An arts academy requires there to be 4 teachers for every 100 students and 3 tutors for every 30 students. How many students does the academy have per teacher? Per tutor? How many Tito’s does the academy need if it has 110 students?

What is the greatest common factor of 6a, 8a^{2}, and 14?

What are potential hypotheses (explanations) regarding why there are ecological equivalents between many metatherians and eutherians? discuss your hypothesis in terms of the processes that could lead to the current ecologies and distributions of metatherians and eutherians.

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?