A 12-sided solid has equal-sized faces numbered 1 to 12. If the 12-sided solid is rolled 200 times, how many times would you expect either a 4, 6 or 9 to be rolled?

The line y = x + passes through (−3, 7) and is parallel to y = 4x − 1.

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?

Given: hf || jk; hg ? jg prove: fhg ? kjg to prove that the triangles are congruent by asa, which statement and reason could be used as part of the proof? fgh ? kgj because vertical angles are congruent. jkg ? hfg because vertical angles are congruent. fhg ? jkg because right angles are congruent. hfg ? kjg because alternate interior angles are congruent.