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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.

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.

Rewrite the following quadratic functions in intercept or factored form. show your work. f(x) = 3x^2 - 12