Points X and Z are on a number line, and point Y partitions line XZ into two parts so that the ratio of the length of line

segment XY to the length of line segment YZ is 5:7. The

coordinate of X is 0.4, and the coordinate of Y is 5.8. What

is the coordinate of Z?

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?