As a block of concrete is put under increasing pressure, engineers measure the pressure X at which the first fracture appears and the pressure Y at which the second fracture appears. X and Y are measured in tons per square inch and have joint density function fXY(x, y) = { 24x(1 - y) for 0 < x < y < 1
0 otherwise.
Calculate the average pressure (in tons per square inch) at which the second fracture appears, given that the first fracture appears at 1/3 ton per square inch.

Which statement accurately explains whether a reflection over the x-axis and a 180° rotation would map figure acb onto itself?

Ateacher noticed 5/8 of the students were wearing either blue shorts or white shorts. write two different ways this could be done.

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.