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consider a linear transformation T on R3 which reflects each vector about the line spanned by [1 2 3 ]. Find a basis B such that B-matrix of T is diagonal.
Let G be a simple graph with no isolated vertex and no induced subgraph with exactly two edges. Prove that G is a complete graph. (Please read carefully the definition of an induced subgraph before you attempt to solve it!).
Calculate the increased odds of CHD in females who have a family history of CHD & exercise three times per week compared to males who do not exercise & have not family history of CHD.
Find the probability distribution, & the cumulative probability distribution of car arrivals.
1) a) How many 16 bit strings of 0's and 1's contain exactly 7 1's? b) How many 16 bit strings of 0's and 1's contain at least one 1?
Matrices are the most common and popular way to solve systems of equations. Provide an example of a matrix that can be solved using Gaussian elimination. Show specifically how row operations can be used to solve the matrix.
For this problem please state the method you used and show the work required to obtain the answer. Find the general solution for each of the systems:
Waiting Lines and Queing Theory Models. Customers enter the waiting line at a cafeteria on a first come, first served basis in two serving lines.
Three marbles are chosen without replacement from a box containing 12 red, 7 blue, and 8 yellow marbles. Let X be the number of blue marbles chosen.
Use the side-angle inequality to show that in triangle ABC if the internal bisector of angle A meets BC at D and AB>AC , then DB>DC.
Find the center (h,k) and radius r of the circle and then use these to Graph the circle
Find whether the given expression is a function or not - Which of the following are functions? The last two problems, i.e., b & c, are multi part relations consider all parts when determining whether or not these relations are functions.
Find the equation of a parabola whose vertex is (0,0) and directrix is the line y=3. Find the vertex, focus, and directrix of (x-2)^2=12(y+1). Find the latus rectum and graph the parabola, making sure that all points and axis are labeled.
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