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Ryan Arts manufactures two types of picture frames--let's call them typeX and typeY. Each typeX frame requires 2 hours of labor and 1 unit of material to make, and each typeY frame requires 1 hour of labor and 2 units of material to make. During the upcoming week the company has 4000 hours of labor and 5000 units of material available. Naturally, during the upcoming week Ryan cannot use more labor or more material than he has available--but he could use less. Write two expressions--one for labor and one for materials--that can be used to model the labor and materials constraints for the upcoming week.
Use vector techniques to prove that a triangle and its medial triangle have the same centroid. You may take it as a given fact that the location of the centroid of triangle ABC is the vector (vector OA + vector OB + vector OC)/3.
Express the following in the polar coordinate form: u(r, theta) + i v(r,theta)
Rational and Jordan Canonical Forms, Find the rational canonical form and the Jordan canonical form(if possible) for the linear tansformations f: R^3->R^3 given by the matrix
How many bit strings of length 6 are there? Explain fully.
Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ½. Either show work or explain how your answer was calculated. Mean = np, Standard Deviation =
Find the expected value and the variance of X, the number of inspected bottles with serious defects.
A wooden artifact from an ancient tomb contains 35 percent of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years.)
Your lamp uses 5 light bulbs to operate. Suppose that each bulb has a lifetime which is exponential with mean 1 year, that the lifetimes are independent random variables and that the lamp does not light if at least one of the bulbs is burnt.
On the other hand, give an example of a metric space in which every Cauchy sequence converges; and then prove this metric space is Cauchy sequence and also converges.
It has been recorded that the average number of errors in a newspaper is 4 mistakes per page. What is the probability of having 0 or one error
In your own words, explain the difference between intersecting and perpendicular lines. Can two lines exist that are not intersecting or parallel? Explain your answer.
Use the Theorem of Pappus to find the volume of the solid obtained by rotating the triangle with vertices (5, 4), (5, 8), and (11, 6) about the x-axis.
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