Introductory Combinatorics
5th Edition
ISBN: 9780134689616
Author: Brualdi, Richard A.
Publisher: Pearson,
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Chapter 4, Problem 44E
To determine
To prove: That R is an equivalence relation.
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What percentage of the general U.S. population have bachelor's degrees? Suppose that the Statistical Abstract of the United States, 120th Edition, gives the following percentage of bachelor’s degrees by state. For convenience, the data are sorted in increasing order.
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Illinois has a bachelor's degree percentage rate of about 18%. Into what quartile does this rate fall?
What percentage of the general U.S. population have bachelor's degrees? Suppose that the Statistical Abstract of the United States, 120th Edition, gives the following percentage of bachelor’s degrees by state. For convenience, the data are sorted in increasing order.
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Illinois has a bachelor's degree percentage rate of about 18%. Into what quartile does this rate fall?
Find the range for the following sample data.
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Chapter 4 Solutions
Introductory Combinatorics
Ch. 4 - Prob. 1ECh. 4 - Determine the mobile integers in
.
Ch. 4 - Use the algorithm of Section 4.1 to generate the...Ch. 4 - Prove that in the algorithm of Section 4.1, which...Ch. 4 - Let i1i2 … in be a permutation of {1, 2, …, n}...Ch. 4 - Determine the inversion sequences of the following...Ch. 4 - Construct the permutations of {1, 2, …,8} whose...Ch. 4 - How many permutations of {1, 2, 3, 4, 5, 6}...Ch. 4 - Show that the largest number of inversions of a...Ch. 4 - Bring the permutations 256143 and 436251 to 123456...
Ch. 4 - Let S = {x7, x6,…, x1, x0}. Determine the 8-tuples...Ch. 4 - Let S = {x7, x6,…, x1, x0}. Determine the subsets...Ch. 4 - Generate the 5-tuples of 0s and 1s by using the...Ch. 4 - Prob. 14ECh. 4 - For each of the following subsets of {x7, x6, …,...Ch. 4 - For each of the subsets (a), (b), (c), and (d) in...Ch. 4 - Which subset of {x7, x6, … , x1, x0} is 150th on...Ch. 4 - Build (the corners and edges of) the 4-cube, and...Ch. 4 - Give an example of a noncyclic Gray code of order...Ch. 4 - Prob. 20ECh. 4 - Construct the reflected Gray code of order 5...Ch. 4 - Prob. 22ECh. 4 - Determine the immediate successors of the...Ch. 4 - Prob. 24ECh. 4 - Prob. 26ECh. 4 - Prob. 27ECh. 4 - Prob. 28ECh. 4 - Determine the 7-subset of {1, 2, … , 15} that...Ch. 4 - Generate the inversion sequences of the...Ch. 4 - Prob. 31ECh. 4 - Generate the 4-permutations of {1, 2, 3, 4, 5,...Ch. 4 - In which position does the subset 2489 occur in...Ch. 4 - Consider the r-subsets of {1, 2, …, n} in...Ch. 4 - The complement of an r-subset A of {1, 2, … , n}...Ch. 4 - Prob. 36ECh. 4 - Let R′ and R″ be two partial orders on a set X....Ch. 4 - Let (X1, ≤1) and (X2, ≤2) be partially ordered...Ch. 4 - Let (J, ≤) be the partially ordered set with J =...Ch. 4 - Prob. 40ECh. 4 - Show that a partial order on a finite set is...Ch. 4 - Describe the cover relation for the partial order...Ch. 4 - Prob. 43ECh. 4 - Prob. 44ECh. 4 - Prob. 45ECh. 4 - Let m be a positive integer and define a relation...Ch. 4 - Consider the partial order ≤ on the set X of...Ch. 4 - Prob. 50ECh. 4 - Let n be a positive integer, and let Xn be the set...Ch. 4 - Verify that a binary n-tuple an − 1, ⋯ ,a1a0 is in...Ch. 4 - Continuing with Exercise 52, show that can be...Ch. 4 - Let (X, ≤) be a finite partially ordered set. By...Ch. 4 - Prob. 56ECh. 4 - Prob. 57ECh. 4 - Prob. 58ECh. 4 - Prob. 59E
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- Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the sample mean for x and for y. Round your answer to the nearest tenth. x: 11 0 36 22 34 24 25 -11 -11 -22 y: 9 -3 28 14 23 16 14 -3 -4 -9arrow_forwardDo bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the range for variable y. X 12 0 36 21 35 23 24 -12 -12 -21 Y 10 -2 26 15 22 18 15 -2 -3 -10arrow_forwardDo bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the range for variable y. X 12 0 36 21 35 23 24 -12 -12 -21 Y 10 -2 26 15 22 18 15 -2 -3 -10arrow_forward
- Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the range for variable x. X 15 0 37 23 33 25 26 -15 -15 -23 Y 6 -1 28 18 24 17 18 -1 -2 -6arrow_forward7.16. If the probability density of X is given by g kx³ for x>0 f(x) = (1+2x)6 0 10-01, elsewhere trolls inf ( 2X density of the random variable Y = where k is an appropriate constant, find the probability 1+2X distribution of Y, and thus determine the value of k. 7 Identify thearrow_forward#2arrow_forward
- 2. We want to find the inverse of f(x) = (x+3)² a. On the graph at right, sketch f(x). (Hint: use what you know about transformations!) (2 points) b. What domain should we choose to get only the part of f (x) that is one- to-one and non-decreasing? Give your answer in inequality notation. (2 points) - c. Now use algebra to find f¯¹ (x). (2 points) -4- 3- 2 1 -4 -3 -2 -1 0 1 -1- -2- --3- -4 -N- 2 3 4arrow_forward1. Suppose f(x) = 2 4 == x+3 and g(x) = ½-½. Find and fully simplify ƒ(g(x)). Be sure to show all x your work, write neatly so your work is easy to follow, and connect your expressions with equals signs. (4 points)arrow_forwardFind the ane sided limit lim 2 x+1-3x-3arrow_forward
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What is a Relation? | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=hV1_wvsdJCE;License: Standard YouTube License, CC-BY
RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY