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Prove the identity (n~r) (r~k) = (n~k) ((n-k)~(r-k)), whenever n, r, and k are nonnegative integers with r less than/equal to n and k less than/equal to r:
a) Using a combinatorial argument.
b) Using an argument based on the formula for the number of r-combinations of a set with n elements.
Compute the integral of xdz (|z|=r) for the positive sense of the circle in two ways first by using parametrization and second by observing that x=(1/2)(z+z conjugate)=(1/2)(z+r^2/z) on the circle.
From the matrix S who columns are the three vectors in your basis for E3, and compute J = (S^-1)AS. Notice that if you order the columns of S in the most logical way, J will be triangular.
The truth table and previously proven logical equivalencies
Consider that two particles are traveling the paths of the following functions: If each particle is to begin at one point of intersection at the same time and travel to the other point of intersection (at the same velocities)
Each individual letter of the word "pfeffernuesse" is placed on a piece of paper, and all 13 pieces of paper are placed in a hat. Three letters are selected at random from the hat. Find the probability of selecting each of the following.
Graph by hand the curve whose parametric equations are given and show its orientation. Find the two different parametric equations for the rectangular equation
Apply normal distribution methods to approximate this binomial distribution.
Explain the importance of appropriately integrating Texas Instruments' CBL 2 (Calculator Based Laboratory), CBR 2 (Calculator Based Ranger), Fathom, a powerful data analysis software tool from Key Curriculum Press, and Excel into the middle school..
In finding the average size of automobile tire that is purchased, the mean or median size might be a tire that does not exist. Therefore, one would want to know the size of tire bought most often.
How much variation does knowledge of Age Score
what is the probability that all will make a purchase and evaluate the probability that a light bulb will burn out in less than 1000 hours.
Evaluate the integral: Where E is the tetrahedron enclosed by the coordinate planes x=0, y=0, z=0 and the plane 2x + y + z = 4.
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