You go to the doctor and he gives you 13 milligrams of radioactive dye which decays exponentially. after 24 minutes, 5 milligrams of dye remain in your system. to leave the doctor's office, you must pass through a radiation detector without sounding the alarm. if the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will you have to remain at the doctor's office, assuming you were given the dye as soon as you arrived? give your answer to the nearest minute.
you will spend?

What is the simplified expression for 6(2(y+x))

Which expression will have the same sum as 3_8 + 1/4?

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?