Tasty bakery sells three kinds of muffins chocolate chip $0.75 each oratmeal$0.80 each and cranberry $0.85 each charles buys some of each kind and chooses three times as many cranberry muffins as choclacte chip muffin's. if he spends $12.20 on 15 muffins how many chocolate chip muffins did he buy?

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?

The? half-life of a radioactive substance is 20 years. if you start with some amount of this? substance, what fraction will remain in 120 ? years

What is the length of the segment, endpoints of which are intersections of parabolas y=x^2− 11/4 x− 7/4 and y=− 7 /8 x^2+x+ 31/8 ?