Acompany found that new employees prefer training sessions of moderate length; shorter training sessions provided too little instruction to complete a task, while longer training sessions contain too much instruction to remember. for a training session on a particular task, the company determined that the ratings new employees gave for the training session could be approximated by upper r (t )equals startfraction 30 t over t squared plus 225 endfraction comma where t is the length of the training session in minutes. find the training session length that received the highest rating.

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- 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. 3- 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 part b?

Elizabeth claims that the fourth root of 2 can be expressed as 2^m since (2^m)^n = 2. find the values of m and n for the case where elizabeth's claim is true.

Use complete sentences to differentiate between a regular tessellation, and a pure tessellation. be sure to include specific types of polygons in your explanation.