The ten sides of a regular decagon are colored with five different colors, so that all five colors are used, and sides that are diametrically opposite have the same color. One possible coloring is shown below.
How many different ways are there to color the sides of the decagon? (Two colorings are considered identical if one can be rotated to form the other.)

F(x)=x/2-2 and g(x)=2x^2+x-3 find (f+g)(x)

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.

What is 0.368,0.380,0.365,and 0.383 in order from least to greatest