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Mathematical Excursions (MindTap Course List)
4th Edition
ISBN: 9781305965584
Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg
Publisher: Cengage Learning
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Chapter 12, Problem 22RE
To determine
How many different 3-stock portfolios can be selected?
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Chapter 12 Solutions
Mathematical Excursions (MindTap Course List)
Ch. 12.1 - In a stack of 12 identical-looking coins, one is...Ch. 12.1 - In a stack of 13 identical-looking coins, one is...Ch. 12.1 - List the elements of the sample space defined by...Ch. 12.1 - List the elements of the sample space defined by...Ch. 12.1 - List the elements of the sample space defined by...Ch. 12.1 - List the elements of the sample space defined by...Ch. 12.1 - List the elements of the sample space defined by...Ch. 12.1 - List the elements of the sample space defined by...Ch. 12.1 - List the elements of the sample space defined by...Ch. 12.1 - List the elements of the sample space defined by...
Ch. 12.1 - Prob. 9ESCh. 12.1 - List the elements of the sample space defined by...Ch. 12.1 - List the sample space of paths that start at A and...Ch. 12.1 - Prob. 12ESCh. 12.1 - Use the counting principle to determine the number...Ch. 12.1 - Use the counting principle to determine the number...Ch. 12.1 - Use the counting principle to determine the number...Ch. 12.1 - Use the counting principle to determine the number...Ch. 12.1 - Prob. 17ESCh. 12.1 - Prob. 18ESCh. 12.1 - Use the following experiment. Two digit numbers...Ch. 12.1 - Prob. 20ESCh. 12.1 - Use the following experiment. Two digit numbers...Ch. 12.1 - Prob. 22ESCh. 12.1 - Prob. 23ESCh. 12.1 - Use the following experiment. Two digit numbers...Ch. 12.1 - Prob. 25ESCh. 12.1 - Use the following experiment. Four cards labeled...Ch. 12.1 - Prob. 27ESCh. 12.1 - Use the following experiment. Four cards labeled...Ch. 12.1 - Prob. 29ESCh. 12.1 - Use the following experiment. A state lottery game...Ch. 12.1 - Use the following experiment. A state lottery game...Ch. 12.1 - Use the following experiment. A state lottery game...Ch. 12.1 - Prob. 33ESCh. 12.1 - Prob. 34ESCh. 12.1 - Prob. 35ESCh. 12.1 - Prob. 36ESCh. 12.2 - For each of the following exercises, assume that a...Ch. 12.2 - For each of the following exercises., assume that...Ch. 12.2 - For each of the following exercises, assume that a...Ch. 12.2 - For each of the following exercises, assume that a...Ch. 12.2 - For each of the following exercises, assume that a...Ch. 12.2 - Prob. 1ESCh. 12.2 - Prob. 2ESCh. 12.2 - Prob. 3ESCh. 12.2 - Prob. 4ESCh. 12.2 - Evaluate the expression. (83)!Ch. 12.2 - Prob. 6ESCh. 12.2 - Evaluate the expression. P(8,5)Ch. 12.2 - Evaluate the expression. P(7,2)Ch. 12.2 - Evaluate the expression. P(9,7)Ch. 12.2 - Prob. 10ESCh. 12.2 - Evaluate the expression. P(8,0)Ch. 12.2 - Evaluate the expression. P(7,0)Ch. 12.2 - Evaluate the expression. P(8,8)Ch. 12.2 - Prob. 14ESCh. 12.2 - Evaluate the expression. P(8,2)P(5,3)Ch. 12.2 - Prob. 16ESCh. 12.2 - Evaluate the expression. P(6,0)P(6,6)Ch. 12.2 - P(10,4)P(8,4) Evaluate the expression....Ch. 12.2 - Evaluate the expression. C(9,2)Ch. 12.2 - Prob. 20ESCh. 12.2 - Evaluate the expression. C(12,0)Ch. 12.2 - Prob. 22ESCh. 12.2 - Prob. 23ESCh. 12.2 - Evaluate the expression. C(8,5)C(9,4)Ch. 12.2 - Prob. 25ESCh. 12.2 - Evaluate the expression. C(4,3)C(5,2)C(9,5)Ch. 12.2 - Prob. 27ESCh. 12.2 - Prob. 28ESCh. 12.2 - Prob. 29ESCh. 12.2 - Evaluate the expression. 5!C(18,0)Ch. 12.2 - How many combinations are possible? Assume that...Ch. 12.2 - How many combinations are possible? Assume that...Ch. 12.2 - How many combinations are possible? Assume that...Ch. 12.2 - Prob. 34ESCh. 12.2 - Is it possible to calculate C(7,9)? Think of your...Ch. 12.2 - Prob. 36ESCh. 12.2 - Music Downloads A student downloaded 5 music tiles...Ch. 12.2 - Elections The board of directors of a corporation...Ch. 12.2 - Elections A committee of 16 students must select a...Ch. 12.2 - The Olympics A gold, a silver, and a bronze medal...Ch. 12.2 - Music Festival Six country music bands and 3 rock...Ch. 12.2 - Prob. 42ESCh. 12.2 - Passwords A password require 8 characters. If a...Ch. 12.2 - Gardening A gardener is planting a row of tulip...Ch. 12.2 - Prob. 45ESCh. 12.2 - Platoons A typical platoon consists of 20...Ch. 12.2 - Exam Questions A professor gives his students 7...Ch. 12.2 - Test Banks A math quiz is generated by randomly...Ch. 12.2 - Committee Selection A committee of 6 people is...Ch. 12.2 - Quality Control In a shipment of 20 smart phones,...Ch. 12.2 - Prob. 51ESCh. 12.2 - Basketball In the Eastern Conference of the...Ch. 12.2 - Prob. 53ESCh. 12.2 - Prob. 54ESCh. 12.2 - Softball Eighteen people decide to play softball....Ch. 12.2 - Bowling Fifteen people decide to form a bowling...Ch. 12.2 - Signal Flags The Coast Guard uses signal flags as...Ch. 12.2 - Pizza Toppings A restaurant offers a special pizza...Ch. 12.2 - Letter Arrangements How many different letter...Ch. 12.2 - Prob. 60ESCh. 12.2 - Coin Tosses Ten identical coins are tossed. How...Ch. 12.2 - Coin Tosses Twelve identical coins are tossed. How...Ch. 12.2 - Prob. 63ESCh. 12.2 - Prob. 64ESCh. 12.2 - Refer to a standard deck of playing cards. Assume...Ch. 12.2 - Prob. 66ESCh. 12.2 - Refer to a standard deck of playing cards. Assume...Ch. 12.2 - Prob. 68ESCh. 12.2 - Prob. 69ESCh. 12.2 - Refer to a standard deck of playing cards. Assume...Ch. 12.2 - Prob. 71ESCh. 12.2 - Prob. 72ESCh. 12.2 - Prob. 73ESCh. 12.3 - Using the recorded data, calculate the empirical...Ch. 12.3 - The theoretical probability that a toothpick will...Ch. 12.3 - Prob. 3EECh. 12.3 - Prob. 4EECh. 12.3 - Prob. 5EECh. 12.3 - Prob. 6EECh. 12.3 - List the elements of the sample space for each...Ch. 12.3 - Prob. 2ESCh. 12.3 - List the elements of the sample space for each...Ch. 12.3 - List the elements of the sample space for each...Ch. 12.3 - List the elements of the sample space for each...Ch. 12.3 - List the elements of the sample space for each...Ch. 12.3 - Assume that it is equally likely for a child to be...Ch. 12.3 - Assume that it is equally likely for a child to be...Ch. 12.3 - Assume that it is equally likely for a child to be...Ch. 12.3 - Prob. 10ESCh. 12.3 - Assume that it is equally likely for a child to be...Ch. 12.3 - Assume that it is equally likely for a child to be...Ch. 12.3 - Assume that it is equally likely for a child to be...Ch. 12.3 - Prob. 14ESCh. 12.3 - Assume that it is equally likely for a child to be...Ch. 12.3 - Prob. 16ESCh. 12.3 - A coin is tossed 4 times. Assuming the coin is...Ch. 12.3 - A coin is tossed 4 times. Assuming the coin is...Ch. 12.3 - In Exercises 19 to 22, a dodecahedral die (one...Ch. 12.3 - In Exercises 19 to 22, a dodecahedral die (one...Ch. 12.3 - In Exercises 19 to 22, a dodecahedral die (one...Ch. 12.3 - Prob. 22ESCh. 12.3 - In Exercises 23 to 32, 2 regular 6-sided dice are...Ch. 12.3 - Prob. 24ESCh. 12.3 - In Exercises 23 to 32, 2 regular 6-sided dice are...Ch. 12.3 - Prob. 26ESCh. 12.3 - In Exercises 23 to 32, 2 regular 6-sided dice are...Ch. 12.3 - Prob. 28ESCh. 12.3 - In Exercises 23 to 32, 2 regular 6-sided dice are...Ch. 12.3 - In Exercises 23 to 32, 2 regular 6-sided dice are...Ch. 12.3 - In Exercises 23 to 32, 2 regular 6-sided dice are...Ch. 12.3 - Prob. 32ESCh. 12.3 - If 2 dice are rolled, compute the probability of...Ch. 12.3 - Prob. 34ESCh. 12.3 - In Exercises 35 to 38. a card is selected at...Ch. 12.3 - Prob. 36ESCh. 12.3 - In Exercises 35 to 38. a card is selected at...Ch. 12.3 - Prob. 38ESCh. 12.3 - Voter Characteristics In Exercises 39 to 44, use...Ch. 12.3 - Prob. 40ESCh. 12.3 - Voter Characteristics In Exercises 39 to 44, use...Ch. 12.3 - Voter Characteristics In Exercises 39 to 44, use...Ch. 12.3 - Voter Characteristics In Exercises 39 to 44, use...Ch. 12.3 - Prob. 44ESCh. 12.3 - Education Levels In Exercises 45 to 48, a survey...Ch. 12.3 - Education Levels In Exercises 45 to 48, a survey...Ch. 12.3 - Education Levels In Exercises 45 to 48, a survey...Ch. 12.3 - Education Levels In Exercises 45 to 48, a survey...Ch. 12.3 - Annual Salaries A random survey asked respondents...Ch. 12.3 - Prob. 50ESCh. 12.3 - Annual Salaries A random survey asked respondents...Ch. 12.3 - Prob. 52ESCh. 12.3 - Prob. 53ESCh. 12.3 - Prob. 54ESCh. 12.3 - Genotypes The eye color of mice is determined by a...Ch. 12.3 - Genotypes The height of a certain plant is...Ch. 12.3 - Prob. 57ESCh. 12.3 - Prob. 58ESCh. 12.3 - The odds in favor of an event are given. Compute...Ch. 12.3 - Prob. 60ESCh. 12.3 - The odds in favor of an event are given. Compute...Ch. 12.3 - Prob. 62ESCh. 12.3 - The odds in favor of an event are given. Compute...Ch. 12.3 - Prob. 64ESCh. 12.3 - The probability of an event is given. Find the...Ch. 12.3 - Prob. 66ESCh. 12.3 - Prob. 67ESCh. 12.3 - Prob. 68ESCh. 12.3 - The probability of an event is given. Find the...Ch. 12.3 - Prob. 70ESCh. 12.3 - Game Shows The game board for the television show...Ch. 12.3 - Prob. 72ESCh. 12.3 - If a single fair die is rolled, what are the odds...Ch. 12.3 - Prob. 74ESCh. 12.3 - A coin is tossed 4 limes. What are the odds...Ch. 12.3 - Prob. 76ESCh. 12.3 - Use the table, which is based on information from...Ch. 12.3 - Prob. 78ESCh. 12.3 - Football A bookmaker has placed 8 to 3 odds...Ch. 12.3 - Candy Colors A snack-size bag of M&Ms candies...Ch. 12.3 - If 4 cards labeled A, B, C, and D are randomly...Ch. 12.3 - Prob. 82ESCh. 12.3 - Prob. 83ESCh. 12.3 - Prob. 84ESCh. 12.3 - Prob. 85ESCh. 12.3 - Prob. 86ESCh. 12.3 - Prob. 87ESCh. 12.3 - Prob. 88ESCh. 12.3 - Roulette Exercises 86(091 use the casino game...Ch. 12.3 - Prob. 90ESCh. 12.3 - Prob. 91ESCh. 12.4 - Prob. 1EECh. 12.4 - Prob. 2EECh. 12.4 - Prob. 3EECh. 12.4 - Prob. 4EECh. 12.4 - Some casinos will let you choose up to 20 numbers....Ch. 12.4 - If 20 numbers are chosen, find the probability of...Ch. 12.4 - Prob. 1ESCh. 12.4 - Prob. 2ESCh. 12.4 - In Exercises 3 to 6, first verify that the...Ch. 12.4 - Prob. 4ESCh. 12.4 - In Exercises 3 to 6, first verify that the...Ch. 12.4 - Prob. 6ESCh. 12.4 - If P(A)=0.2,P(B)=0.5, and P(AandB)=0.1. find...Ch. 12.4 - Prob. 8ESCh. 12.4 - If P(A)=0.3,P(B)=0.8, and P(AorB)=0.9. Find...Ch. 12.4 - Prob. 10ESCh. 12.4 - In Exercises 11 to 14, suppose you ask a friend to...Ch. 12.4 - Prob. 12ESCh. 12.4 - In Exercises 11 to 14, suppose you ask a friend to...Ch. 12.4 - Prob. 14ESCh. 12.4 - In Exercises 15 to 20, two dice are rolled....Ch. 12.4 - Prob. 16ESCh. 12.4 - In Exercises 15 to 20, two dice are rolled....Ch. 12.4 - Prob. 18ESCh. 12.4 - In Exercises 15 to 20, two dice are rolled....Ch. 12.4 - In Exercises 15 to 20, two dice are rolled....Ch. 12.4 - In Exercises 21 to 26, a single card is drawn from...Ch. 12.4 - Prob. 22ESCh. 12.4 - In Exercises 2110 26. a single card is drawn from...Ch. 12.4 - Prob. 24ESCh. 12.4 - In Exercises 2110 26. a single card is drawn from...Ch. 12.4 - Prob. 26ESCh. 12.4 - Employment In Exercises 27 to 30, use the data in...Ch. 12.4 - Employment In Exercises 27 to 30, use the data in...Ch. 12.4 - Employment In Exercises 27 to 30, use the data in...Ch. 12.4 - Prob. 30ESCh. 12.4 - Contests If the probability of winning a...Ch. 12.4 - Prob. 32ESCh. 12.4 - Professional Sports The National Collegiate -...Ch. 12.4 - Prob. 34ESCh. 12.4 - Use the formula for the probability of the...Ch. 12.4 - Prob. 36ESCh. 12.4 - Use the formula for the probability of the...Ch. 12.4 - Prob. 38ESCh. 12.4 - Use the formula for the probability of the...Ch. 12.4 - Use the formula for the probability of the...Ch. 12.4 - Prob. 41ESCh. 12.4 - Prob. 42ESCh. 12.4 - Prob. 43ESCh. 12.4 - Prob. 44ESCh. 12.4 - Prob. 45ESCh. 12.4 - Prob. 46ESCh. 12.4 - Prob. 47ESCh. 12.4 - If a person draws 3 cards from a standard deck...Ch. 12.4 - Prob. 49ESCh. 12.4 - Prob. 50ESCh. 12.4 - Prob. 51ESCh. 12.4 - Coins A bag contains 44 U.S. quarters and 6...Ch. 12.4 - Prob. 53ESCh. 12.4 - Prob. 54ESCh. 12.4 - Door Codes A planned community has 300 homes, each...Ch. 12.4 - Monty Hall Problem When someone is first presented...Ch. 12.4 - Prob. 57ESCh. 12.4 - Prob. 58ESCh. 12.5 - Prob. 1EECh. 12.5 - Prob. 2EECh. 12.5 - Prob. 3EECh. 12.5 - Prob. 4EECh. 12.5 - Prob. 1ESCh. 12.5 - Prob. 2ESCh. 12.5 - In Exercises 3 to 6, compute the conditional...Ch. 12.5 - Prob. 4ESCh. 12.5 - In Exercises 3 to 6, compute the conditional...Ch. 12.5 - In Exercises 3 to 6, compute the conditional...Ch. 12.5 - Employment In Exercises 7 to 10, use the data in...Ch. 12.5 - Employment In Exercises 7 to 10, use the data in...Ch. 12.5 - Employment In Exercises 7 to 10, use the data in...Ch. 12.5 - Prob. 10ESCh. 12.5 - Video Games In Exercises 11 to 14, use the data in...Ch. 12.5 - Video Games In Exercises 11 to 14, use the data in...Ch. 12.5 - Video Games In Exercises 11 to 14, use the data in...Ch. 12.5 - Prob. 14ESCh. 12.5 - A pair of dice is tossed. Find the probability...Ch. 12.5 - Prob. 16ESCh. 12.5 - A pair of dice is tossed. What is the probability...Ch. 12.5 - Prob. 18ESCh. 12.5 - What is the probability of drawing 2 cards in...Ch. 12.5 - Prob. 20ESCh. 12.5 - Two cards are drawn from a standard deck without...Ch. 12.5 - Prob. 22ESCh. 12.5 - Candy Colors In Exercises 23 to 26, a snack-size...Ch. 12.5 - Prob. 24ESCh. 12.5 - Candy Colors In Exercises 23 to 26, a snack-size...Ch. 12.5 - Prob. 26ESCh. 12.5 - In Exercises 27 to 30, 3 cards are dealt from a...Ch. 12.5 - Prob. 28ESCh. 12.5 - In Exercises 27 to 30, 3 cards are dealt from a...Ch. 12.5 - Prob. 30ESCh. 12.5 - Student Attendance In Exercises 31 to 34, the...Ch. 12.5 - Prob. 32ESCh. 12.5 - Student Attendance In Exercises 31 to 34, the...Ch. 12.5 - Student Attendance In Exercises 31 to 34, the...Ch. 12.5 - Prob. 35ESCh. 12.5 - Prob. 36ESCh. 12.5 - Prob. 37ESCh. 12.5 - Prob. 38ESCh. 12.5 - Prob. 39ESCh. 12.5 - Prob. 40ESCh. 12.5 - Prob. 41ESCh. 12.5 - In Exercises 39 to 44, a pair of dice is tossed...Ch. 12.5 - Prob. 43ESCh. 12.5 - Prob. 44ESCh. 12.5 - Prob. 45ESCh. 12.5 - Prob. 46ESCh. 12.5 - Prob. 47ESCh. 12.5 - Prob. 48ESCh. 12.5 - Prob. 49ESCh. 12.5 - In Exercises 4910 54, a card is drawn from a...Ch. 12.5 - Prob. 51ESCh. 12.5 - Prob. 52ESCh. 12.5 - Prob. 53ESCh. 12.5 - Prob. 54ESCh. 12.5 - A standard deck of playing cards is shuffled, and...Ch. 12.5 - Prob. 56ESCh. 12.5 - A hag contains 5 red marbles, 4 green marbles, and...Ch. 12.5 - Prob. 58ESCh. 12.5 - Prob. 59ESCh. 12.5 - Prob. 60ESCh. 12.5 - Prob. 61ESCh. 12.5 - Prob. 62ESCh. 12.5 - Monty Hall Problem This is another explanation,...Ch. 12.6 - Compute the probability that if a bet is placed on...Ch. 12.6 - Prob. 2EECh. 12.6 - Prob. 3EECh. 12.6 - Prob. 4EECh. 12.6 - Prob. 5EECh. 12.6 - Determine the expectation for wagering $1 on the...Ch. 12.6 - Prob. 7EECh. 12.6 - Prob. 8EECh. 12.6 - Prob. 1ESCh. 12.6 - The outcomes of an experiment and the probability...Ch. 12.6 - Roulette One of the wagers in the game of roulette...Ch. 12.6 - Roulette One of the wagers in roulette is to bet...Ch. 12.6 - Casino Games Many casinos have a game called the...Ch. 12.6 - Casino Games Many casinos have a game called the...Ch. 12.6 - Casino Games Many casinos have a game called the...Ch. 12.6 - Casino Games Many casinos have a game called the...Ch. 12.6 - Life Insurance Exercises 9 to 14 use data taken...Ch. 12.6 - Life Insurance Exercises 9 to 14 use data taken...Ch. 12.6 - Prob. 11ESCh. 12.6 - Prob. 12ESCh. 12.6 - Prob. 13ESCh. 12.6 - Prob. 14ESCh. 12.6 - Construction A construction company has been hired...Ch. 12.6 - Prob. 16ESCh. 12.6 - Design Consultant A consultant has been hired to...Ch. 12.6 - Prob. 18ESCh. 12.6 - If a pair of regular dice is tossed once, use the...Ch. 12.6 - Consider rolling a pair of unusual dice, for which...Ch. 12.6 - Prob. 21ESCh. 12.6 - Suppose you purchase a ticket for a prize and your...Ch. 12.6 - Prob. 23ESCh. 12.6 - Prob. 24ESCh. 12 - List the elements of the sample space for the...Ch. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Prob. 4RECh. 12 - An athletic shoe store sells running shoes in 3...Ch. 12 - Prob. 6RECh. 12 - Prob. 7RECh. 12 - Prob. 8RECh. 12 - Prob. 9RECh. 12 - Prob. 10RECh. 12 - Prob. 11RECh. 12 - Prob. 12RECh. 12 - Prob. 13RECh. 12 - Prob. 14RECh. 12 - Prob. 15RECh. 12 - A matching test has 7 definitions that are to be...Ch. 12 - A matching test has 7 definitions to be matched...Ch. 12 - Prob. 18RECh. 12 - Twelve identical coins are tossed. How many...Ch. 12 - Work Shifts Three positions are open at a...Ch. 12 - A professor assigns 25 homework problems, of which...Ch. 12 - Prob. 22RECh. 12 - Quality Control A quality control inspector...Ch. 12 - Prob. 24RECh. 12 - 25. How many 5-card poker hands consist of 4 of a...Ch. 12 - Prob. 26RECh. 12 - Prob. 27RECh. 12 - Prob. 28RECh. 12 - Use the table below, which shows the number of...Ch. 12 - Use the table below, which shows the number of...Ch. 12 - Prob. 31RECh. 12 - Prob. 32RECh. 12 - Prob. 33RECh. 12 - Prob. 34RECh. 12 - Prob. 35RECh. 12 - Prob. 36RECh. 12 - Prob. 37RECh. 12 - Prob. 38RECh. 12 - Prob. 39RECh. 12 - Prob. 40RECh. 12 - Prob. 41RECh. 12 - Prob. 42RECh. 12 - Prob. 43RECh. 12 - Prob. 44RECh. 12 - Two cards are drawn, without replacement, from a...Ch. 12 - Prob. 46RECh. 12 - A box contains 24 different colored chips that are...Ch. 12 - Prob. 48RECh. 12 - A box contains 24 different colored chips that are...Ch. 12 - Prob. 50RECh. 12 - A box contains 24 different colored chips that are...Ch. 12 - Prob. 52RECh. 12 - Use the table below, which shows the number of...Ch. 12 - Use the table below, which shows the number of...Ch. 12 - Use the table below, which shows the number of...Ch. 12 - Prob. 56RECh. 12 - Prob. 57RECh. 12 - Prob. 58RECh. 12 - Prob. 59RECh. 12 - Prob. 60RECh. 12 - Prob. 61RECh. 12 - Prob. 62RECh. 12 - Prob. 63RECh. 12 - Prob. 64RECh. 12 - 1 will flip 2 coins. If both coins come up tails,...Ch. 12 - Raffle Tickets For a fundraiser, an elementary...Ch. 12 - Prob. 67RECh. 12 - Prob. 68RECh. 12 - Life Insurance The probability that a 19-year-old...Ch. 12 - Construction A construction company has bid on a...Ch. 12 - Prob. 1TCh. 12 - Computer Systems A computer system can be...Ch. 12 - Prob. 3TCh. 12 - Prob. 4TCh. 12 - Prob. 5TCh. 12 - Prob. 6TCh. 12 - Prob. 7TCh. 12 - Prob. 8TCh. 12 - Prob. 9TCh. 12 - Prob. 10TCh. 12 - Prob. 11TCh. 12 - Prob. 12TCh. 12 - Prob. 13TCh. 12 - Prob. 14T
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- Given sets X and Y and Z, can you prove that (X-(Y u Z)) u (Y-(X u Z)) is a subset of (X u Y) - (X intersection Y)arrow_forward4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown in the table. For each problem, approximate the distance the car traveled (in miles) using the given method, on the provided interval, and with the given number of rectangles or trapezoids, n. Time (min) 0 6 12 18|24|30|36|42|48|54|60 Speed (mph) 0 10 20 40 60 50 40 30 40 40 65 a.) Left Rectangles, [0, 30] n=5 b.) Right Rectangles, [24, 42] n=3 c.) Midpoint Rectangles, [24, 60] n=3 d.) Trapezoids, [0, 24] n=4arrow_forwardGiven the functions A and B, can you prove that if B ◦ A is bijective, then A is injective and B is surjectivearrow_forward
- - + ++ Table 2: Crack Experiment for Exercise 2 A B C D Treatment Combination (1) Replicate I II 7.037 6.376 14.707 15.219 |++++ 1 བྱ॰༤༠སྦྱོ སྦྱོཋཏྟཱུ a b ab 11.635 12.089 17.273 17.815 с ас 10.403 10.151 4.368 4.098 bc abc 9.360 9.253 13.440 12.923 d 8.561 8.951 ad 16.867 17.052 bd 13.876 13.658 abd 19.824 19.639 cd 11.846 12.337 acd 6.125 5.904 bcd 11.190 10.935 abcd 15.653 15.053 Question 3 Continuation of Exercise 2. One of the variables in the experiment described in Exercise 2, heat treatment method (C), is a categorical variable. Assume that the remaining factors are continuous. (a) Write two regression models for predicting crack length, one for each level of the heat treatment method variable. What differences, if any, do you notice in these two equations? (b) Generate appropriate response surface contour plots for the two regression models in part (a). (c) What set of conditions would you recommend for the factors A, B, and D if you use heat treatment method C = +? (d) Repeat…arrow_forwardTerry has a square plot of land measuring 500 meters by 500 meters. She divided the land into 25 100-m by 100-m plots and created three raster maps showing the type of mineral, fruit tree, and energy available on each plot. Use the maps below to shade the blank maps according to each problem.arrow_forwardThe bracket BCD is hinged at C and attached to a control cable at B. Let F₁ = 275 N and F2 = 275 N. F1 B a=0.18 m C A 0.4 m -0.4 m- 0.24 m Determine the reaction at C. The reaction at C N Z F2 Darrow_forward
- Question 2 A nickel-titanium alloy is used to make components for jet turbine aircraft engines. Cracking is a potentially serious problem in the final part because it can lead to nonrecoverable failure. A test is run at the parts producer to determine the effect of four factors on cracks. The four factors are: pouring temperature (A), titanium content (B), heat treatment method (C), amount of grain refiner used (D). Two replicates of a 24 design are run, and the length of crack (in mm x10-2) induced in a sample coupon subjected to a standard test is measured. The data are shown in Table 2. 1 (a) Estimate the factor effects. Which factor effects appear to be large? (b) Conduct an analysis of variance. Do any of the factors affect cracking? Use a = 0.05. (c) Write down a regression model that can be used to predict crack length as a function of the significant main effects and interactions you have identified in part (b). (d) Analyze the residuals from this experiment. (e) Is there an…arrow_forwardShow the stepsarrow_forwardThe correct answer is C,i know that we need to use stokes theorem and parametrize the equations then write the equation F with respect to the curve but i cant seem to find a way to do it, the integral should be from 0 to 2pi but i might be wrongcould you show me the steps to get to 18piarrow_forward
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