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Draw a game tree for nim if the starting position consists of three piles with one, two, and three stones, respectively. When drawing the tree represent by the same vertex symmetric positions that result from the same move. Find the value of each vertex of the game tree. Who wins the game if both players follow an optimal strategy?
Water is poured into a conical reservoir at a rate of pi cubic feet per second (about 3 ft/sec). The reservoir has a radius of 6 ft across the top and a height of 12 ft. At what rate is the level of the water inside the reservoir increasing when th..
Make sure you build or generate at least five more Pythagorean Triples using one of the many formulas available online for doing this. After building your triples, verify each of them in the Pythagorean Theorem equation.
A cooling has an eccentricity of 5/3. If the cooling tower is 150 feet wide at its narrowest point, determine an equation of the hyperbola used to generate the hyperboloid.
Show from the definition that f : R → R given by f(x) = x^1/2 is differentiable with f'(x) = (1/2)*x^-1/2.
The forward price of one share Goggle with delivery date in 9 months is $600. The risk-free rate is 5% per annum with continuous compounding. Construct an arbitrage opportunity involving one Google share. What is the prot from this opportunity?
We are designing a computer graphic in which we zoom in on a cube. The volume V, surface area S, and side length z of the cube are all varying with respect to time. With this information, compute the following quantities using the steps described ..
Control A certain machine that is used to manufacture screws produces a defect rate of .01. A random sample of 20 screws is selected. Find the probabilities that the sample contains the following
One end of a rope is attached to the top of a pole 100 ft high. If the rope is 150 ft long, what is the maximum distance along the ground from the base of the pole to where the other end can be attached? You may assume that the pole is perpendicul..
as a hospital administrator of a large hospital you are concerned with the absenteeism among nurses aides. the issue
1. Simple Interest: Jerry borrowed $10,657.50 from his bank to build an attached garage and work space on his house. Jerry's simple interest loan had a rate of 13% and required him to pay $12,250 under the agreed terms. What was the duration of hi..
Find the probability that Clair will win the third game in the next series of games palyed against Helen.
Solving problem on distributive Laws
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