Ajar of marbles contains 5 blue 12 red, and 8 yellow marbles. what is is probability that you you select a blue marble, keep it, and then select a red marble?

Abby is preparing fruit punch for her party. she starts with a bowl filled with liquid that has 1/2 fruit juice and 1/2 sprite, but she decides it's too fruity. so she pours out 1/4 of the liquid, and then fills the bowl up again with sprite. what fraction of the punch is now sprite?

Prove that the value of the expression 7^8–7^7+7^6 is divisible by 43.

Segment an is an altitude of right δabc with a right angle at a. if ab = 2, squared 5 in and nc = 1 in, find bn, an, ac.