Brock is training for a crossfit competition. he began the training by completing pull-ups and box jumps. originally, his training plan had him completing pull-ups and box jumps at a ratio of 5: 4. after two months of training, he decided to focus on his leg strength and adjusted his ratio to 2: 7. if he completed 53 box jumps at the end of his training, how many pull-ups did he complete in the initial stage of training?

If a(0,0,0) and b(2,2,2) are points in coordinate space, how many paths are there from a to b that move from one lattice point to another in the positive x-,y- or z- direction?

Tanya has $42 to spend at the dolphin island store. tshirts sell for $7 each and a pair of sunglases sells for $6.tanya buys 3 tshirts. how many pairs of sunglases can she buys with the amount of money she has left

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?