Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 4\le x \le 74≤x≤7. xxf(x)f(x)
4422
5544
6688
771616
883232
996464

An automated water dispenser fills packets with one liter of water on average, with a standard deviation of 5 milliliter. the manual says that after a year of operation the dispenser should be tested to see if it needs recalibration. a year later a number of filled packets are set aside and measured separately. it is found that the average packet now contains about 0.995 liters. does the dispenser need calibration? explain your answer.

Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 4p cubedplusx squaredequals38 comma 400. determine the rate at which sales are changing at a time when xequals80, pequals20, and the price is falling at the rate of $.20 per week.

Solve x+3y=6 and 4x-6y=6 by elimination . show work !