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Modern Algebra
Set Theory (XVII)
Laws of Algebra of Sets
Distributive Laws (I)
Prove that A intersection (B union C) = (A intersection B) union (A intersection C)
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.
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?
Determine 2 numbers such that the difference of its squares is 120 and the sum is 6. If I have 30 coins of two kinds 5 cents and 1 cent can I have a total of 78? A rectangle has a perimeter of 392 m calculate its dimensions if the length is 52 m long..
A farmer wants to fence o a rectangular ?eld and then divide the ?eld in half with a fence down the middle (see diagram below). If he can only a ord 240 ft. of fencing material, what is the width y which gives the maximum area of the ?eld?
Let B(r,t) compute the balance (in dollars) of account after t years with an r% interest rate. What are the units of dB/dr? (dB/dr is in partials notation)
Important information about Probability and combinations. Assume you have five cards are chosen from a standard deck of 52 playings cards. How many hands contain four aces?
Show that the mass, momentum, and energy are constants of motion (invariants) for the KdV equation by direct differentiation with respect to time.
Why would we want to do this? Why not just use Newton's Interpolatory Divided Difference formula to get an nth degree interpolating polynomial? Write down the conditions required for the spline S(x) to fit the data and have 6 continuous derivative..
Find the variation constant and an equation of variation where y varies directly as x and y= 72 and x=8
Objective questions based on regression
Use the regression model to predict the shipments
A Norman window is constructed by adjoining a semicircle to the top of a rectangular window. Find the dimensions of the Norman window of maximum area if the total perimeter is 16 feet.
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