1. A cube 4 units on each side is composed of 64 unit cubes. Two faces of the larger cube that share an edge are painted blue, and the cube is disassembled into 64 unit cubes. Two of the unit cubes are selected uniformly at random. What is the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces?

2. Below is a portion of the graph of a function, $y = h(x):$

https://latex.artofproblemsolving.com/a/7/c/a7c10a072bf15de60a6052b7012b53a8640afc26.png

If the graph of $y=h(x-3)$ is drawn on the same set of axes as the graph above, then the two graphs intersect at one point. What is the sum of the coordinates of that point?

TYSM!!!

Guest Feb 10, 2021