Sophia is making brownies. her recipe uses a ratio of 3 cups of sugar to 2 cups of cocoa powder.

which sentence best describes this situation?



a.

sophia needs 23
23
cup of cocoa powder for 2 cups of sugar.



b.

sophia needs 23
23
cup of sugar for 3 cups of cocoa powder.



c.

sophia needs 32
32
cups of cocoa powder for each cup of sugar.



d.

sophia needs 32
32
cups of sugar for each cup of cocoa powder.









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?

Factor the polynomial, if possible. if the polynomial cannot be factored, write prime. 9n^3 + 27n^2 – 25n – 75

The volume of the a sphere whoes diameter is 18 cm is cubic cm . if it's diameter were reduced by half, it's volume would be of its original volume