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A building casts a shadow 345 ft long when the angle of elevation of the sun is 48°. Find the height of the building.
A box with a square base of side x is three times higher than it is wide. Express the volume V of the box as a function of x.
The stopping distance of a car after the brakes have been applied varies directly as the square of the speed. If a car traveling at 60 mph can stop in 180 ft., what is the distance needed to stop the same car traveling at 70 mph?
A club consists of 16 men and 19 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people?
Let f be Lebesgue integrable on [0,1]. Prove that the limit, as k goes to infinity, of the integral from 0 to 1 of (x^k)f(x)dx is equal to 0.
Two-thirds of the people in a room are seated in three-fourths of the chairs. The rest of the people are standing. If there are 6 empty chairs, how many people are in the room?
Show the solution sets written algebraically and as a union or intersection of intervals. Describe in words what the solution sets mean, and then display a simple line graph for each solution set as demonstrated
Probability : Selection Without Replacement and Stirling's Formula, A box contains 3n red balls and 3n white balls. 2n balls are selected at random without replacement, express the probability p
Evaluate critical points, end points, local extrema and global extrema - Evaluate f at its critical points and at the endpoints of the given interval. Identify local and global maxima and minima of f in the interval.
A 8788 ft3 tank with a square base and open top is to be constructed of sheet steel of a given thickness. Find the dimensions of the tank with minimum weight.
A boat's crew rowed 9 miles downstream, with the current, in 1.5 hours. The return trip upstream, against the current, covered the same distance, but took 3 hours. Find the crew's rowing rate in still water and the rate of the current.
I was one-tenth of a mile from the intersection, while she was three-twentieths of a mile from it. How fast were we approaching each other at that instant?
find 95% of confidence interval for variance of the heights of maple tree same of 11 trees has standard dev of 14.
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