Find the value of z that makes the equation true. 5 x z +3 = 23

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).

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?

Ametal rod is 2/5 meters long. it will be cut into pieces that are each 1/30 meters long. how many pieces will be made from the rod?