Mathematics All Around (6th Edition)
6th Edition
ISBN: 9780134434681
Author: Tom Pirnot
Publisher: PEARSON
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Textbook Question
Chapter 3.2, Problem 28E
In Exercise 25-28, determine whether we are using the inclusive or or the exclusive or in each statement.
The penalty is a $500 fine or 40 hours of community service.
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Chapter 3 Solutions
Mathematics All Around (6th Edition)
Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...
Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - Consider the following statements: g: Global...Ch. 3.1 - Consider the following statements: g: Global...Ch. 3.1 - Consider the following statements: g: Global...Ch. 3.1 - Consider the following statements: g: Global...Ch. 3.1 - Consider the following statements: t: The radial...Ch. 3.1 - Prob. 26ECh. 3.1 - Consider the following statements: t: The radial...Ch. 3.1 - Consider the following statements: t: The radial...Ch. 3.1 - In Exercises 2934, negate each quantified...Ch. 3.1 - In Exercises 2934, negate each quantified...Ch. 3.1 - In Exercises 2934, negate each quantified...Ch. 3.1 - In Exercises 2934, negate each quantified...Ch. 3.1 - In Exercises 2934, negate each quantified...Ch. 3.1 - In Exercises 2934, negate each quantified...Ch. 3.1 - Applying What Youve Learned Use the following...Ch. 3.1 - Applying What Youve Learned Use the following...Ch. 3.1 - Applying What Youve Learned Use the following...Ch. 3.1 - Applying What Youve Learned Use the following...Ch. 3.1 - Applying What Youve Learned Use the following...Ch. 3.1 - Applying What Youve Learned Use the following...Ch. 3.1 - Consider the happy and sad faces below. Determine...Ch. 3.1 - Consider the happy and sad faces below. Determine...Ch. 3.1 - Consider the happy and sad faces below. Determine...Ch. 3.1 - Consider the happy and sad faces below. Determine...Ch. 3.1 - In Exercises 4548, examine each statement to...Ch. 3.1 - In Exercises 4548, examine each statement to...Ch. 3.1 - In Exercises 4548, examine each statement to...Ch. 3.1 - In Exercises 4548, examine each statement to...Ch. 3.1 - Because the English language is so complex, it is...Ch. 3.1 - Because the English language is so complex, it is...Ch. 3.1 - Because the English language is so complex, it is...Ch. 3.1 - Prob. 52ECh. 3.1 - Prob. 53ECh. 3.1 - Prob. 54ECh. 3.1 - Prob. 55ECh. 3.1 - In 1937, Claude Shannon showed that computer...Ch. 3.1 - Prob. 57ECh. 3.1 - In 1937, Claude Shannon showed that computer...Ch. 3.1 - In Exercises 5962, determine if the following...Ch. 3.1 - In Exercises 5962, determine if the following...Ch. 3.1 - Prob. 61ECh. 3.1 - Prob. 62ECh. 3.1 - Prob. 63ECh. 3.1 - Prob. 64ECh. 3.1 - Prob. 65ECh. 3.1 - Prob. 66ECh. 3.1 - 6772. In symbolic logic, the form of statements is...Ch. 3.1 - Prob. 68ECh. 3.1 - Prob. 69ECh. 3.1 - Prob. 70ECh. 3.1 - Prob. 71ECh. 3.1 - 6772. In symbolic logic, the form of statements is...Ch. 3.1 - Think of real-life situation that you might want...Ch. 3.1 - Provide arguments for or against the view that...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - Prob. 8ECh. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - State whether the numbers given in Exercise 11-14...Ch. 3.2 - State whether the numbers given in Exercise 11-14...Ch. 3.2 - State whether the numbers given in Exercise 11-14...Ch. 3.2 - State whether the numbers given in Exercise 11-14...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 25-28, determine whether we are using...Ch. 3.2 - In Exercise 25-28, determine whether we are using...Ch. 3.2 - In Exercise 25-28, determine whether we are using...Ch. 3.2 - In Exercise 25-28, determine whether we are using...Ch. 3.2 - In Exercise 29-34, use DeMorgans laws to rewrite...Ch. 3.2 - In Exercise 29-34, use DeMorgans laws to rewrite...Ch. 3.2 - In Exercise 29-34, use DeMorgans laws to rewrite...Ch. 3.2 - In Exercise 29-34, use DeMorgans laws to rewrite...Ch. 3.2 - In Exercise 29-34, use DeMorgans laws to rewrite...Ch. 3.2 - In Exercise 29-34, use DeMorgans laws to rewrite...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - Exercise 43-48, deal with three-valued logic....Ch. 3.2 - Exercise 43-48, deal with three-valued logic....Ch. 3.2 - Exercise 43-48, deal with three-valued logic....Ch. 3.2 - Exercise 43-48, deal with three-valued logic....Ch. 3.2 - Exercise 43-48, deal with three-valued logic....Ch. 3.2 - Exercise 43-48, deal with three-valued logic....Ch. 3.2 - Applying What Youve Learned Use the following...Ch. 3.2 - Applying What Youve Learned Use the following...Ch. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.2 - Prob. 53ECh. 3.2 - Prob. 54ECh. 3.2 - Prob. 55ECh. 3.2 - Prob. 56ECh. 3.2 - Prob. 57ECh. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Prob. 61ECh. 3.2 - Prob. 62ECh. 3.2 - Use this graph based on data from the National Pet...Ch. 3.2 - Prob. 64ECh. 3.2 - In Section 3.1 page 94, we showed how to represent...Ch. 3.2 - Prob. 66ECh. 3.2 - Prob. 67ECh. 3.2 - Prob. 68ECh. 3.2 - Prob. 69ECh. 3.2 - What advantage do you see in using truth tables to...Ch. 3.2 - Prob. 71ECh. 3.2 - The and connective is necessary in the sense that...Ch. 3.2 - The stroke connective has the following truth...Ch. 3.2 - The stroke connective has the following truth...Ch. 3.2 - The stroke connective has the following truth...Ch. 3.2 - The stroke connective has the following truth...Ch. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Assume that you begin with a statement of the form...Ch. 3.3 - Prob. 30ECh. 3.3 - Assume that you begin with a statement of the form...Ch. 3.3 - Assume that you begin with a statement of the form...Ch. 3.3 - In Exercises 3336, write the indicated statement...Ch. 3.3 - In Exercises 3336, write the indicated statement...Ch. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - In Exercises 3740, determine which pairs of...Ch. 3.3 - In Exercises 3740, determine which pairs of...Ch. 3.3 - Prob. 39ECh. 3.3 - Prob. 40ECh. 3.3 - In Exercises 4148, rewrite each statement using...Ch. 3.3 - Prob. 42ECh. 3.3 - In Exercises 4148, rewrite each statement using...Ch. 3.3 - Prob. 44ECh. 3.3 - Prob. 45ECh. 3.3 - Prob. 46ECh. 3.3 - In Exercises 4148, rewrite each statement using...Ch. 3.3 - Prob. 48ECh. 3.3 - Find the truth value for each statement in...Ch. 3.3 - Find the truth value for each statement in...Ch. 3.3 - Find the truth value for each statement in...Ch. 3.3 - Find the truth value for each statement in...Ch. 3.3 - Prob. 53ECh. 3.3 - Prob. 54ECh. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - According to an Accountemps survey appearing in...Ch. 3.3 - According to an Accountemps survey appearing in...Ch. 3.3 - According to an Accountemps survey appearing in...Ch. 3.3 - According to an Accountemps survey appearing in...Ch. 3.3 - Perhaps you have heard the term helicopter...Ch. 3.3 - Perhaps you have heard the term helicopter...Ch. 3.3 - Perhaps you have heard the term helicopter...Ch. 3.3 - Perhaps you have heard the term helicopter...Ch. 3.3 - In Exercises 6568, write the converse, inverse, or...Ch. 3.3 - In Exercises 6568, write the converse, inverse, or...Ch. 3.3 - In Exercises 6568, write the converse, inverse, or...Ch. 3.3 - In Exercises 6568, write the converse, inverse, or...Ch. 3.3 - Prob. 69ECh. 3.3 - Prob. 70ECh. 3.3 - Communicating Mathematics Give an example of a...Ch. 3.3 - Communicating Mathematics Is it possible to have a...Ch. 3.3 - Communicating Mathematics Explain why it is...Ch. 3.3 - Communicating Mathematics Why is it reasonable to...Ch. 3.3 - In Exercises 75 and 76, assume that a credit card...Ch. 3.3 - In Exercises 75 and 76, assume that a credit card...Ch. 3.3 - Challenge Yourself In Exercises 79 and 80, use...Ch. 3.3 - Challenge Yourself In Exercises 79 and 80, use...Ch. 3.3 - Prob. 81ECh. 3.3 - Prob. 82ECh. 3.3 - Prob. 83ECh. 3.3 - Prob. 84ECh. 3.3 - Exercises 85 and 86 are based on the exercise sets...Ch. 3.3 - Exercises 85 and 86 are based on the exercise sets...Ch. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Prob. 25ECh. 3.4 - Prob. 26ECh. 3.4 - Prob. 27ECh. 3.4 - Prob. 28ECh. 3.4 - Prob. 29ECh. 3.4 - Prob. 30ECh. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Prob. 42ECh. 3.4 - We have emphasized that the form of a logical...Ch. 3.4 - We have emphasized that the form of a logical...Ch. 3.4 - We have emphasized that the form of a logical...Ch. 3.4 - We have emphasized that the form of a logical...Ch. 3.4 - Challenge Yourself Exercises 49-52 are puzzles...Ch. 3.4 - Challenge Yourself Exercises 49-52 are puzzles...Ch. 3.4 - Challenge Yourself Exercises 49-52 are puzzles...Ch. 3.4 - In a complicated argument with many variables, it...Ch. 3.4 - In a complicated argument with many variables, it...Ch. 3.4 - In addition to the argument forms that you studies...Ch. 3.4 - In addition to the argument forms that you studies...Ch. 3.4 - In addition to the argument forms that you studies...Ch. 3.4 - In addition to the argument forms that you studies...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 1724, complete each syllogism so that...Ch. 3.5 - Prob. 18ECh. 3.5 - In Exercise 1724, complete each syllogism so that...Ch. 3.5 - Prob. 20ECh. 3.5 - In Exercise 1724, complete each syllogism so that...Ch. 3.5 - Prob. 22ECh. 3.5 - In Exercise 1724, complete each syllogism so that...Ch. 3.5 - Prob. 24ECh. 3.5 - In Exercises 25 28, write two syllogisms that can...Ch. 3.5 - In Exercises 25 28, write two syllogisms that can...Ch. 3.5 - In Exercises 25 28, write two syllogisms that can...Ch. 3.5 - In Exercises 25 28, write two syllogisms that can...Ch. 3.5 - Give an example of a valid syllogism that has a...Ch. 3.5 - Give an example of a invalid syllogism that has a...Ch. 3.5 - Draw an Euler diagram for the statements All As...Ch. 3.5 - Draw an Euler diagram for the statements Some As...Ch. 3.5 - Draw an Euler diagram for the statements No As are...Ch. 3.5 - In each of your drawings for Exercises 31 33,...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In a Exercises 9-12, calculate the truth value of...Ch. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - In a Exercises 9-12, calculate the truth value of...Ch. 3.6 - In Exercises 13-16, consider the following fuzzy...Ch. 3.6 - In Exercises 13-16, consider the following fuzzy...Ch. 3.6 - In Exercise 13-16, consider the following fuzzy...Ch. 3.6 - In Exercise 13-16, consider the following fuzzy...Ch. 3.6 - In Exercises 17-24, assume that p has a truth...Ch. 3.6 - In Exercises 17-24, assume that p has a truth...Ch. 3.6 - Prob. 19ECh. 3.6 - In Exercises 17-24, assume that p has a truth...Ch. 3.6 - Prob. 21ECh. 3.6 - Prob. 22ECh. 3.6 - In Exercises 17-24, assume that p has a truth...Ch. 3.6 - Prob. 24ECh. 3.6 - In exercises 25-28, use the method described in...Ch. 3.6 - Prob. 26ECh. 3.6 - In exercises 25-28, use the method described in...Ch. 3.6 - In exercises 25-28, use the method described in...Ch. 3.6 - How are the rules for computing the truth tables...Ch. 3.6 - Discuss some situations in which using fuzzy logic...Ch. 3.6 - Choose a situation you will face in which you must...Ch. 3.6 - Do you have any criticisms of the decision-making...Ch. 3.CR - Prob. 1CRCh. 3.CR - Let v represent the statement I will buy a new...Ch. 3.CR - Let f represent Antonio is fluent in Spanish and...Ch. 3.CR - Negate each quantified statement and then rewrite...Ch. 3.CR - Let p represent some true statement, q represent...Ch. 3.CR - How many rows will be in the table for each...Ch. 3.CR - Construct a truth table for each statement. a....Ch. 3.CR - Negate each statement and then rewrite the...Ch. 3.CR - Which pairs of statements are logically...Ch. 3.CR - Assume we are dealing with three- valued logic and...Ch. 3.CR - Assume that p represent a true statement, q a...Ch. 3.CR - Construct a truth table for each statement. a. pq...Ch. 3.CR - Prob. 13CRCh. 3.CR - Rewrite each statement using the words if then. a....Ch. 3.CR - Section 3.4 15. Identify the form of each...Ch. 3.CR - Determine whether the form represents a valid...Ch. 3.CR - Use a truth table to determine whether the...Ch. 3.CR - In Exercises 18 and 19, use Euler diagrams to...Ch. 3.CR - In Exercises 18 and 19, use Euler diagrams to...Ch. 3.CR - Assume that p and q are fuzzy statements having...Ch. 3.CT - Which of the following are statements? a. New York...Ch. 3.CT - Negate each quantified statement and then rewrite...Ch. 3.CT - Let p represent the statement I will pass my...Ch. 3.CT - Let t represent The Tigers will win the series and...Ch. 3.CT - Prob. 5CTCh. 3.CT - If p is false and q is true and r is false, what...Ch. 3.CT - Prob. 7CTCh. 3.CT - Construct a truth table for each statement. a....Ch. 3.CT - Prob. 9CTCh. 3.CT - Negate each statement and then rewrite the...Ch. 3.CT - Determine whether the following pairs of...Ch. 3.CT - Write in words the converse, inverse, and...Ch. 3.CT - If p is true, q is false, and r is true, what is...Ch. 3.CT - Assume we are dealing with three-valued logic and...Ch. 3.CT - Prob. 15CTCh. 3.CT - Determine whether the form represents a valid...Ch. 3.CT - Identify the form of each argument. If it aint...Ch. 3.CT - In fuzzy logic, we replaced the conditional pq by...Ch. 3.CT - Use a truth table to determine if the argument is...Ch. 3.CT - Use an Euler diagram to determine whether the...
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- Test 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_forwardThere 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_forward
- A 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_forwardUse 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_forward
- The 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_forward
- 3:56 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_forwardplease work out more details give the solution.arrow_forwardProblem #5 Suppose you flip a two sided fair coin ("heads" or "tails") 8 total times. a). How many ways result in 6 tails and 2 heads? b). How many ways result in 2 tails and 6 heads? c). Compare your answers to part (a) and (b) and explain in a few sentences why the comparison makes sense.arrow_forward
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