Precalculus Enhanced with Graphing Utilities (7th Edition)
7th Edition
ISBN: 9780134119281
Author: Michael Sullivan, Michael Sullivan III
Publisher: PEARSON
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Textbook Question
Chapter 13.2, Problem 46AE
Forming License Plate Numbers How many different license plate numbers can be made using 2 letters followed by 4 digits selected from the digits 0 through 9, if:
(a) Letters and digits may be repeated?
(b) Letters may be repeated, but digits may not be repeated?
(c) Neither letters nor digits may be repeated?
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1. (i) Give the definition of a metric on a set X.
[5 Marks]
(ii) Let X = {a, b, c} and let a function d : XxX → [0, ∞) be defined
as d(a, a) = d(b,b) = d(c, c) 0, d(a, c) = d(c, a) 1, d(a, b) = d(b, a) = 4,
d(b, c) = d(c,b) = 2. Decide whether d is a metric on X. Justify your answer.
=
(iii) Consider a metric space (R, d.), where
=
[10 Marks]
0
if x = y,
d* (x, y)
5
if xy.
In the metric space (R, d*), describe:
(a) open ball B2(0) of radius 2 centred at 0;
(b) closed ball B5(0) of radius 5 centred at 0;
(c) sphere S10 (0) of radius 10 centred at 0.
[5 Marks]
[5 Marks]
[5 Marks]
(c) sphere S10 (0) of radius 10 centred at 0.
[5 Marks]
2. Let C([a, b]) be the metric space of continuous functions on the interval
[a, b] with the metric
doo (f,g)
=
max f(x)g(x)|.
xЄ[a,b]
= 1x. Find:
Let f(x) = 1 - x² and g(x):
(i) do(f, g) in C'([0, 1]);
(ii) do(f,g) in C([−1, 1]).
[20 Marks]
[20 Marks]
Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties
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Chapter 13 Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
Ch. 13.1 - Prob. 1AYPCh. 13.1 - Prob. 2AYPCh. 13.1 - True or false The intersection of two sets is...Ch. 13.1 - Prob. 4AYPCh. 13.1 - Prob. 5CVCh. 13.1 - If the number of elements in a set is a...Ch. 13.1 - Prob. 7CVCh. 13.1 - True or False If a task consists of a sequence of...Ch. 13.1 - Prob. 9SBCh. 13.1 - Prob. 10SB
Ch. 13.1 - If n( A )=15 , n( B )=20 , and n( AB )=10 , find...Ch. 13.1 - If n( A )=30 , n( B )=40 , and n( AB )=45 , find...Ch. 13.1 - If n( AB )=50 , n( AB )=10 , and n( B )=20 , find...Ch. 13.1 - If n( AB )=60 , n( AB )=40 , and n( A )=n( B ) ,...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - Shirts and Ties A man has 5 shirts and 3 ties. How...Ch. 13.1 - Blouses and Skirts A woman has 5 blouses and 8...Ch. 13.1 - Four-digit Numbers How many four-digit numbers can...Ch. 13.1 - Five-digit Numbers How many five-digit numbers can...Ch. 13.1 - Analyzing Survey Data In a consumer survey of 500...Ch. 13.1 - Analyzing Survey Data In a student survey, 200...Ch. 13.1 - Analyzing Survey Data In a survey of 100 investors...Ch. 13.1 - Prob. 30AECh. 13.1 - Demographics The following data represent the...Ch. 13.1 - Prob. 32AECh. 13.1 - Stock Portfolios As a financial planner, you are...Ch. 13.1 - Make up a problem different from any found in the...Ch. 13.1 - Problems 36-39 are based on material learned...Ch. 13.1 - Problems 36-39 are based on material learned...Ch. 13.1 - Problems 36-39 are based on material learned...Ch. 13.1 - Problems 36-39 are based on material learned...Ch. 13.2 - 0!= ; 1!= . (p. 642)Ch. 13.2 - True or False n!= ( n+1 )! n . (p. 642)Ch. 13.2 - A(n) __________ is an ordered arrangement of r...Ch. 13.2 - A(n) ___________ is an arrangement of r objects...Ch. 13.2 - P( n,r )= __________________.Ch. 13.2 - C( n,r )= _______________________.Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - List all the ordered arrangements of 5 objects a ,...Ch. 13.2 - List all the ordered arrangements of 5 objects a ,...Ch. 13.2 - List all the ordered arrangements of 4 objects 1,...Ch. 13.2 - List all the ordered arrangements of 6 objects 1,...Ch. 13.2 - List all the combinations of 5 objects a , b , c ,...Ch. 13.2 - List all the combinationss of 5 objects a , b , c...Ch. 13.2 - List all the combinations of 4 objects 1, 2, 3,...Ch. 13.2 - List all the combinationss of 6 objects 1, 2, 3,...Ch. 13.2 - Forming Codes How many two-letter codes can be...Ch. 13.2 - Forming Codes How many two-letter codes can be...Ch. 13.2 - Forming Numbers How many three-digit numbers can...Ch. 13.2 - Forming Numbers How many three-digit numbers can...Ch. 13.2 - Lining People Up In how many ways can 4 people be...Ch. 13.2 - Stacking Boxes In how many ways can 5 different...Ch. 13.2 - Forming Codes How many different three-letter...Ch. 13.2 - Forming Codes How many different four-letter codes...Ch. 13.2 - Stocks on the NYSE Companies whose stocks are...Ch. 13.2 - Stocks on the NASDAQ Companies whose stocks are...Ch. 13.2 - Establishing Committees In how many ways can a...Ch. 13.2 - Establishing Committees In how many ways can a...Ch. 13.2 - Possible Answers on a True/False Test How many...Ch. 13.2 - Possible Answers on a Multiple-choice Test How...Ch. 13.2 - Arranging Books Five different mathematics books...Ch. 13.2 - Forming License Plate Numbers How many different...Ch. 13.2 - Birthday Problem In how many ways can 2 people...Ch. 13.2 - Birthday Problem In how many ways can 5 people all...Ch. 13.2 - Forming a Committee A student dance committee is...Ch. 13.2 - Forming a Committee The student relations...Ch. 13.2 - Forming Words How many different 9-letter words...Ch. 13.2 - Forming Words How many different 11-letter words...Ch. 13.2 - Selecting Objects An urn contains 7 white balls...Ch. 13.2 - Selecting Objects An urn contains 15 red balls and...Ch. 13.2 - Senate Committees The U.S. Senate has 100 members....Ch. 13.2 - Football Teams A defensive football squad consists...Ch. 13.2 - Baseball In the American Baseball League, a...Ch. 13.2 - Baseball In the National Baseball League, the...Ch. 13.2 - Baseball Teams A baseball team has 15 members....Ch. 13.2 - World Series In the World Series the American...Ch. 13.2 - Basketball Teams A basketball team has 6 players...Ch. 13.2 - Basketball Teams On a basketball team of 12...Ch. 13.2 - Combination Locks A combination lock displays 50...Ch. 13.2 - Create a problem different from any found in the...Ch. 13.2 - Create a problem different from any found in the...Ch. 13.2 - Explain the difference between a permutation and a...Ch. 13.2 - Problems 67-70 are based on material learned...Ch. 13.2 - Problems 67-70 are based on material learned...Ch. 13.2 - Problems 67-70 are based on material learned...Ch. 13.2 - Problems 67-70 are based on material learned...Ch. 13.3 - When the same probability is assigned to each...Ch. 13.3 - The _____________of an event E is the set of all...Ch. 13.3 - True or False The probability of an event can...Ch. 13.3 - True or False In a probability model, the sum of...Ch. 13.3 - In a probability model, which of the following...Ch. 13.3 - In a probability model, which of the following...Ch. 13.3 - Determine whether the following is a probability...Ch. 13.3 - Determine whether the following is a probability...Ch. 13.3 - Determine whether the following is a probability...Ch. 13.3 - Determine whether the following is a probability...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 23-26, consider the experiment of...Ch. 13.3 - In Problems 23-26, consider the experiment of...Ch. 13.3 - Prob. 25SBCh. 13.3 - Prob. 26SBCh. 13.3 - Assigning Probabilities A coin is weighted so that...Ch. 13.3 - Assigning Probabilities A coin is weighted so that...Ch. 13.3 - Assigning Probabilities A die is weighted so that...Ch. 13.3 - Assigning Probabilities A die is weighted so that...Ch. 13.3 - For Problems 31-34, the sample space is S={...Ch. 13.3 - For Problems 31-34, the sample space is S={...Ch. 13.3 - For Problems 31-34, the sample space is S={...Ch. 13.3 - For Problems 31-34, the sample space is S={...Ch. 13.3 - For Problems 35 and 36, an urn contains 5 white...Ch. 13.3 - For Problems 35 and 36, an urn contains 5 white...Ch. 13.3 - In Problems 37-40, assume equally likely outcomes....Ch. 13.3 - In Problems 37-40, assume equally likely outcomes....Ch. 13.3 - In Problems 37-40, assume equally likely outcomes....Ch. 13.3 - In Problems 37-40, assume equally likely outcomes....Ch. 13.3 - For Problems 41-44, two fair dice are rolled....Ch. 13.3 - For Problems 41-44, two fair dice are rolled....Ch. 13.3 - For Problems 41-44, two fair dice are rolled....Ch. 13.3 - In Problems 45-48, find the probability of the...Ch. 13.3 - In Problems 45-48, find the probability of the...Ch. 13.3 - In Problems 45-48, find the probability of the...Ch. 13.3 - In Problems 45-48, find the probability of the...Ch. 13.3 - If P( A )=0.60 , P( AB )=0.85 , and P( AB )=0.05 ,...Ch. 13.3 - Prob. 50SBCh. 13.3 - Prob. 51SBCh. 13.3 - Prob. 52SBCh. 13.3 - Prob. 53SBCh. 13.3 - Doctorate Degrees According to the National...Ch. 13.3 - Prob. 55SBCh. 13.3 - For Problems 57-60, a golf ball is selected at...Ch. 13.3 - Prob. 57SBCh. 13.3 - Prob. 58SBCh. 13.3 - Prob. 59SBCh. 13.3 - Prob. 60SBCh. 13.3 - On The Price Is Right, there is a game in which a...Ch. 13.3 - Prob. 62SBCh. 13.3 - Prob. 63SBCh. 13.3 - Prob. 64SBCh. 13.3 - Prob. 65SBCh. 13.3 - Prob. 66SBCh. 13.3 - Prob. 67SBCh. 13.3 - Checkout Lines Through observation, it has been...Ch. 13.3 - Prob. 69SBCh. 13.3 - Prob. 70SBCh. 13.3 - Prob. 71SBCh. 13.3 - Birthday Problem What is the probability that at...Ch. 13.3 - Prob. 73SBCh. 13.3 - Prob. 74RYKCh. 13.3 - Prob. 75RYKCh. 13.3 - Prob. 76RYKCh. 13.3 - Solve the given system using matrices. { 3x+y+2z=1...Ch. 13.R - Prob. 1RECh. 13.R - If n( A )=8 , n( B )=12 , and n( AB )=3 , find n(...Ch. 13.R - Prob. 3RECh. 13.R - Prob. 4RECh. 13.R - Prob. 5RECh. 13.R - Prob. 6RECh. 13.R - Prob. 7RECh. 13.R - Prob. 8RECh. 13.R - Prob. 9RECh. 13.R - In Problems 10 and 11, compute the value of the...Ch. 13.R - In Problems 10 and 11, compute the value of the...Ch. 13.R - Stocking a Store A clothing store sells pure wool...Ch. 13.R - Baseball On a given day, the American Baseball...Ch. 13.R - Choosing Seats If 4 people enter a bus that has 9...Ch. 13.R - Choosing a Team In how many ways can a squad of 4...Ch. 13.R - Baseball In how many ways can 2 teams from 14...Ch. 13.R - Telephone Numbers Using the digits 0, 1, 2,...,9,...Ch. 13.R - Prob. 18RECh. 13.R - Binary Codes Using the digits 0 and 1, how many...Ch. 13.R - Arranging Flags How many different vertical...Ch. 13.R - Forming Committees A group of 9 people is going to...Ch. 13.R - Birthday Problem For this problem, assume that a...Ch. 13.R - Unemployment According to the U.S. Bureau of Labor...Ch. 13.R - Prob. 24RECh. 13.R - Each of the numbers 1, 2,..., 100 is written on an...Ch. 13.R - At the Milex tune-up and brake repair shop, the...
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