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a uniform solid consists of a hemisphere of radius r and a right circular cone of base radius r fixed together so that their plane faces coincide. If the solid can rest in equilibrium with any point of the curved surface of a hemisphere in contact with the horizontal plane, find the height of the cone in terms of r.
Find the equation of a sphere of radius 3 which is tangent to both the planes x-2y+2z=3 and 3x+4z=8
Radium-221 has a half-life of 30 sec. How long will it take for 79% of a sample to decay?
Suppose that X1 and X2 are Gaussian random variables with means µ1 and µ2 respectively. Assume that µ1 ≠ µ2. The variance for each of the two random variables is σ2. Find the value of x for which fx1(x) = fx2(x).
Find an equation in the form y=ms +b (where possible) for each line. Solve each system of equation. Let z be the parameter.
List the factors which would tend to reduce the variation of a prediction from a simple linear regression.
Find the point on the graph of the given function at which the slope of the tangent line is the given slope.
A chef wants to make 1 gallon (128 ounces) of a 35% vinegar-to-oil salad dressing. He only has pure vinegar and a mild 4% vinegar-to-oil salad dressing on hand. How many ounces of each should he mix to make the desired dressing?
The mean batting average in a certain baseball league is about 0.210. Supposing that batting averages are normally distributed, that the standard deviation in the averages is 0.08, and that there are 210 batters, what is the expected number of bat..
Determine the type I and type II error
Probability problems based on normal distribution
Draw a rectangular box that has P and Q as opposite vertices and has its faces parallel to the coordinate planes. Then find the coordinates of the other six vertices of the box and the length of the diagonal of the box
Write a linear equation to estimate the weight of a person of any height. Estimate the weight of a person that is 72 inches tall
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