An open-top box is to be made by cutting congruent squares from the corners of a 15cm x 15 cm sheet of metal by bending up the sides a) what equation relates the side length z of the removed squares and the volume v of the box?
b) determine the region of feasibility for x. show all algebra for the solution
c) compute a formula for dV/dx
d) find all critical points for the curve V. show all algebra for the solution
e) find the maximum volume a box constructed in this way can have, as well as the dimensions that achieve that volume. show all substitutions for the solution. do not approximate your value

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.