Derek is deciding what to wear to school. he has a green shirt, a purple shirt, and a red shirt, and he has beige, gray, and blue pants. he also has sandals, running shoes, and boots, and yellow and gray socks. if he can wear any color shirt, any pair of pants, any pair of shoes, and any color socks, how many different combinations can derek pick?

The average number of vehicles waiting in line to enter a parking lot can be modeled by the function f left parenthesis x right x squared over 2 left parenthesis 1 minus x right parenthesis endfraction , where x is a number between 0 and 1 known as the traffic intensity. find the rate of change of the number of vehicles waiting with respect to the traffic intensity for the intensities (a) xequals0.3 and (b) xequals0.6.