Using & Understanding Mathematics, Books a la Carte edition (7th Edition)
Using & Understanding Mathematics, Books a la Carte edition (7th Edition)
7th Edition
ISBN: 9780134716015
Author: Jeffrey O. Bennett, William L. Briggs
Publisher: PEARSON
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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Chapter 1.E, Problem 5QQ
To determine

Choose the best answer to the following question. Explain your reasoning with one or more complete sentences.

You need to buy a car and are considering loans from two banks. The loan terms are otherwise identical, but Bank 1 is offering a loan at 7% interest plus an application fee and Bank 2 is at 7.5% interest plus an application fee. Based on this, you can conclude that

a) Bank 1 is the better deal.

b) Bank 2 is probably the better deal, since it probably has a lower application fee.

c) There is no way to tell which deal is better without knowing the application fees.

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Chapter 1 Solutions

Using & Understanding Mathematics, Books a la Carte edition (7th Edition)

Ch. 1.A - Prob. 1QQCh. 1.A - A fallacy is a. a statement that is untrue. b. a...Ch. 1.A - Which of the following could not qualify as a...Ch. 1.A - An argument in which the conclusion essentially...Ch. 1.A - The fallacy of appeal to ignorance occurs when a....Ch. 1.A - Consider the argument ‘‘I don’t support the...Ch. 1.A - Consider again the argument ‘‘I don’t support the...Ch. 1.A - Prob. 8QQCh. 1.A - Suppose that the fact that an event A occurs...Ch. 1.A - When we speak of a straw man in an argument, we...
Ch. 1.A - What is logic? Briefly explain how logic can be...Ch. 1.A - How do we define an argument? What is the basic...Ch. 1.A - What is a fallacy? Choose three examples of...Ch. 1.A - Prob. 4ECh. 1.A - Prob. 5ECh. 1.A - I persuaded my father that I was right with a...Ch. 1.A - I didn’t believe the premises on which he based...Ch. 1.A - Prob. 8ECh. 1.A - I disagree with your conclusion, so your argument...Ch. 1.A - Even though your argument contains a fallacy, your...Ch. 1.A - Analyzing Fallacies. Consider the following...Ch. 1.A - 11-20: Analyzing Fallacies. Consider the following...Ch. 1.A - Analyzing Fallacies. Consider the following...Ch. 1.A - 11-20: Analyzing Fallacies. Consider the following...Ch. 1.A - Analyzing Fallacies. Consider the following...Ch. 1.A - Prob. 16ECh. 1.A - Analyzing Fallacies. Consider the following...Ch. 1.A - Prob. 18ECh. 1.A - Analyzing Fallacies. Consider the following...Ch. 1.A - Prob. 20ECh. 1.A - Media Claims. Each of the following claims can...Ch. 1.A - Prob. 22ECh. 1.A - Prob. 23ECh. 1.A - Prob. 24ECh. 1.A - Recognizing Fallacies. In the following arguments,...Ch. 1.A - 25-40: Recognizing Fallacies. In the following...Ch. 1.A - Recognizing Fallacies. In the following arguments,...Ch. 1.A - Recognizing Fallacies. In the following arguments,...Ch. 1.A - Prob. 29ECh. 1.A - Prob. 30ECh. 1.A - 25-40: Recognizing Fallacies. In the following...Ch. 1.A - Prob. 32ECh. 1.A - Prob. 33ECh. 1.A - Recognizing Fallacies. In the following arguments,...Ch. 1.A - Recognizing Fallacies. In the following arguments,...Ch. 1.A - Prob. 36ECh. 1.A - Prob. 37ECh. 1.A - 25-40: Recognizing Fallacies. In the following...Ch. 1.A - 25-40: Recognizing Fallacies. In the following...Ch. 1.A - 25-40: Recognizing Fallacies. In the following...Ch. 1.A - Prob. 41ECh. 1.A - Prob. 42ECh. 1.A - Additional Fallacies. Consider the blowing...Ch. 1.A - Additional Fallacies. Consider the blowing...Ch. 1.A - Evaluating Media Information. Choose a current...Ch. 1.A - Snopes. Visit the Snopes.com website and choose...Ch. 1.A - Prob. 47ECh. 1.A - Prob. 48ECh. 1.A - Fallacies in Politics. Discuss the tactics used by...Ch. 1.A - Prob. 50ECh. 1.A - 51. Comment Fallacies. The “reader comments” that...Ch. 1.A - 52. Fake News Sites. Visit a fake news site that...Ch. 1.B - The statement Mathematics is fun is a. an...Ch. 1.B - Suppose you know the truth value of a proposition...Ch. 1.B - Which of the following has the form of a...Ch. 1.B - Suppose you want to make a truth table for the...Ch. 1.B - Suppose the statement p or q is true. Then you can...Ch. 1.B - Suppose the statement p is false and the statement...Ch. 1.B - The statement If it’s a dog, then it is a mammal...Ch. 1.B - The statement If the engine is running, then the...Ch. 1.B - Two statements are logically equivalent if a. they...Ch. 1.B - Prob. 10QQCh. 1.B - What is a proposition? Give a few examples, and...Ch. 1.B - What do we mean by the negation of a proposition?...Ch. 1.B - Define conjunction, disjunction, and conditional,...Ch. 1.B - 4. What is the difference between an inclusive or...Ch. 1.B - 5. Make a truth table for each of the following: p...Ch. 1.B - Prob. 6ECh. 1.B - 7. My logical proposition is a question that you...Ch. 1.B - The mayor opposes repealing the ban on handguns,...Ch. 1.B - Prob. 9ECh. 1.B - Prob. 10ECh. 1.B - Prob. 11ECh. 1.B - Prob. 12ECh. 1.B - Prob. 13ECh. 1.B - Prob. 14ECh. 1.B - 13-18: A proposition? Determine whether the...Ch. 1.B - Prob. 16ECh. 1.B - Prob. 17ECh. 1.B - Prob. 18ECh. 1.B - Negation. Write the negation of the given...Ch. 1.B - Prob. 20ECh. 1.B - Prob. 21ECh. 1.B - Prob. 22ECh. 1.B - Prob. 23ECh. 1.B - Multiple Negations. Explain the meaning of the...Ch. 1.B - Prob. 25ECh. 1.B - Multiple Negations. Explain the meaning of the...Ch. 1.B - Prob. 27ECh. 1.B - Multiple Negations. Explain the meaning of the...Ch. 1.B - Truth Tables. Make a truth table for the given...Ch. 1.B - Prob. 30ECh. 1.B - Prob. 31ECh. 1.B - And Statements. The following propositions have...Ch. 1.B - Prob. 33ECh. 1.B - And Statements. The following statements have the...Ch. 1.B - Prob. 35ECh. 1.B - 31-36: And Statements. The following statements...Ch. 1.B - Truth Tables. Make a truth table for the given...Ch. 1.B - 37-38: Truth Tables. Make a truth table for the...Ch. 1.B - Prob. 39ECh. 1.B - 39-44: Interpreting or. State whether or is used...Ch. 1.B - Prob. 41ECh. 1.B - Interpreting or. State whether or is used in the...Ch. 1.B - 39-44: Interpreting or. State whether or is used...Ch. 1.B - Interpreting or. State whether or is used in the...Ch. 1.B - Truth Table. Make a truth table for the given...Ch. 1.B - Truth Table. Make a truth table for the given...Ch. 1.B - Truth Table. Make a truth table for the given...Ch. 1.B - Truth Table. Make a truth table for the given...Ch. 1.B - Truth Table. Make a truth table for the given...Ch. 1.B - Prob. 50ECh. 1.B - Prob. 51ECh. 1.B - Prob. 52ECh. 1.B - Prob. 53ECh. 1.B - Prob. 54ECh. 1.B - Prob. 55ECh. 1.B - 51-56: Or Statements. The following statements...Ch. 1.B - 57-58: Truth Tables. Make a truth table for the...Ch. 1.B - 57-58: Truth Tables. Make a truth table for the...Ch. 1.B - Prob. 59ECh. 1.B - Prob. 60ECh. 1.B - Prob. 61ECh. 1.B - Prob. 62ECh. 1.B - If... then Statements. Identify the hypothesis and...Ch. 1.B - Prob. 64ECh. 1.B - Prob. 65ECh. 1.B - If... then Statements. Identify the hypothesis and...Ch. 1.B - Rephrasing Conditional Statements. Express the...Ch. 1.B - 67-72: Rephrasing Conditional Statements. Express...Ch. 1.B - 67-72: Rephrasing Conditional Statements. Express...Ch. 1.B - 67-72: Rephrasing Conditional Statements. Express...Ch. 1.B - Prob. 71ECh. 1.B - Prob. 72ECh. 1.B - Converse, Inverse, and Contrapositive. Write the...Ch. 1.B - Converse, Inverse, and Contrapositive. Write the...Ch. 1.B - Converse, Inverse, and Contrapositive. Write the...Ch. 1.B - Prob. 76ECh. 1.B - Converse, Inverse, and Contrapositive. Write the...Ch. 1.B - Converse, Inverse, and Contrapositive. Write the...Ch. 1.B - Prob. 79ECh. 1.B - Prob. 80ECh. 1.B - 79-82: Famous Quotes. Rephrase the following...Ch. 1.B - 79-82: Famous Quotes. Rephrase the following...Ch. 1.B - 83-87: Writing Conditional Propositions. Create...Ch. 1.B - Prob. 84ECh. 1.B - Writing Conditional Propositions. Create your own...Ch. 1.B - 83-87: Writing Conditional Propositions. Create...Ch. 1.B - 83-87: Writing Conditional Propositions. Create...Ch. 1.B - Prob. 88ECh. 1.B - Necessary and Sufficient. Write the following...Ch. 1.B - Necessary and Sufficient. Write the following...Ch. 1.B - Prob. 91ECh. 1.B - 89-92: Necessary and Sufficient. Write the...Ch. 1.B - Logical Equivalence. Consider the following pairs...Ch. 1.B - Logical Equivalence. Consider the following pairs...Ch. 1.B - Logical Equivalence. Consider the following pairs...Ch. 1.B - Prob. 96ECh. 1.B - Logical Equivalence. Consider the following pairs...Ch. 1.B - Prob. 98ECh. 1.B - Prob. 99ECh. 1.B - Prob. 100ECh. 1.B - Prob. 101ECh. 1.B - Prob. 102ECh. 1.C - Consider the set {Alabama, Alaska, Arizona,…,...Ch. 1.C - Which of the following is not a member of the set...Ch. 1.C - Based on the Venn diagram below, we conclude that...Ch. 1.C - Suppose that A represents the set of all boys and...Ch. 1.C - Suppose that A represents the set of all apples...Ch. 1.C - Suppose that A represents the set of all high...Ch. 1.C - In the Venn diagram below, the X tells us that a....Ch. 1.C - Prob. 8QQCh. 1.C - Consider again the Venn diagram from Exercise 8....Ch. 1.C - Look at the data in Table 1.1 (p.34). The total...Ch. 1.C - Prob. 1ECh. 1.C - What is a Venn diagram? How do we show that one...Ch. 1.C - List the four standard categorical propositions....Ch. 1.C - Briefly discuss how you can put a categorical...Ch. 1.C - Explain how to draw a Venn diagram for three...Ch. 1.C - 6. Explain how to read a table such as Table 1.1...Ch. 1.C - The people who live in Chicago form a subset of...Ch. 1.C - All jabbers are wocks, so there must be no wocks...Ch. 1.C - I counted an irrational number of students in my...Ch. 1.C - I surveyed my class to find out whether students...Ch. 1.C - My professor asked me to draw a Venn diagram for a...Ch. 1.C - I used a Venn diagram with three circles to show...Ch. 1.C - Classifying Numbers. Choose the first set in the...Ch. 1.C - Prob. 14ECh. 1.C - Classifying Numbers. Choose the first set in the...Ch. 1.C - Prob. 16ECh. 1.C - 13-28: Classifying Numbers. Choose the first set...Ch. 1.C - 13-28: Classifying Numbers. Choose the first set...Ch. 1.C - 13-28: Classifying Numbers. Choose the first set...Ch. 1.C - Prob. 20ECh. 1.C - Prob. 21ECh. 1.C - Prob. 22ECh. 1.C - Prob. 23ECh. 1.C - Prob. 24ECh. 1.C - Prob. 25ECh. 1.C - Prob. 26ECh. 1.C - Prob. 27ECh. 1.C - Prob. 28ECh. 1.C - Prob. 29ECh. 1.C - Prob. 30ECh. 1.C - Prob. 31ECh. 1.C - Prob. 32ECh. 1.C - Prob. 33ECh. 1.C - Prob. 34ECh. 1.C - Prob. 35ECh. 1.C - Prob. 36ECh. 1.C - Prob. 37ECh. 1.C - Prob. 38ECh. 1.C - Prob. 39ECh. 1.C - Venn Diagrams for Two Sets. Draw Venn diagrams...Ch. 1.C - 37-44: Venn Diagrams for Two Sets. Draw Venn...Ch. 1.C - 37-44: Venn Diagrams for Two Sets. Draw Venn...Ch. 1.C - 37-44: Venn Diagrams for Two Sets. Draw Venn...Ch. 1.C - 37-44: Venn Diagrams for Two Sets. Draw Venn...Ch. 1.C - Categorical Propositions. For the given...Ch. 1.C - Categorical Propositions. For the given...Ch. 1.C - Categorical Propositions. For the given...Ch. 1.C - 45-52: Categorical Propositions. For the given...Ch. 1.C - Categorical Propositions. For the given...Ch. 1.C - Categorical Propositions. For the given...Ch. 1.C - Categorical Propositions. For the given...Ch. 1.C - Categorical Propositions. For the given...Ch. 1.C - Prob. 53ECh. 1.C - Prob. 54ECh. 1.C - Prob. 55ECh. 1.C - Prob. 56ECh. 1.C - Prob. 57ECh. 1.C - Prob. 58ECh. 1.C - Prob. 59ECh. 1.C - Prob. 60ECh. 1.C - Two-Circle Venn Diagram with Numbers. Use the Venn...Ch. 1.C - Two-Circle Venn Diagram with Numbers. Use the Venn...Ch. 1.C - Three-Circle Venn Diagram with Numbers. Use the...Ch. 1.C - Three-Circle Venn Diagram with Numbers. Use the...Ch. 1.C - Hospital Drug Use. The following numbers of...Ch. 1.C - Technology Survey. A survey of 150 college...Ch. 1.C - Venn Diagram Analysis. 67. A movie critic reviewed...Ch. 1.C - Venn Diagram Analysis. 68. All runners who...Ch. 1.C - Venn Diagram Analysis. 69. One hundred people who...Ch. 1.C - Venn Diagram Analysis. 70. In a trial of a new...Ch. 1.C - Prob. 71ECh. 1.C - Prob. 72ECh. 1.C - Prob. 73ECh. 1.C - Prob. 74ECh. 1.C - 86. Categorical Propositions. Find at least three...Ch. 1.C - Prob. 76ECh. 1.C - Prob. 77ECh. 1.C - Prob. 78ECh. 1.C - Prob. 79ECh. 1.C - Prob. 80ECh. 1.C - Prob. 81ECh. 1.C - State Politics. Find out how many states have a...Ch. 1.C - Prob. 83ECh. 1.D - To prove a statement true, you must use a. an...Ch. 1.D - If a deductive argument is valid, its conclusion...Ch. 1.D - Prob. 3QQCh. 1.D - 4. Consider an argument in which Premise 1 is "All...Ch. 1.D - 5. Consider again the argument from question 4....Ch. 1.D - Consider an argument in which Premise 1 is “ If p,...Ch. 1.D - 7. Consider an argument in which Premise 1 is “ If...Ch. 1.D - Prob. 8QQCh. 1.D - 9. The longest side of a right triangle is called...Ch. 1.D - Prob. 10QQCh. 1.D - Summarize the differences between deductive and...Ch. 1.D - Briefly explain the idea of strength and how it...Ch. 1.D - Briefly explain the ideas of validity and...Ch. 1.D - Describe the procedure used to test the validity...Ch. 1.D - Prob. 5ECh. 1.D - What is a chain of conditionals? Give an example...Ch. 1.D - Prob. 7ECh. 1.D - Prob. 8ECh. 1.D - 9. My inductive argument provides absolute proof...Ch. 1.D - Prob. 10ECh. 1.D - 11. My argument is deductively valid, so if you...Ch. 1.D - Prob. 12ECh. 1.D - Prob. 13ECh. 1.D - Prob. 14ECh. 1.D - Prob. 15ECh. 1.D - Prob. 16ECh. 1.D - Argument Type. Explain whether the following...Ch. 1.D - Argument Type. Explain whether the following...Ch. 1.D - Argument Type. Explain whether the following...Ch. 1.D - Argument Type. Explain whether the following...Ch. 1.D - Argument Type. Explain whether the following...Ch. 1.D - Prob. 22ECh. 1.D - Prob. 23ECh. 1.D - Prob. 24ECh. 1.D - Prob. 25ECh. 1.D - Prob. 26ECh. 1.D - Prob. 27ECh. 1.D - Analyzing Deductive Arguments. Consider the...Ch. 1.D - Prob. 30ECh. 1.D - 29-36: Analyzing Deductive Arguments. Consider the...Ch. 1.D - Analyzing Deductive Arguments. Consider the...Ch. 1.D - Analyzing Deductive Arguments. Consider the...Ch. 1.D - Analyzing Deductive Arguments. Consider the...Ch. 1.D - Prob. 35ECh. 1.D - Prob. 36ECh. 1.D - Prob. 37ECh. 1.D - 37-44: Deductive Arguments with Conditional...Ch. 1.D - 37-44: Deductive Arguments with Conditional...Ch. 1.D - 37-44: Deductive Arguments with Conditional...Ch. 1.D - Prob. 41ECh. 1.D - Prob. 42ECh. 1.D - Prob. 43ECh. 1.D - Deductive Arguments with Conditional Propositions....Ch. 1.D - Prob. 45ECh. 1.D - Prob. 46ECh. 1.D - Prob. 47ECh. 1.D - Prob. 48ECh. 1.D - Prob. 49ECh. 1.D - Prob. 50ECh. 1.D - Testing Mathematical Rules. Test the following...Ch. 1.D - It is true for all positive integers n that...Ch. 1.D - 53-57: Validity and Soundness. State whether it is...Ch. 1.D - 53-57: Validity and Soundness. State whether it is...Ch. 1.D - Prob. 55ECh. 1.D - Prob. 56ECh. 1.D - Validity and Soundness. State whether it is...Ch. 1.D - Prob. 58ECh. 1.D - Prob. 59ECh. 1.D - Prob. 60ECh. 1.D - Prob. 61ECh. 1.D - Prob. 62ECh. 1.D - Conditionals in Books. Consider the following...Ch. 1.D - Prob. 64ECh. 1.D - 63-66: Conditionals in Books. Consider the...Ch. 1.D - 63-66: Conditionals in Books. Consider the...Ch. 1.D - 62. The Goldbach Conjecture. Recall that a prime...Ch. 1.D - Twin Primes Conjecture. If you write out the first...Ch. 1.D - The Pythagorean Theorem. Learn more about the...Ch. 1.D - Prob. 70ECh. 1.D - 69. Inductive Reasoning in Your Life. Give an...Ch. 1.D - Prob. 72ECh. 1.D - Prob. 73ECh. 1.D - Prob. 74ECh. 1.E - What does it mean to think critically about the...Ch. 1.E - "If you want to save the social services that...Ch. 1.E - 2. Suppose that an argument is deductively valid...Ch. 1.E - 9. A teacher claims that, because spell checkers...Ch. 1.E - 3. You need to buy a car and are considering loans...Ch. 1.E - 4. You get your hair cut at a shop that charges...Ch. 1.E - You buy a cell phone plan that gives you up to...Ch. 1.E - Prob. 8QQCh. 1.E - Prob. 9QQCh. 1.E - The Smiths have a picnic every Saturday provided t...Ch. 1.E - Describe critical thinking and why it is important...Ch. 1.E - Prob. 2ECh. 1.E - Prob. 3ECh. 1.E - Prob. 4ECh. 1.E - Reed was relieved because his insurance company...Ch. 1.E - 6. Although the plane crashed in Nevada, the...Ch. 1.E - Sue prefers the Red shuttle because it gets her to...Ch. 1.E - Prob. 8ECh. 1.E - There was no price difference, so Michael chose...Ch. 1.E - Prob. 10ECh. 1.E - Prob. 11ECh. 1.E - Interpreting Policies. A city charters sole policy...Ch. 1.E - Reading a Ballot Initiative. Consider the...Ch. 1.E - Prob. 14ECh. 1.E - Hidden Assumptions. Identify at least two hidden...Ch. 1.E - Prob. 16ECh. 1.E - Hidden Assumptions. Identify at least two hidden...Ch. 1.E - Hidden Assumptions. Identify at least two hidden...Ch. 1.E - 29-30: Unstated Issues. The following arguments...Ch. 1.E - Unstated Issues. The following arguments give...Ch. 1.E - Airline Options. In planning a trip to New Zealand...Ch. 1.E - Buy vs. Lease. You are deciding whether to buy a...Ch. 1.E - You've Won! You receive the following e-mail...Ch. 1.E - Reading a Lease. Consider the following excerpt...Ch. 1.E - Prob. 25ECh. 1.E - Prob. 26ECh. 1.E - Prob. 27ECh. 1.E - 27-28. Fake News. The following are fake news...Ch. 1.E - 29-40: Read and Think Carefully. The following...Ch. 1.E - Prob. 30ECh. 1.E - Prob. 31ECh. 1.E - Prob. 32ECh. 1.E - Prob. 33ECh. 1.E - Prob. 34ECh. 1.E - Prob. 35ECh. 1.E - Prob. 36ECh. 1.E - Prob. 37ECh. 1.E - 29-40: Read and Think Carefully. The following...Ch. 1.E - 29-40: Read and Think Carefully. The following...Ch. 1.E - 29-40: Read and Think Carefully. The following...Ch. 1.E - Decision Making. Analyze the situations. and...Ch. 1.E - Prob. 42ECh. 1.E - Prob. 43ECh. 1.E - Prob. 44ECh. 1.E - IRS Guidelines on Who Must File a Federal Tax...Ch. 1.E - Prob. 46ECh. 1.E - Credit Card Agreement. The following rules are...Ch. 1.E - Prob. 48ECh. 1.E - Texas Ethics. In its Guide to Ethics the Texas...Ch. 1.E - Prob. 50ECh. 1.E - 50-54: Critical Thinking. Consider the following...Ch. 1.E - 57-65: Critical Thinking. Consider the following...Ch. 1.E - 50-54: Critical Thinking. Consider the following...Ch. 1.E - Prob. 54ECh. 1.E - Prob. 55ECh. 1.E - Interpreting the Second Amendment. Much of the...Ch. 1.E - Prob. 57ECh. 1.E - Prob. 58ECh. 1.E - Prob. 59ECh. 1.E - Prob. 60ECh. 1.E - Prob. 61ECh. 1.E - Conspiracy Theories. Choose some well-known...
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