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Show, a subset K of a discrete metric space X is compact if and only if it is finite. In particular, if X is infinite, then X is complete (and thus closed) and bounded, but not compact.
Four Points, Two Distances. How many ways can four distinct points be arranged in the plane so that the six distances between pairs of points take on only two different values
Probability & Statistics : Outcome of Dice Rolls, Two people play a game. A single die is thrown. If the outcome is a 2 or a 3, then player A pays player B $6.00.
The demand equation for a product is p=0.01q2-1.1q+30 and the supply equation is p=0.01q2+8. Find the equilibrium point (po,qo) and determine the consumer surplus under market equilibrium.
Find which two variables have the weakest strength of relationship?
At the beginning of 2012, Mazzaro Company acquired equipment costing $120,000. It was estimated that this equipment would have a useful life of 6 years.
(a) What is the probability that a single randomly-selected shopped for either clothing or electronics yesterday, but not both? (b) Let C = {customers shopping for clothes} and E = {customers shopping for electronics}.
Suppose that f (x) is a degree 4 polynomial with coefficients in a field F, and let K be the splitting field of f (x). What are the possible values for [K : F]?
The cross-sections perpendicular to the v-axis are circular disks with diameters running from the y-axis to the parabola x = √15y2. Find the volume of the solid.
1. What is the role of the leader in business? 2. What keys to success did the leader describe?
An agricultural sprinkler distributes water in a circular pattern of radius 85ft. It supplies water to a depth of e-r feet per hour at a distance of r feet from the sprinkler. (Do not substitute numerical values; use variables only.)
The derivative from the rate of changes
How is the simulation process used in Decision Sciences models? What are the advantages of using simulation? What are its limitations? How can a simulation model be verified? Give a real world example where using simulation is appropriate.
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