Five hundred chances are sold at $7 apiece for a raffle. there is a grand prize of $400, two second prizes of $275, and five third prizes of $50. first calculate the expected value of the lottery. determine whether the lottery is a fair game.

The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 12611261 chips and a standard deviation of 118118 chips. (a) determine the 2626th percentile for the number of chocolate chips in a bag. (b) determine the number of chocolate chips in a bag that make up the middle 9696% of bags. (c) what is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?

1) prove that 731^3−631^3 is divisible by 100 2) prove that 99^3−74^3 is divisible by 25

Can someone plz me understand how to do these. plz, show work. in exercises 1-4, rewrite the expression in rational exponent form.[tex]\sqrt[4]{625} \sqrt[3]{512} (\sqrt[5]{4} )³ (\sqrt[4]{15} )^{7}\\ (\sqrt[3]{27} )^{2}[/tex]