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a box with no lid is created from a square of cardboard with a side length of 60 cm by cutting rectangles of length x by 2x from each corner (the extra side length of this square of 2x is folded over to create a double thickness side for added strength).
a) Express the length, width and height in terms of the variable xb) Find the expression for the volume of the box in terms of xc) Find the expression for the surface area of the box in terms of xd) What are the restrictions of the variable? Explain.
Let (X,d) be a compact metric space, and let Con(X) denote the set of contraction maps on X. We shall define the distance between two maps f,g which belongs to Con(X) as follows:
verify that E is a constant of motion for the system of the first two equations and find the equilibria of the system of the first two equations
Calculate the probability that a person for whom the test result is positive has the disease
Random variable and a probability distribution, Discuss the concepts of random variable and a probability distribution. A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 stude..
Create a system of linear equations from your own life. Keep in mind that a system of linear equations will consist of two equations using the same variables and the variables will represent the same thing for both equations
You pick cards one at a time without replacement from an ordinary deck of 52 playing cards. What is the minimum number of cards you must pick in order to guarantee that you get (a) a pair
Two armies are advancing on two cities. The first army has 4 regiments and the second army has 3 regiments. At each city, the army that send more regiments to the city captures both the city and the opposing army regiment.
Assume that f(z) is analytic at the origin and f(0) = first derivative of f at 0 = 0. Prove that f(z) can be written in the form f(z) = [z^2]g(z), where g(z) is analytic at z = 0.
What is the probability of drawing three queens in a row from a deck of cards when the drawn card is returned each time?
Suppose that each time that you buy a car, you choose between Ford and General Motors. Suppose that each time after the first, you stay with the same company with probability 2/3 and switch with probability 1/3
Six people are going to travel to Mexico City by car. There are six seats available in the car. In how many different ways can the six people be seated in the car if only three of them can drive?
A large cube is 2 feet on each edge. How many cubes - one inch on each edge- will it take to fill the large cube? If the base of a triangle is increased by 20% and the altitude to that base is decreased by 40% then by what percent is the area chang..
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