
Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 4, Problem 69E
To determine
To show:
More than
Expert Solution & Answer

Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
1.
2.
Define f: ZZ and 9: ZZ by f(x)=3x+1 and g(x) = x².
(a) Calculate (go f)(2).
(b) Find an explicit formula for the function gof.
Define f: R2 R2 by f(x, y) = (3x+y, 5x+2y). Give an explicit formula for f-1.
Verify that it is the inverse of f. Do not include a derivation for f¹ unless it is for the verification.
Suppose that two toothpaste companies compete for customers in a fixed market in which each
customer uses either Brand A or Brand B. Suppose also that a market analysis shows that the
buying habits of the customers fit the following pattern in the quarters that were analyzed:
each quarter (three-month period), 30% of A users will switch to B, while the rest stay with
A. Moreover, 40% of B users will switch to A in a given quarter, while the remaining B users
will stay with B. Finally assume that this pattern does not vary from quarter to quarter.
(a) If A initially has all of the customers, what are the market shares 2 quarters later?
(b) If A initially has all of the customers, what are the market shares 20 quarters later?
(c) If B initially has all of the customers, what are the market shares 2 quarters later?
(d) If B initially has all of the customers, what are the market shares 20 quarters later?
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…
Chapter 4 Solutions
Excursions in Modern Mathematics (9th Edition)
Ch. 4 - The Bandana Republic is a small country consisting...Ch. 4 - The Republic of Wadiya is a small country...Ch. 4 - The Scotia Metropolitan Area Rapid Transit Service...Ch. 4 - University Hospital has five major units:...Ch. 4 - The Republic of Tropicana is a small country...Ch. 4 - Tasmania State University is made up of five...Ch. 4 - There are 435 seats in the U.S. House of...Ch. 4 - There are 435 seats in the U.S. House of...Ch. 4 - The Interplanetary Federation of Fraternia...Ch. 4 - The small island nation of Margarita is made up of...
Ch. 4 - Find the apportionment under Hamiltons method of...Ch. 4 - Find the apportionment under Hamiltons method of...Ch. 4 - Find the apportionment under Hamiltons method of...Ch. 4 - Find the apportionment under Hamiltons method of...Ch. 4 - Find the apportionment under Hamiltons method of...Ch. 4 - Find the apportionment under Hamiltons method of...Ch. 4 - Find the apportionment under Hamiltons method of...Ch. 4 - Find the apportionment under Hamiltons method of...Ch. 4 - Happy Rivers County consists of three towns:...Ch. 4 - Plainville Hospital has three wings A, B, and C....Ch. 4 - The small nation of Fireland is divided into four...Ch. 4 - The Republic of Galatia is divided into four...Ch. 4 - Find the apportionment under Jeffersons method of...Ch. 4 - Find the apportionment under Jeffersons method of...Ch. 4 - Find the apportionment under Jeffersons method of...Ch. 4 - The small republic of Guayuru see Example 4.11...Ch. 4 - Find the apportionment under Jeffersons method of...Ch. 4 - Find the apportionment under Jeffersons method of...Ch. 4 - Find the apportionment under Jeffersons method of...Ch. 4 - Find the apportionment under Jeffersons method of...Ch. 4 - Find the apportionment under Adamss method of the...Ch. 4 - Find the apportionment under Adamss method of the...Ch. 4 - Find the apportionment under Adamss method of the...Ch. 4 - Find the apportionment under Adamss method of the...Ch. 4 - Find the apportionment under Websters method of...Ch. 4 - Find the apportionment under Websters method of...Ch. 4 - Find the apportionment under Websters method of...Ch. 4 - Find the apportionment under Websters method of...Ch. 4 - Find the apportionment under Websters method of...Ch. 4 - Find the apportionment under Websters method of...Ch. 4 - Round each number using the Huntington-Hill...Ch. 4 - Round each number using the Huntington-Hill...Ch. 4 - In the 2010 apportionment of the U.S. House of...Ch. 4 - In the 2010 apportionment of the U.S. House of...Ch. 4 - A small country consists of five states: A, B, C,...Ch. 4 - A small country consists of five states: A, B, C,...Ch. 4 - A small country consists of five states: A, B, C,...Ch. 4 - A small country consists of five states: A, B, C,...Ch. 4 - A country consists of six states, with the states...Ch. 4 - A country consists of six states, with the states...Ch. 4 - If the standard quota of state X is 35.41, then...Ch. 4 - If the standard quota of state Y is 78.24, then...Ch. 4 - If the standard quota of state X is 35.41, then...Ch. 4 - If the standard quota of state Y is 78.24, then...Ch. 4 - If the standard quota of state X is 35.41, then...Ch. 4 - If the standard quota of state Y is 78.24, then...Ch. 4 - At the time of the 2000 Census, Californias...Ch. 4 - At the time of the 2000 Census, Californias...Ch. 4 - This exercise refers to the apportionment of...Ch. 4 - This exercise refers to the apportionment of...Ch. 4 - Exercises 61 and 62 are based on the following...Ch. 4 - Exercises 61 and 62 are based on the following...Ch. 4 - This exercise comes in two parts. Read Part I and...Ch. 4 - This exercise comes in two parts. Read Part I and...Ch. 4 - The small island nation of Margarita consists of...Ch. 4 - Prob. 66ECh. 4 - Prob. 67ECh. 4 - Prob. 68ECh. 4 - Prob. 69ECh. 4 - Consider the problem of apportioning M seats...Ch. 4 - Prob. 71ECh. 4 - Prob. 72ECh. 4 - Lowndess Method. Exercises 73 and 74 refer to a...Ch. 4 - Prob. 74ECh. 4 - Prob. 75ECh. 4 - Explain why the Jeffersons method cannot produce...Ch. 4 - Explain why the Adamss method cannot produce a.the...Ch. 4 - Explain why the Websters method cannot produce...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- 3.12 (B). A horizontal beam AB is 4 m long and of constant flexural rigidity. It is rigidly built-in at the left-hand end A and simply supported on a non-yielding support at the right-hand end B. The beam carries Uniformly distributed vertical loading of 18 kN/m over its whole length, together with a vertical downward load of 10KN at 2.5 m from the end A. Sketch the S.F. and B.M. diagrams for the beam, indicating all main values. Cl. Struct. E.] CS.F. 45,10,376 KN, B.M. 186, +36.15 kNm.7arrow_forwardDraw the isoclines with their direction markers and sketch several solution curves, including the curve satisfying the given initial conditions. 1) y'=x + 2y ; y(0) = 1 and 2) y' = x², y(0)=1arrow_forwardQize f(x) = x + 2x2 - 2 x² + 4x²² - Solve the equation using Newton Raphsonarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education

Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education

Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON


Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON

Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,

Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
Propositional Logic, Propositional Variables & Compound Propositions; Author: Neso Academy;https://www.youtube.com/watch?v=Ib5njCwNMdk;License: Standard YouTube License, CC-BY
Propositional Logic - Discrete math; Author: Charles Edeki - Math Computer Science Programming;https://www.youtube.com/watch?v=rL_8y2v1Guw;License: Standard YouTube License, CC-BY
DM-12-Propositional Logic-Basics; Author: GATEBOOK VIDEO LECTURES;https://www.youtube.com/watch?v=pzUBrJLIESU;License: Standard Youtube License
Lecture 1 - Propositional Logic; Author: nptelhrd;https://www.youtube.com/watch?v=xlUFkMKSB3Y;License: Standard YouTube License, CC-BY
MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY