In part a, you determined that you can make 40 servings from five packages of buns and four packages of hot dogs without anything left over. this means that you can also make 80, 120, 160, and so forth, servings without anything left over. these numbers are called multiples of 40.you need to find the smallest integer multiple of 40 that is greater than or equal to 700. then, use this to determine the number of packages of buns and hot dogs.

ceiling(700/40) = ceiling(17.5) = 18 . . . . ceiling(x) is the smallest integer ≥ x.

The smallest integer multiple of 40 that is larger than 700 is 18.

The number of packages of buns will be 18*5 = 90.

The number of packages of hotdogs will be 18*4 = 72.

These numbers will ensure that you have 20 bun/hotdog combinations left over. If you want to minimize leftovers, you would use 88 packages of buns and 70 packages of hotdogs. That would give you 4 buns and no hotdogs left over.

hello!

to begin with, we're given that on earth, a rock weighs 20 pounds, and while on jupiter, that same rock weighs 42 pounds. now, we're trying to find the weight of a rock that weighs 10.5 pounds on earth, on jupiter.

to solve this, first, set up a proportion, cross-multiply, and solve it algebraically.

setting up the proportion is the hardest and the most confusing part of the problem, but it's simple.

if on earth, the rock weighs 20 lbs, and on jupiter it weighs 42 lbs, our first part of our proportion is 20/42 lbs. the second part has to be equal to each other. this means that 10.5 has to be on the numerator of the fraction, and x, the value we're trying to find, has to be on the denominator. remember that the rock weighs 10.5 lbs on earth, and we're trying to find the weight of it on jupiter (which is x).

20/42 = 10.5/x

next, you would cross-multiply.

20x = 42(10.5)

20x = 441

now, solve it algebraically by using division.

x = 22.05 lbs

this can be rounded to 22.1 lbs.

therefore, the weight of the rock on jupiter is 22.1 lbs, the fourth choice.

the answer on ed. is:

c. "the graph of f(x) has exactly two x-intercepts."

hope i could someone! : )