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Why do we measure perimeter in ft, area in ft^2 (or feet squared), and volume in ft^3 (or feet cubed)? What does each mean within the strand of measurement? Why do you think so many students label their measurements with the incorrect exponent?
Suppose that E is a normed linear space, and C is a subset. Prove that C is weakly bounded if and only if C is norm bounded. Conclude that weakly convergent sequences in E are bounded.
Set up different integrals to find the mass of the solid bounded by the equations z=8-2x, z=0, y=0, y=3 and x=0. the density of the solid at (x,y,z) is d(x,y,z)=kx, k>0. evaluate ONE of the integrals.
Probability: Problems and Solutions, How many ways are there of drawing a red, a black, and a green ball from a bucket with 2-Red, 2-Black, and 5-Green balls?
Let alpha = {x_1, x_2, ..., x_n} be an arbitrary orthonormal basis for V. Prove that T is orthogonal iff [T]_alphaalpha is an orthogonal matrix.
Let ubar and vbar be nonzero vectors in 2 or 3 space and let k=||u|| and m=||v||. Show that the vector Wbar=mubar +kvbar bisects the angle between ubar and vbar.
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)
Write the statement in symbolic form (Let p: The tent is pitched. q: The bonfire is burning. #40, The bonfire is not burning, however the tent is pitched.
Let A be a symmetric and positive definite (SPD) matrix. Is A^-1 ( inverse of matrix A) a SPD matrix? If so, prove it. If not, explain and give an example.
Calculate the simple linear regression equation
Problem solving on single mean
A glass manufacturer finds that one in every 1000 items produced is warped . What is the probability that in a random sample of 5000 glass items there will be
A function of two variables f(x,y) is integrated over the square [0,2] x [-1,1]. ex: integral from 0 to 2 , integral from -1 to 1 f(x,y) dx dy. (I wanted to input integral symbols there but didn't know how).
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