Suppose that a large pack of haribo gummi bears can have anywhere between 30 and 50 gummi bears. there are 5 delicious flavors: pineapple (clear), raspberry (red), orange (orange), strawberry (green, mysteriously), and lemon (yellow). there are 0 non- delicious flavors. how many possibilities are there for the composition of such a pack of gummi bears?

The graph of y = ax^2 + bx + c is a parabola that opens up and has a vertex at (0, 5). what is the solution set of the related equation 0 = ax%2 + bx + c?

The trigonometric ratios sine and secant are reciprocals of each other

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?