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Suppose that f is continuous on [a,b]. Prove that f is integrable, i.e., ( the integral symbol with b at top and a at the bottom) f exists.
You are the process improvement manager and have developed a new machine to cut insoles for the company's top-of-the-line running shoes. You are excited because the company's goal is no more than 3.4 defects per million
A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 46.5ft^3. What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary.
Correctly match each of the following descriptions to a graph below by inserting the letter of the description that correctly describes the graph in the open box under the graph. The graph has both an Euler circuit and a Hamilton circuit.
The answer to finite abelian group, Suppose that G is a finite Abelian group and G has no element of order 2. Show that the mapping g-->g^2 is an automorphism of G.
Sketch both graphs. Find and label the intersection points. Find the area between the graphs using integration. Give the full integral, including limits, in proper notation.
Let A be a real n x n matrix. Show that a linear subspace E of R^n is A-invariant if and only if E is e^{tA} -invariant for all t in R, where e^{tA} is the exponential matrix associated to A.
Filling a tank. A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened.
What are some of the benefits of being able to find the expected value of a probability distribution? Give an example of how this could be used your advantage in a business setting
The exact value of the indicated trigonometric function.
Calculate the mean and standard deviation of the distribution for your example. Binomial and Poisson Distributions in Real Life
Write the fitted regression equation.
Solve The heat equation du/dt = d^2u / dx^2 (note: partial derivatives), u(x, 0) = sin^2(x), u(0, t) = 0, u(Pi, t) = 0, 0
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