A three-dimensional tolerance that independently controls how much a surface can deviate within a tolerance zone formed by two parallel planes is:

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?

Simplify the expression 10/11(22z) + (a+5) -1

Evaluate cos2θ for cosθ = square root of 3/2