A gambler has 4 packs of cards, each of which is well shuffled and has equal numbers of red, green and blue cards. For each turn he pays 2$ and draws a card from each pack. He wins 3$ if he gets 2 red cards, 5$ if he gets 3 red cards and 10$ if he gets 4 red cards. Let the random variable X represent how much the gambler earned and Y represent the number of blue cards chosen. Find the joint distribution of X and Y.

Estimate the area under the curve f(x) = 16 - x^2 from x = 0 to x = 3 by using three inscribed (under the curve) rectangles. answer to the nearest integer.

Ascientist places 24 cells in a petri dish. she knows the cells grow at an exponential rate, doubling in number every hour. how long will it take (in hours) for there to be 1100 cells in the dish? time to 1100 cells: 5.51832530 hours how long will it take to reach 110 cells? time to 110 cells : 2.1963972 hours what is the average rate of change in the number of cells between 9 hours and 11 hours? average rate of change: cells per hour what is the instantaneous rate of change after 7 hours? instantaneous rate of change: cells per hour note: you can earn partial credit on this problem.

What is the value of the discrimination for the quadratic equation 0=×2+2+×2