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Among 500 freshmen pursuing a business degree at a university, 338 are enrolled in an economics course, 238 are enrolled in a mathematics course, and 158 are enrolled in both an economics and a mathematics course. What is the probability that a freshman selected at random from this group is enrolled in each of the following? (Enter your answers to three decimal places.)(a) exactly one of these two courses(b) neither an economics course nor a mathematics course
We have defined space X to be contractible in two ways: Show that these two definitions are equivalent.
Water flows in a 400mm diameter drain to a depth of 150mm. Calculate the wetted perimeter of the drain and the cross sectional area of the water
If the sun is 55 above the horizon, find the length of the shadow cast by a building 86 ft tall. round your answer to the nearest tenth.
Find the solutions of the congruence 12x^2 + 25x = 10 (mod 11). [Hint: Show the congruence is equivalent to the congruence 12x^2 + 25x + 12 = 0 (mod 11).
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 were to graph these functions, what feature would appear in the graph at the limiting value? Why?
Let F(u,v) be a function of two variables. Find f '(x) for each of the following. Use F_u and F_v for F_u and F_v
Two boxes of brazils are mathematically similar, their lengths are 12cm and 24cm. The surface area and volume of the smaller box are 250cm2 and 240cm2 respectively.
Find the maximum margin separating hyperplane by solving the dual lagrangian constrained optimization problem. What is the value of the margin?
Objective questions on regression
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
Suppose that V is a complex (i.e. F = C) inner-product space. Prove that if N, an element of L(V), is normal and nilpotent, then N = 0.
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