Measure the height of a stack of 50 pennies (in centimeters).

1. Measure the height of a stack of 50 pennies (in centimeters). 2.Convert the height of the stack of pennies into meters 3.Calculate how many pennies would be needed to make a tower 1 billion meters tall. Give answer in both standard calculation and in scientific notation.

Group Theory, Computing number of odd order subgroups

Question: Let G be a group of order 2k , that contains a cyclic subgroup of order k, where k is odd. Determine a formula to compute the number of subgroups of G that are of odd order.

Show that the center of GL(2,R) is the set of all scalar matrices aI with a different from zero.

Problem 1: Show that the center of GL(2,R) is the set of all scalar matrices aI with a different from zero. Problem 2: prove that no pair of the following groups of order 8, I8; I4 x I2; I2 x I2; D8; Q, are isomorphic.

Algebraic Structures

Problem #1 Prove that Aut(V)= (S3)and that Aut(S3)= S3. Problem #2 If H and K are normal subgroups of a group G with HK = G. Prove that G/(H n K) = (G/H) x (G/K).

Algebraic Structures

The problem I do need help in this attached sheet is problem # 264. Thanks in advance.

Algebraic Structure

I would love to have a usual word format answer with detailed proofs. The problems are 6 in total, the numbers are: from attached page #1: #2.82; 2.86; 2.87, from attached page #2: # 2.97; 2.98; 2.99. Thanks in advance. The student.

Tree diagram

The Knicks won the first game against the Lakers in a basketball playoff. If the first team to win four games is the winner, construct a tree diagram for this playoff. Hint: Some of the branches in the tree diagram will end sooner than the other , as one of the teams would have one four games.

Probability

Use a tree diagram. Use a diagram to list the sample space showing possible arrangements of heads and tails when four coins are tossed . Then use the sample space to find the probability that: 1. at most two coins come up heads 2. at least two coins come up heads 3. no more than three coins come up tails.