Game Theory Problem dealing with personal choices

Problem 1 1. Suppose you and one of your two roommates have just finished cleaning your dorm suite and found 13 quarters which you put on a table in the middle of the room. The third roommate who did none of the cleaning comes in from an afternoon of fun and relaxation and proposes that you divide the coins up the fol ...continues

Cutting a Cake-Game Theory Problem dealing with personal choices

Problem dealing with cutting a cake and personal choices Problem 2 There is a cake that is half lemon and half coffee. Steve values a whole lemon cake at $6, and a whole coffee cake at $10. Kevin values a whole lemon cake at $6 and a whole coffee cake at $4. Professor Raiffa suggests that they should divide the cake by ...continues

Allocation between two persons of a list of items and their preference

This is an allocation of ten estates between two individuals

Statistics: Percentages from Groups and Venn Diagrams

When the members of the Eye and I Photo Club discussed what type of film they had used during the past month, the following information was obtained; 77 used black and white film, 24 used only black and white, 65 used color, 18 used only color, 101 used black and white or color, 27 used infrared, 9 used all three types, and 8 di ...continues

Modern/Abstract Algebra Problem (Group Theory)

Show that the group generated by two elements where all the elements have order 3 is finite.

Modern/Abstract Algebra Problem (Group Theory)

What is the number of different conjugated classes of elements of order 2 in S_5.

Modern/Abstract Algebra Problem (Group Theory)

What are the normal subgroups in S_4?

Modern/Abstract Algebra Problem (Group Theory)

What are the normal subgroups in S_4? I would appreciate it if someone could also give a thourough explanation of how they came up with the answer.

Trigonometry: Addition Theorems

Please see the attached file for the fully formatted problems. Deduce the addition theorems for trigonometric functions: cos (x ± y) = cosx cosy sinx siny; sin (x ± y) = sinx cosy ± cosx siny as the simplest consequence of the representation of a complex plane’s rotational group.

Central Extension Problem

Describe all nonisomorphic central extensions of Z_n by Z_2 x Z_2 meaning central group extensions of the following form 1 --> Z_n --> G --> Z_2 x Z_2 --> 1 Meaning, determine those nonisomorphic groups G that can be described by such an extension. Please also explain how you came up with the answer.