Recall that the center of a group G is the set Z(G)={x∈G:xg=gx for all g∈G}.

a. Calculate the center of S3.
b. Calculate the center of GL2(R).
c. Show that the center of any group G is a normal subgroup of G .
d. If G/Z(G) is cyclic, show that G is abelian.

Given the box plot, will the mean or the median provide a better description of the center? box plot with min at 10.5, q1 at 11.5, median at 12.5, q3 at 13.5, max at 15

Joel wants to buy a new tablet computer fram a store having a 20% off sale on all tablets. the tablet he wants has an original cost of $190. he also wants to make sure he has enough money to pay the 5% sales tax. part one joel uses the incorect expression 0.95(190)(0.8) to calculate that the tablet will cost him a total of $144.40. describe his error and write the correct expression part two how much will joel pay for the tablet show your work if you answer this question correctly you will receive a prize of 99 points good luck

The amount spent on food and drink by 20 customers is shown below what is the modal amount spent and the median amount spent? 40 25 8 36 18 15 24 27 43 9 12 19 22 34 31 20 26 19 17 28