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Find the area of the region bounded by the x-axis and the function f(x)=2x/(x^2+4) over the interval [-2,2].
Suppose G is an abelian group of order m. Let m, n be relatively prime. Show that for every element g in G, there exists an element x in G such that x^m=g. Abelian Groups and Relatively Prime Order
Prove that the set of all onto mapping from A to A is closed under composition of mappings. Prove that the set of all one-to-one mappings from A to A is closed under mapping composition.
A machine produces bolts with an average diameter of 0.30 inches and a standard deviation of 0.01 inches. What is the probability that a bolt will have a diameter greater than 0.32 inches? Assume the distribution is normal.
Write an equation to represent volume of an open box constructed by cutting congruent squares from the corners of a 24" by 14" piece of cardboard. What is the domain or this model?
The base of a solid is a circular disk with radius 7. Parallel cross sections perpendicular to the base are squares. Find the volume of the solid.
If you plan to drive the new car for 120,000 miles over the next 10 years, which car is the better buy? Use mathematical reasoning to justify your responses.
If 2 cards are drawn from a regular deck of 52 cards without replacement, what is the probability that the second card is a queen? (Note: your final answer must be a single probability)
A fireplace arch is to be constructed in the shape of a semi ellipse. The opening is to have a height of 40 inches at the center and a width of 82 inches along the base.
Determine if the given function can be extended to a continuous function at x=0. If so, approximate the extended function's value at x=0 (rounded to four decimal places if necessary).
What is the probability that the rat will turn left on the second trial?
There are 3 suspects, A, B, and C, for a robbery that presumably happened in a shop. We know that the following facts are true:
Use critical value z0 method from the normal distribution
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