Medical researchers have determined that for exercise to be beneficial, a person’s desirable heart rate, r, in beats per minute, can be approximated by the formulas

for women
for men,

where a represents the person’s age. if the desirable heart rate for a man is 135 beats per minute, how old is he?

a.
22.5 years old
b.
40 years old
c.
45 years old
d.
42.5 years old

select the best answer from the choices provided

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?