A square is cut from a rectangle. The side length of the square is half of the unknown width w . The area of the shaded region is 84 square inches. Write an equation you can use to find the width (in inches).

Passengers usually start to board their flights 1 hour before the scheduled take off time. the gate will be closed 15 minutes before the takeoff time. jack’s plane is scheduled to take off at 12: 05 a. m. if he arrives at the gate at 11: 45 p. m., can he board the flight?

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.

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.