Describes how a matrix represents a finite graph. Be sure to explain what the zeros and ones represent and provide an example

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?

The center of the circumscribed circle lies on line segment and the longest side of the triangle is equal to the of the circle.

The pyramid shown has a square base that is 24 centimeters on each side. the slant height is 16 centimeters. what is the lateral surface area?