For mutually exclusive events upper r 1? , upper r 2? , and upper r 3? , we have ? p(upper r 1? )=0. p(upper r 2? )=0.4? , and ? p(upper r 3? )=0.55. ? also, p(q? | upper r 1? )=0.4? , ? p(q | upper r 2? )=0.3? , and? p(q | upper r 3? )=0.4. find ? p(upper r 1 ? | q).

Ametalworker has a metal alloy that is 30? % copper and another alloy that is 55? % copper. how many kilograms of each alloy should the metalworker combine to create 90 kg of a 50? % copper? alloy?

How to choose the sign of the radical in the denominator of the formula for the distance from a point to a line.

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?