Let x be a real number such that x + (1/x) is an integer. Prove that (x^n) + 1/(x^n) is an integer for every positive integer n.

Even if a person is in very good shape, applying to be a police officer requires commitment to fitness. applicants must pass a physical fitness test. in order to prepare for the test, janet purchases an activity tracker to court her steps. her goal is to walk 10,000 steps each day. she measures heard average step length to be 30 inches. play janet runs, her average steps length increases to 36 in. how many steps would she have to take to run 1 mile 50280 round to the nearest step

The letters g e o r g i a are placed in a bag . if you picked a card and knew it was a vowel , what is the probability that it is an a ?

Arace is 10 kilometers long.markers will be placed at the beginning and end of the race course and at each 500 meter mark.how many markers are needed to mark the course for the race?