If g is a group, then a subgroup h is called characteristic if whenever ø : g -> g is an automorphism, ø(h) = h. prove that a characteristic subgroup is a normal subgroup. the opposite is not true in general. give an example of a group and a proper characteristic subgroup (hint: think about cyclic groups, or the center of a group)

Suppose a ball is dropped fromca height of 6ft. it bounces back up but time it bounces, it reaches only 7/10 of its pervious height. what is the total of each height that the ball reaches after 5 bounces

What is the length of the unknown leg in the right triangle ?

33% of college students say they use credit cards because of the rewards program. you randomly select 10 college students and ask each to name the reason he or she uses credit cards. find the probability that the number of college students who say they use credit cards because of the rewards program is (a) exactly two, (b) more than two, and (c) between two and five inclusive. if convenient, use technology to find the probabilities.