Josh leans the ladder against a side of her house which is 10 feet. if the base of the latter is 3 feet away from the house, how tall is the ladder? ( use pythagorean theorem )

Anumber cube is rolled and a coin is tossed. the number cube and the coin are fair. what is the probability that the number rolled is less than 4 and the coin toss is tails?

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?

Find the volume of the solid whose base is the region bounded by f(x), g(x) and the x-axis on the interval [0, 1], and whose cross-sections perpendicular to the y-axis are squares. your work must show the integral, but you may use your calculator to evaluate it. give 3 decimal places for your answe