Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
14th Edition
ISBN: 9780137400126
Author: Raymond Barnett, Michael Ziegler
Publisher: PEARSON+
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Chapter 11, Problem 12RE
To determine
To check: Whether
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1. The regular representation of a finite group G is a pair (Vreg, Dreg). Vreg is a vector space
and Dreg is a homomorphism.
(a) What is the dimension of Vreg?
(b) Describe a basis for Vreg and give a formula for Dreg. Hence explain why the homo-
morphism property is satisfied by Dreg.
(c) Prove that the character ✗reg (g) defined by tr Dreg (g) is zero if g is not the identity
element of the group.
(d) A finite group of order 60 has five irreducible representations R1, R2, R3, R4, R5. R₁
is the trivial representation. R2, R3, R4 have dimensions (3,3,4) respectively. What is the
dimension of R5? Explain how your solution is related to the decomposition of the regular
representation as a direct sum of irreducible representations (You can assume without proof
the properties of this decomposition which have been explained in class and in the lecture
notes).
(e) A
group element
has characters in the irreducible representations R2, R3, R4 given
as
R3
R2 (g)
= -1
X³ (g) = −1 ; XR4 (g) = 0…
it's not algebra 4th grade
Not use ai please
Chapter 11 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MPCh. 11.1 - Prob. 3MPCh. 11.1 - Prob. 4MPCh. 11.1 - Prob. 5MPCh. 11.1 - Prob. 6MPCh. 11.1 - Prob. 1EDCh. 11.1 - Prob. 2EDCh. 11.1 - Prob. 1ECh. 11.1 - Prob. 2E
Ch. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Prob. 8ECh. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - Prob. 13ECh. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - In Problems 2934, graph y = f(x) and find the...Ch. 11.1 - Prob. 31ECh. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - In Problems 3538, discuss the validity of each...Ch. 11.1 - Prob. 37ECh. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.1 - Prob. 44ECh. 11.1 - Prob. 45ECh. 11.1 - Prob. 46ECh. 11.1 - Prob. 47ECh. 11.1 - Prob. 48ECh. 11.1 - Prob. 49ECh. 11.1 - Prob. 50ECh. 11.1 - Prob. 51ECh. 11.1 - Prob. 52ECh. 11.1 - Prob. 53ECh. 11.1 - Prob. 54ECh. 11.1 - Prob. 55ECh. 11.1 - Prob. 56ECh. 11.1 - Prob. 57ECh. 11.1 - Prob. 58ECh. 11.1 - Prob. 59ECh. 11.1 - Prob. 60ECh. 11.1 - Prob. 61ECh. 11.1 - Prob. 62ECh. 11.1 - Prob. 63ECh. 11.1 - Prob. 64ECh. 11.1 - Prob. 65ECh. 11.1 - Prob. 66ECh. 11.1 - Prob. 67ECh. 11.1 - Prob. 68ECh. 11.1 - Prob. 69ECh. 11.1 - Prob. 70ECh. 11.1 - Prob. 71ECh. 11.1 - Prob. 72ECh. 11.2 - Let f(x)={6x6x2if0x10otherwise Graph f and verify...Ch. 11.2 - Prob. 2MPCh. 11.2 - Prob. 3MPCh. 11.2 - Prob. 4MPCh. 11.2 - Repeat Example 5 if the pharmacist wants the...Ch. 11.2 - For each of the following experiments, determine...Ch. 11.2 - Prob. 2EDCh. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - Prob. 3ECh. 11.2 - Prob. 4ECh. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Prob. 8ECh. 11.2 - Prob. 9ECh. 11.2 - In Problems 9 and 10, graph f, and show that f...Ch. 11.2 - Prob. 11ECh. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Prob. 14ECh. 11.2 - Use the function in Problem 9 to find the...Ch. 11.2 - Use the function in Problem 10 to find the...Ch. 11.2 - Use the function in Problem 9 to find the...Ch. 11.2 - Use the function in Problem 10 to find the...Ch. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Use the cumulative distribution function from...Ch. 11.2 - In Problems 25 and 26, graph f, and show that f...Ch. 11.2 - In Problems 25 and 26, graph f, and show that f...Ch. 11.2 - Prob. 27ECh. 11.2 - Use the function in Problem 26 to find the...Ch. 11.2 - Prob. 29ECh. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.2 - In Problems 3336, find the associated cumulative...Ch. 11.2 - Prob. 35ECh. 11.2 - Prob. 36ECh. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - Prob. 39ECh. 11.2 - Prob. 40ECh. 11.2 - Prob. 41ECh. 11.2 - Prob. 42ECh. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Prob. 45ECh. 11.2 - Prob. 46ECh. 11.2 - Prob. 47ECh. 11.2 - Prob. 48ECh. 11.2 - Prob. 49ECh. 11.2 - Prob. 50ECh. 11.2 - Prob. 51ECh. 11.2 - Prob. 52ECh. 11.2 - Prob. 53ECh. 11.2 - Prob. 54ECh. 11.2 - In Problems 53 and 58, find the associated...Ch. 11.2 - In Problems 53 and 58, find the associated...Ch. 11.2 - Prob. 57ECh. 11.2 - In Problems 53 and 58, find the associated...Ch. 11.2 - Demand. The weekly demand for hamburger (in...Ch. 11.2 - Prob. 60ECh. 11.2 - Prob. 61ECh. 11.2 - Prob. 62ECh. 11.2 - Prob. 63ECh. 11.2 - Shelf life. Repeat Problem 63 if...Ch. 11.2 - Prob. 65ECh. 11.2 - Prob. 66ECh. 11.3 - Find the expected value (mean), variance, and...Ch. 11.3 - Repeat Example 2 if the probability density...Ch. 11.3 - Prob. 3MPCh. 11.3 - Prob. 4MPCh. 11.3 - Prob. 5MPCh. 11.3 - Prob. 6MPCh. 11.3 - Prob. 1EDCh. 11.3 - Prob. 2EDCh. 11.3 - In Problems 16, find the mean, variance, and...Ch. 11.3 - In Problems 16, find the mean, variance, and...Ch. 11.3 - In Problems 16, find the mean, variance, and...Ch. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - In Problems 712, find the median....Ch. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - In Problems 712, find the median....Ch. 11.3 - In Problems 712, find the median....Ch. 11.3 - Prob. 12ECh. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - In Problems 1720, find the mean, variance, and...Ch. 11.3 - Prob. 18ECh. 11.3 - In Problems 1720, find the mean, variance, and...Ch. 11.3 - In Problems 1720, find the mean, variance, and...Ch. 11.3 - In Problems 21 and 22, use a graphing calculator...Ch. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Prob. 37ECh. 11.3 - Prob. 38ECh. 11.3 - Prob. 39ECh. 11.3 - Prob. 40ECh. 11.3 - Prob. 41ECh. 11.3 - Prob. 42ECh. 11.3 - Prob. 43ECh. 11.3 - Prob. 44ECh. 11.3 - Prob. 45ECh. 11.3 - Electricity consumption. The daily consumption of...Ch. 11.3 - Prob. 47ECh. 11.3 - Product life. The life expectancy (in years) of an...Ch. 11.3 - Prob. 49ECh. 11.3 - Prob. 50ECh. 11.3 - Prob. 51ECh. 11.3 - Prob. 52ECh. 11.3 - Prob. 53ECh. 11.3 - Prob. 54ECh. 11.3 - Learning. The number of hours it takes a...Ch. 11.3 - Prob. 56ECh. 11.4 - Use the probability density function given in...Ch. 11.4 - Prob. 2MPCh. 11.4 - Prob. 3MPCh. 11.4 - In Example 4, what percentage of the lightbulbs...Ch. 11.4 - Prob. 5MPCh. 11.4 - Prob. 2EDCh. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - In Problems 914, use Table 2 in Appendix C to find...Ch. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - In Problems 914, use Table 2 in Appendix C to find...Ch. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Prob. 27ECh. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - Prob. 31ECh. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.4 - Prob. 36ECh. 11.4 - Prob. 37ECh. 11.4 - Prob. 38ECh. 11.4 - Prob. 39ECh. 11.4 - Prob. 40ECh. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - Prob. 44ECh. 11.4 - Prob. 45ECh. 11.4 - Prob. 46ECh. 11.4 - Prob. 47ECh. 11.4 - Prob. 48ECh. 11.4 - Prob. 49ECh. 11.4 - Prob. 50ECh. 11.4 - Prob. 51ECh. 11.4 - Prob. 52ECh. 11.4 - Prob. 53ECh. 11.4 - Prob. 54ECh. 11.4 - Prob. 55ECh. 11.4 - Prob. 56ECh. 11.4 - Problems 5558 refer to the normal random variable...Ch. 11.4 - Prob. 58ECh. 11.4 - Prob. 59ECh. 11.4 - Prob. 60ECh. 11.4 - Prob. 61ECh. 11.4 - Prob. 62ECh. 11.4 - Prob. 63ECh. 11.4 - Prob. 64ECh. 11.4 - Prob. 65ECh. 11.4 - Prob. 66ECh. 11.4 - Prob. 67ECh. 11.4 - Prob. 68ECh. 11.4 - Waiting time. The time (in minutes) applicants...Ch. 11.4 - Prob. 70ECh. 11.4 - Communications. The length of time for telephone...Ch. 11.4 - Prob. 72ECh. 11.4 - Prob. 73ECh. 11.4 - Prob. 74ECh. 11.4 - Prob. 75ECh. 11.4 - Prob. 76ECh. 11.4 - Prob. 77ECh. 11.4 - Prob. 78ECh. 11.4 - Prob. 79ECh. 11.4 - Prob. 80ECh. 11.4 - Prob. 81ECh. 11.4 - Prob. 82ECh. 11.4 - Prob. 83ECh. 11.4 - Prob. 84ECh. 11.4 - Prob. 85ECh. 11.4 - Prob. 86ECh. 11 - Prob. 1RECh. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Prob. 15RECh. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - Prob. 21RECh. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Prob. 24RECh. 11 - Prob. 25RECh. 11 - Prob. 26RECh. 11 - Prob. 27RECh. 11 - Prob. 28RECh. 11 - Prob. 29RECh. 11 - Prob. 30RECh. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Prob. 33RECh. 11 - Prob. 34RECh. 11 - Prob. 35RECh. 11 - Prob. 36RECh. 11 - Prob. 37RECh. 11 - Prob. 38RECh. 11 - Prob. 39RECh. 11 - Credit applications. The percentage of...Ch. 11 - Prob. 41RECh. 11 - Prob. 42RECh. 11 - Prob. 43RECh. 11 - Medicine. The shelf life (in months) of a certain...Ch. 11 - Life expectancy. The life expectancy (in months)...Ch. 11 - Prob. 46RECh. 11 - Prob. 47RECh. 11 - Prob. 48RE
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