EBK USING & UNDERSTANDING MATHEMATICS
7th Edition
ISBN: 8220106844434
Author: Briggs
Publisher: PEARSON
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Textbook Question
Chapter 1.D, Problem 68E
Twin Primes Conjecture. If you write out the first several prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23, …) you will see that occasionally the gap between two consecutive primes is 2 (for example, 5, 7 and 17, 19). These pairs of closely spaced primes are called twin primes. A famous conjecture states that the number of twin primes is infinite. While a deductive proof of this conjecture has never been found, twin primes with nearly 400,000 digits have been identified, which gives experimental support to the conjecture. Find the first ten pairs of twin primes and present an inductive proof for the truth of the conjecture. Do you think the conjecture is true? Why or why not?
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Students have asked these similar questions
Example: For what odd primes p is 11 a quadratic residue modulo p?
Solution:
This is really asking "when is (11 | p) =1?"
First, 11 = 3 (mod 4). To use LQR, consider two cases p = 1 or 3 (mod 4):
p=1 We have 1 = (11 | p) = (p | 11), so p is a quadratic residue modulo 11. By
brute force:
121, 224, 3² = 9, 4² = 5, 5² = 3 (mod 11)
so the quadratic residues mod 11 are 1,3,4,5,9.
Using CRT for p = 1 (mod 4) & p = 1,3,4,5,9 (mod 11).
p = 1
(mod 4)
&
p = 1
(mod 11
gives p
1
(mod 44).
p = 1
(mod 4)
&
p = 3
(mod 11)
gives p25
(mod 44).
p = 1
(mod 4)
&
p = 4
(mod 11)
gives p=37
(mod 44).
p = 1
(mod 4)
&
p = 5
(mod 11)
gives p
5
(mod 44).
p = 1
(mod 4)
&
p=9
(mod 11)
gives p
9
(mod 44).
So p =1,5,9,25,37 (mod 44).
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Jamal wants to save $48,000 for a down payment on a home. How much will he need to invest in an
account with 11.8% APR, compounding daily, in order to reach his goal in 10 years? Round to the
nearest dollar.
Chapter 1 Solutions
EBK USING & UNDERSTANDING MATHEMATICS
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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- r nt Use the compound interest formula, A (t) = P(1 + 1)". An account is opened with an intial deposit of $7,500 and earns 3.8% interest compounded semi- annually. Round all answers to the nearest dollar. a. What will the account be worth in 10 years? $ b. What if the interest were compounding monthly? $ c. What if the interest were compounded daily (assume 365 days in a year)? $arrow_forwardKyoko has $10,000 that she wants to invest. Her bank has several accounts to choose from. Her goal is to have $15,000 by the time she finishes graduate school in 7 years. To the nearest hundredth of a percent, what should her minimum annual interest rate be in order to reach her goal assuming they compound daily? (Hint: solve the compound interest formula for the intrerest rate. Also, assume there are 365 days in a year) %arrow_forwardTest the claim that a student's pulse rate is different when taking a quiz than attending a regular class. The mean pulse rate difference is 2.7 with 10 students. Use a significance level of 0.005. Pulse rate difference(Quiz - Lecture) 2 -1 5 -8 1 20 15 -4 9 -12arrow_forward
- There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three investment? STEP 1: The formula for compound interest is A = nt = P(1 + − − ) n², where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to A = Pert Find r and n for each model, and use these values to write A in terms of t for each case. Annual Model r=0.10 A = Y(t) = 1150 (1.10)* n = 1 Quarterly Model r = 0.10 n = 4 A = Q(t) = 1150(1.025) 4t Continuous Model r=0.10 A = C(t) =…arrow_forwardThe following ordered data list shows the data speeds for cell phones used by a telephone company at an airport: A. Calculate the Measures of Central Tendency from the ungrouped data list. B. Group the data in an appropriate frequency table. C. Calculate the Measures of Central Tendency using the table in point B. D. Are there differences in the measurements obtained in A and C? Why (give at least one justified reason)? I leave the answers to A and B to resolve the remaining two. 0.8 1.4 1.8 1.9 3.2 3.6 4.5 4.5 4.6 6.2 6.5 7.7 7.9 9.9 10.2 10.3 10.9 11.1 11.1 11.6 11.8 12.0 13.1 13.5 13.7 14.1 14.2 14.7 15.0 15.1 15.5 15.8 16.0 17.5 18.2 20.2 21.1 21.5 22.2 22.4 23.1 24.5 25.7 28.5 34.6 38.5 43.0 55.6 71.3 77.8 A. Measures of Central Tendency We are to calculate: Mean, Median, Mode The data (already ordered) is: 0.8, 1.4, 1.8, 1.9, 3.2, 3.6, 4.5, 4.5, 4.6, 6.2, 6.5, 7.7, 7.9, 9.9, 10.2, 10.3, 10.9, 11.1, 11.1, 11.6, 11.8, 12.0, 13.1, 13.5, 13.7, 14.1, 14.2, 14.7, 15.0, 15.1, 15.5,…arrow_forwardA tournament is a complete directed graph, for each pair of vertices x, y either (x, y) is an arc or (y, x) is an arc. One can think of this as a round robin tournament, where the vertices represent teams, each pair plays exactly once, with the direction of the arc indicating which team wins. (a) Prove that every tournament has a direct Hamiltonian path. That is a labeling of the teams V1, V2,..., Un so that vi beats Vi+1. That is a labeling so that team 1 beats team 2, team 2 beats team 3, etc. (b) A digraph is strongly connected if there is a directed path from any vertex to any other vertex. Equivalently, there is no partition of the teams into groups A, B so that every team in A beats every team in B. Prove that every strongly connected tournament has a directed Hamiltonian cycle. Use this to show that for any team there is an ordering as in part (a) for which the given team is first. (c) A king in a tournament is a vertex such that there is a direct path of length at most 2 to any…arrow_forward
- Use a graphing utility to find the point of intersection, if any, of the graphs of the functions. Round your result to three decimal places. (Enter NONE in any unused answer blanks.) y = 100e0.01x (x, y) = y = 11,250 ×arrow_forwardhow to construct the following same table?arrow_forwardThe following is known. The complete graph K2t on an even number of vertices has a 1- factorization (equivalently, its edges can be colored with 2t - 1 colors so that the edges incident to each vertex are distinct). This implies that the complete graph K2t+1 on an odd number of vertices has a factorization into copies of tK2 + K₁ (a matching plus an isolated vertex). A group of 10 people wants to set up a 45 week tennis schedule playing doubles, each week, the players will form 5 pairs. One of the pairs will not play, the other 4 pairs will each play one doubles match, two of the pairs playing each other and the other two pairs playing each other. Set up a schedule with the following constraints: Each pair of players is a doubles team exactly 4 times; during those 4 matches they see each other player exactly once; no two doubles teams play each other more than once. (a) Find a schedule. Hint - think about breaking the 45 weeks into 9 blocks of 5 weeks. Use factorizations of complete…arrow_forward
- . The two person game of slither is played on a graph. Players 1 and 2 take turns, building a path in the graph. To start, Player 1 picks a vertex. Player 2 then picks an edge incident to the vertex. Then, starting with Player 1, players alternate turns, picking a vertex not already selected that is adjacent to one of the ends of the path created so far. The first player who cannot select a vertex loses. (This happens when all neighbors of the end vertices of the path are on the path.) Prove that Player 2 has a winning strategy if the graph has a perfect matching and Player 1 has a winning strategy if the graph does not have a perfect matching. In each case describe a strategy for the winning player that guarantees that they will always be able to select a vertex. The strategy will be based on using a maximum matching to decide the next choice, and will, for one of the cases involve using the fact that maximality means no augmenting paths. Warning, the game slither is often described…arrow_forwardLet D be a directed graph, with loops allowed, for which the indegree at each vertex is at most k and the outdegree at each vertex is at most k. Prove that the arcs of D can be colored so that the arcs entering each vertex must have distinct colors and the arcs leaving each vertex have distinct colors. An arc entering a vertex may have the same color as an arc leaving it. It is probably easiest to make use of a known result about edge coloring. Think about splitting each vertex into an ‘in’ and ‘out’ part and consider what type of graph you get.arrow_forward3:56 wust.instructure.com Page 0 Chapter 5 Test Form A of 2 - ZOOM + | Find any real numbers for which each expression is undefined. 2x 4 1. x Name: Date: 1. 3.x-5 2. 2. x²+x-12 4x-24 3. Evaluate when x=-3. 3. x Simplify each rational expression. x²-3x 4. 2x-6 5. x²+3x-18 x²-9 6. Write an equivalent rational expression with the given denominator. 2x-3 x²+2x+1(x+1)(x+2) Perform the indicated operation and simplify if possible. x²-16 x-3 7. 3x-9 x²+2x-8 x²+9x+20 5x+25 8. 4.x 2x² 9. x-5 x-5 3 5 10. 4x-3 8x-6 2 3 11. x-4 x+4 x 12. x-2x-8 x²-4 ← -> Copyright ©2020 Pearson Education, Inc. + 5 4. 5. 6. 7. 8. 9. 10. 11. 12. T-97arrow_forward
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