Every integer is a divisor of itself. a proper divisor of an integer means a positive divisor other than the integer itself. for example, the divisors of 8 are 1, 2,4, and 8, but the proper divisors of 8 are just 1,2, and 4.

what is the smallest positive integer whose proper divisors add up to more than the integer itself?

Both the red and blue line segments stretch from the center of the circle to a point on the circle. the length of the blue segment is 5. how long is the red line segment?

Can you me find the missing length. i attached an image.

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?