch. 7.1 - Explain the meaning of a universal set, and give...Ch. 7.1 - Is the set of outcomes when two indistinguishable...Ch. 7.1 - Design a database scenario that leads to the...Ch. 7.1 - Design a database scenario that leads to the...Ch. 7.1 - Rewrite in set notation: She prefers movies that...Ch. 7.1 - Rewrite in set notation: He will cater for any...Ch. 7.1 - When this book was being written, the copy editor...Ch. 7.1 - When an older version of this book was being...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Verify that n(AB)=n(A)+n(B)n(AB) with A and B as...Ch. 7.2 - Verify that n(AC)=n(A)+n(C)n(AC) with A and C as...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - If n(A)=43,n(B)=20, and n(AB)=3, find n(AB).Ch. 7.2 - If n(A)=60, n(B)=20, and n(AB)=1 find n(AB).Ch. 7.2 - If n(AB)=100andn(A)=n(B)=60, fi0nd n(AB).Ch. 7.2 - If n(A)=100,n(AB)=150, and n(AB)=40, find n(B).Ch. 7.2 - Let S={Barnsley, Manchester United, Southend,...Ch. 7.2 - Let S={Barnsley, Manchester United, Southend,...Ch. 7.2 - Let S={Barnsley, Manchester United, Southend,...Ch. 7.2 - Let S={Barnsley, Manchester United, Southend,...Ch. 7.2 - Let S={Barnsley, Manchester United, Southend,...Ch. 7.2 - Let S={Barnsley, Manchester United, Southend,...Ch. 7.2 - With S,A, and B as above, verify that n((AB))=n(A...Ch. 7.2 - With S,A,andB as above, verify that...Ch. 7.2 - In Exercises 2730, use the given information to...Ch. 7.2 - In Exercises 2730, use the given information to...Ch. 7.2 - In Exercises 2730, use the given information to...Ch. 7.2 - In Exercises 2730, use the given information to...Ch. 7.2 - Web Searches In November 2011 a search using the...Ch. 7.2 - Web Searches In November 2011 a search using the...Ch. 7.2 - Amusement On a particularly boring transatlantic...Ch. 7.2 - Restaurant Menus While scanning through the...Ch. 7.2 - Mobile Gamers Of a total of 132 million mobile...Ch. 7.2 - Mobile Gamers Of a total of 208 million mobile...Ch. 7.2 - Publishing Exercises 3742 are based on the...Ch. 7.2 - Publishing Exercises 3742 are based on the...Ch. 7.2 - Publishing Exercises 3742 are based on the...Ch. 7.2 - Publishing Exercises 3742 are based on the...Ch. 7.2 - Publishing Exercises 3742 are based on the...Ch. 7.2 - Publishing Exercises 3742 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Medicine In a study of Tibetan children,10 a total...Ch. 7.2 - Medicine In a study of Tibetan children,11 a total...Ch. 7.2 - Entertainment According to a survey of 100 people...Ch. 7.2 - Athletics Of the 4,700 students at Medium Suburban...Ch. 7.2 - Entertainment In a survey of 100 Enormous State...Ch. 7.2 - Entertainment Refer back to Exercise 59. You are...Ch. 7.2 - If A and B are finite sets with AB, how are n(A)...Ch. 7.2 - If A and B are subsets of the finite set S with...Ch. 7.2 - Why is the Cartesian product referred to as a...Ch. 7.2 - Refer back to your answer to Exercise 63. What set...Ch. 7.2 - Formulate an interesting application whose answer...Ch. 7.2 - Formulate an interesting application whose answer...Ch. 7.2 - When is n(AB)n(A)+n(B)?Ch. 7.2 - When is n(AB)=n(A)?Ch. 7.2 - When is n(AB)=n(A)?Ch. 7.2 - When is n(AB)=n(A)?Ch. 7.2 - Use a Venn diagram or some other method to obtain...Ch. 7.2 - Suppose that A and B are sets with AB and n(A) at...Ch. 7.3 - An experiment requires a choice among three...Ch. 7.3 - A surgical procedure requires choosing among four...Ch. 7.3 - An experiment requires a sequence of three steps....Ch. 7.3 - A surgical procedure requires four steps. The...Ch. 7.3 - For the decision algorithms in Exercises 512, find...Ch. 7.3 - For the decision algorithms in Exercises 512, find...Ch. 7.3 - For the decision algorithms in Exercises 512, find...Ch. 7.3 - For the decision algorithms in Exercises 512, find...Ch. 7.3 - For the decision algorithms in Exercises 512, find...Ch. 7.3 - For the decision algorithms in Exercises 512, find...Ch. 7.3 - For the decision algorithms in Exercises 512, find...Ch. 7.3 - For the decision algorithms in Exercises 512, find...Ch. 7.3 - How many different four-letter sequences can be...Ch. 7.3 - How many different five-letter sequences can be...Ch. 7.3 - Ice Cream When Baskin-Robbins was founded in 1945,...Ch. 7.3 - Ice Cream At the beginning of 2002, Baskin-Robbins...Ch. 7.3 - Binary Codes A binary digit, or bit, is either 0...Ch. 7.3 - Ternary Codes A ternary digit is either 0, 1, or...Ch. 7.3 - Ternary Codes A ternary digit is either 0, 1, or...Ch. 7.3 - Binary Codes A binary digit, or bit, is either 0...Ch. 7.3 - Reward While selecting candy for students in his...Ch. 7.3 - Productivity Professor Oger must choose between an...Ch. 7.3 - DVD Discs DVD discs at your local computer store...Ch. 7.3 - Radar Detectors Radar detectors are either powered...Ch. 7.3 - Multiple-Choice Tests Professor Easys final...Ch. 7.3 - Multiple-Choice Tests Professor Toughs final...Ch. 7.3 - Tests A test requires that you answer either Part...Ch. 7.3 - Tests A test requires that you answer first Part A...Ch. 7.3 - Stock Portfolios Your broker has suggested that...Ch. 7.3 - Menus The local diner offers a meal combination...Ch. 7.3 - Computer Codes A computer byte consists of eight...Ch. 7.3 - Computer Codes Some written languages, such as...Ch. 7.3 - Symmetries of a Five-Pointed Star A five-pointed...Ch. 7.3 - Symmetries of a Six-Pointed Star A six-pointed...Ch. 7.3 - Variables in Visual Basic A variable name in the...Ch. 7.3 - Employee IDs A company assigns to each of its...Ch. 7.3 - Tournaments How many ways are there of filling in...Ch. 7.3 - Tournaments How many ways are there of filling in...Ch. 7.3 - Telephone Numbers Suppose a telephone number...Ch. 7.3 - Social Security Numbers A Social Security Number...Ch. 7.3 - Credit Card Numbers The vast majority of Visa and...Ch. 7.3 - Credit Card Numbers Credit cards issued by...Ch. 7.3 - DNA Chains: Life in Nature DNA (deoxyribonucleic...Ch. 7.3 - DNA Chains: Synthetic Life (Refer to Exercise 43.)...Ch. 7.3 - HTML Colors in HTML (the language in which many...Ch. 7.3 - Telephone Numbers In the past, a local telephone...Ch. 7.3 - Romeo and Juliet Here is a list of the main...Ch. 7.3 - Swan Lake The Enormous State Universitys...Ch. 7.3 - License Plates Many U.S. license plates display a...Ch. 7.3 - License Plates17 License plates in Montana have a...Ch. 7.3 - Mazes a. How many four-letter sequences are...Ch. 7.3 - Mazes a. How many six-letter sequences are...Ch. 7.3 - Car Engines18 In a six-cylinder V6 engine, the...Ch. 7.3 - Car Engines Repeat Exercise 53 for an...Ch. 7.3 - Minimalist Art You are exhibiting your collection...Ch. 7.3 - Combination Locks Dripping wet after your shower,...Ch. 7.3 - Product Design Your company has patented an...Ch. 7.3 - Product Design Your company has patented an...Ch. 7.3 - Calendars The World Almanac19 features a perpetual...Ch. 7.3 - Calendars How many possible calendars are there...Ch. 7.3 - Programming in Visual Basic (Some programming...Ch. 7.3 - Programming in Java Script (Some programming...Ch. 7.3 - Building Blocks Use a decision algorithm to show...Ch. 7.3 - Matrices (Some knowledge of matrices is assumed...Ch. 7.3 - Morse Code In Morse code, each letter of the...Ch. 7.3 - Numbers How many odd numbers between 10 and 99...Ch. 7.3 - Complete the following sentence: The...Ch. 7.3 - Complete the following sentence: The addition...Ch. 7.3 - You are packing for a short trip and want to take...Ch. 7.3 - You are designing an advertising logo that...Ch. 7.3 - Construct a decision algorithm that gives the...Ch. 7.3 - Find an interesting application that requires a...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - How many ordered lists are there of four items...Ch. 7.4 - How many ordered sequences are possible that...Ch. 7.4 - How many unordered sets are possible that contain...Ch. 7.4 - How many unordered sets are there of four items...Ch. 7.4 - How many five-letter sequences are possible that...Ch. 7.4 - How many six-letter sequences are possible that...Ch. 7.4 - How many three-letter sequences are possible that...Ch. 7.4 - How many three-letter sequences are possible that...Ch. 7.4 - How many three-letter (unordered) sets are...Ch. 7.4 - How many three-letter (unordered) sets are...Ch. 7.4 - How many six-letter sequences are possible that...Ch. 7.4 - How many six-letter sequences are possible that...Ch. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Dice If a die is rolled 30 times, there are 630...Ch. 7.4 - Dice If a die is rolled 30 times, there are 630...Ch. 7.4 - Dice If a die is rolled 30 times, there are 630...Ch. 7.4 - Dice If a die is rolled 30 times, there are 630...Ch. 7.4 - In Exercises 4752, calculate how many different...Ch. 7.4 - In Exercises 4752, calculate how many different...Ch. 7.4 - In Exercises 4752, calculate how many different...Ch. 7.4 - In Exercises 4752, calculate how many different...Ch. 7.4 - In Exercises 4752, calculate how many different...Ch. 7.4 - In Exercises 4752, calculate how many different...Ch. 7.4 - Itineraries Your international diplomacy trip...Ch. 7.4 - Itineraries Refer back to Exercise 53. How many...Ch. 7.4 - Poker Hands A poker hand consists of 5 cards from...Ch. 7.4 - Poker Hands A poker hand consists of 5 cards from...Ch. 7.4 - Poker Hands A poker hand consists of 5 cards from...Ch. 7.4 - Poker Hands A poker hand consists of 5 cards from...Ch. 7.4 - Poker Hands A poker hand consists of 5 cards from...Ch. 7.4 - Poker Hands A poker hand consists of 5 cards from...Ch. 7.4 - Dogs of the Dow The Dogs of the Dow are the stocks...Ch. 7.4 - Dogs of the Dow The Dogs of the Dow are the stocks...Ch. 7.4 - Day Trading Day traders typically buy and sell...Ch. 7.4 - Day Trading Day traders typically buy and sell...Ch. 7.4 - Elimination Tournaments In an elimination...Ch. 7.4 - Elimination Tournaments In an elimination...Ch. 7.4 - Elimination Tournaments In an elimination...Ch. 7.4 - Elimination Tournaments In an elimination...Ch. 7.4 - Popular Movies in 2011 Exercises 69 and 70 are...Ch. 7.4 - Popular Movies in 2011 Exercises 69 and 70 are...Ch. 7.4 - Traveling Salesperson Suppose you are a...Ch. 7.4 - Traveling Salesperson Refer back to Exercise 71...Ch. 7.4 - (From the GMAT) Ben and Ann are among seven...Ch. 7.4 - (Based on a question from the GMAT) Ben and Ann...Ch. 7.4 - (From the GMAT exam) If 10 persons meet at a...Ch. 7.4 - (Based on a question from the GMAT exam) If 12...Ch. 7.4 - Product Design The Honest Lock Company plans to...Ch. 7.4 - Product Design Repeat Exercise 77 for a lock based...Ch. 7.4 - Theory of Linear Programming (Some familiarity...Ch. 7.4 - More Theory of Linear Programming (Some...Ch. 7.4 - If you were hard pressed to study for an exam on...Ch. 7.4 - The formula for C(n,r) is written as a ratio of...Ch. 7.4 - Which of the following represent permutations? (A)...Ch. 7.4 - Which of the following represent combinations? (A)...Ch. 7.4 - When you click on Get Driving Directions on...Ch. 7.4 - If you want to know how many possible lists,...Ch. 7.4 - You are tutoring your friend for a test on sets...Ch. 7.4 - Complete the following: If a counting procedure...Ch. 7.4 - A textbook has the following exercise: Three...Ch. 7.4 - Explain why the coefficient of a a2b2 in (a+b)6 is...Ch. 7 - In Exercises 15, list the elements of the given...Ch. 7 - In Exercises 15, list the elements of the given...Ch. 7 - In Exercises 15, list the elements of the given...Ch. 7 - In Exercises 15, list the elements of the given...Ch. 7 - In Exercises 15, list the elements of the given...Ch. 7 - In Exercises 610, write the indicated set in terms...Ch. 7 - In Exercises 610, write the indicated set in terms...Ch. 7 - In Exercises 610, write the indicated set in terms...Ch. 7 - In Exercises 610, write the indicated set in terms...Ch. 7 - In Exercises 610, write the indicated set in terms...Ch. 7 - In Exercises 1114, give a formula for the...Ch. 7 - In Exercises 1114, give a formula for the...Ch. 7 - In Exercises 1114, give a formula for the...Ch. 7 - In Exercises 1114, give a formula for the...Ch. 7 - Recall that a poker hand consists of 5 cards from...Ch. 7 - Recall that a poker hand consists of 5 cards from...Ch. 7 - Recall that a poker hand consists of 5 cards from...Ch. 7 - Recall that a poker hand consists of 5 cards from...Ch. 7 - In Exercises 1924, consider a bag containing four...Ch. 7 - In Exercises 1924, consider a bag containing four...Ch. 7 - In Exercises 1924, consider a bag containing four...Ch. 7 - In Exercises 1924, consider a bag containing four...Ch. 7 - In Exercises 1924, consider a bag containing four...Ch. 7 - In Exercises 1924, consider a bag containing four...Ch. 7 - Inventories OHaganBooks.com currently operates...Ch. 7 - Inventories OHaganBooks.com currently operates...Ch. 7 - Inventories OHaganBooks.com currently operates...Ch. 7 - Inventories OHaganBooks.com currently operates...Ch. 7 - Inventories OHaganBooks.com currently operates...Ch. 7 - Inventories OHaganBooks.com currently operates...Ch. 7 - Customers OHaganBooks.com has two main...Ch. 7 - Customers OHaganBooks.com has two main...Ch. 7 - Customers OHaganBooks.com has two main...Ch. 7 - Customers OHaganBooks.com has two main...Ch. 7 - Customers OHaganBooks.com has two main...Ch. 7 - Customers OHaganBooks.com has two main...Ch. 7 - Online IDs As the customer base at OHaganBooks.com...Ch. 7 - Online IDs As the customer base at OHaganBooks.com...Ch. 7 - Online IDs As the customer base at OHaganBooks.com...Ch. 7 - Online IDs As the customer base at OHaganBooks.com...Ch. 7 - Degree Requirements After an exhausting day at the...Ch. 7 - Degree Requirements After an exhausting day at the...Ch. 7 - Degree Requirements After an exhausting day at the...

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