A chemical company makes two brands of antifreeze. The first brand is 60% pure antifreeze, and the second brand is 85% pure antifreeze. In order to obtain 170 gallons of a mixture that contains 65% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Acompany produces packets of soap powder labeled “giant size 32 ounces.” the actual weight of soap powder in such a box has a normal distribution with a mean of 33 oz and a standard deviation of 0.7 oz. to avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. to avoid losing money, it labels the top 5% (the heaviest 5%) overweight. how heavy does a box have to be for it to be labeled overweight?

Solve the system of equations using the substitution method. {y=−3x+7x=−2y−16 enter your answers in the boxes.

Parabolas y=−2x^2 and y=2x^2+k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.