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Let A_0 be contained in A_1 contained in A_2 and so on be a nested sequence of subspaces of X such that the union of all A_n is X and such that An contained in the interior of A_(n+1). Suppose for each n, there is a retraction r_n:A_(n+1) to An. Prove there is a retraction r: X to A_0.
Please sketch a graph of a function f have the indicated characteristics. Please explain.
What similarities and differences do you see between functions and linear equations? Are all linear equations functions? Is there an instance when a linear equation is not a function?
The sum of three numbers is 98. The ratio of the first to the second is 2:3, and the ratio of the second to the third is 5:8. Find the value of the second number?
Identify the definite integral that represents the volume of the solid formed by revolving the region bounded by y=x^3, y=1, and x=2 about the line y=10.
The mean tuition cost at university though the United State is 4260 per year. Use this value as the population mean and assume that population standard deviation is USD 900. Assume that random sample of so university will be selected. What is the pro..
Based on exponential growth function how long will it take the world population to reach exactly 7 billion? How about 10 billion? Based on the population how long before it will reach 400 million? and 500 million?
Develop a joint probability table and show the marginal probabilities. What is the probability of a household whose income exceeds $40,000 and who rejects the offer?
Description of Joint probability, However in this problem what do I do with 2X in my upper y limit, can I plug in the max x value and just make it 0
Suppose that in a company with 775 employees, the monthly salaries are normally distributed. The mean salary is $6400 and the standard deviation is $800. About how many employees earn more than $4200 per month?
Suppose that g: Y-->R is a function which is differentiable at y_0. Then the function g o f: X-->R is differentiable at x_0, and (g o f)' (x_0) = g'(y_0)f '(x_0)
Evaluate the nearest distance between two tunnels using cosine rule. In a mine, two tunnels are dug starting at the same point.
Given the following matrices/vectors:linear systems: find x,y such that Ax=b and Ay=a (note x, y with vector character over each)
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