Verify that the functions below are inverses by showing that (fog)(x)=x and (g o f)(x) = x f(x) = X + 4 and g(x) = 3x - 4

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Apinhole camera is made out of a light-tight box with a piece of film attached to one side and pinhole on the opposite side. the optimum diameter d(in millimeters) of the pinhole can be modeled by d=1.9[ (5.5 x 10^-4) l) ] ^1/2, where l is the length of the camera box (in millimeters). what is the optimum diameter for a pinhole camera if the camera box has a length of 10 centimeters

Awoman has 14 different shirts: 10 white shirts and 4 red shirts. if she randomly chooses 2 shirts to take with her on vacation, then what is the probability that she will choose two white shirts? show your answer in fraction and percent, round to the nearest whole percent.

The base of a rectangular pyramid is 13 inches long and 12 inches wide. the height of the pyramid is 8 inches. what is the volume of the pyramid