Math Answers

Find the centroid of the triangle whose vertices are (−1,0), (1,0), 𝑎𝑛𝑑 (0,3

Find the moment about the x-axis of a wire of constant density that lies along The curve

𝑦 = √𝑥 from 𝑥 = 0 𝑡𝑜 𝑥 = 2

Find the Center of mass of a thin plate of constant density 𝛿 covering the region bounded by the parabola 𝑦 = 𝑥² and the line 𝑦 = 4.

A sample of 25 women had a variance in IQ scores of 62. A sample of 18 men had a variance of 72. Do the women have a smaller variance in IQ scores at the 0.01 level of significance? Assume both populations are normally distributed

Two Children balance on the seesaw. The 40 lb child is 5 ft from the fulcrum. How far from the fulcrum is the 50 lb child ?

A storage tank is a right circular cylinder 20 ft long and 8 ft in diameter with

its axis horizontal. If the tank is half full of olive oil weighing 57 lb/ft3, find the

work done in emptying it through a pipe that runs from the bottom of the

tank to an outlet that is 6 ft above the top of the tank.

A spring, whose unstretched length is 2.0 m is compressed to a length of 1/2 m

when a force of 10 N is applied. Find the work required to compress the spring

to a length of 1.0 m.

A researcher claims that 10 year olds watch 6.6 hours of TV daily with SD = 2.5 hours. You try to verify this with the following sample data of 100 and a sample mean of 6.1 hours. Test the claim of the researcher. Test at α = .01

A Research Director of a certain university wants to replicate the result of the study 10 years ago with a standard deviation of 0.14. He wants to estimate the population mean to within an error of 0.04 of its true value. Using 95% confidence level, what is the sample size that he needs?

The joint probability density of X, Y is

f(x, y) = e ^{−(x + y)} xi > 0 i = 1, 2

0 otherwise

Using the change of variable technique, determine the joint distribution of Z = X and W = X + Y