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G is a finite group with elements a and b. Let the conjugacy classes of these elements be A and B respectively and suppose |A|^2, |B|^2 < |G|. Prove that there is a non-identity element x in G s.t. x commutes with both a and b.
Find the area, in square units, of the region determined by the intersections of y = x^1/2 and y = x^2/8.
To determine whether the system described is a group. G = set of all integers, a.b = a - b
Define the function f: (0, 1) -> A as follows: For x in the open interval (0,1), let f(x) be the element of A with the property that for every positive integer k, the digit i_k in the kth decimal place of f(x) is the least i in I such that x has a..
If order of the draw were important in a lottery, what would be the effect on odds of winning, if any? Explain. Find Probability and data representation
The Friendly Sausage Factory (FSF) can produce hot dogs at a rate of 5,000 per day. FSF suppies hot dogs to local restaurants at a steady rate of 250 per day.
Find an equation for the surface consisting of all points that are equidistant from the point (-1,0,0) and the plane x = 1. Identify the surface.
Risk-adjusted NPV of Projects. The Bartram-Pulley Company (BPC) must decide between two mutually exclusive
In each case make a conjecture about a possible generalisation, and explore it (i.e. attempt to prove your conjectures true or false).
Consider a Lagrangian system, with configuration space R^n, given by (x^1, ... x^n); and Lagrangian L(x', ..., x^n; v^1, ... v^n). Now consider a new system of coordinates, (y^1,... ^n),
Find the maximum depth using the given function - What is her depth after 4 sec? After 6 sec?
What is the probability of drawing a red ball on the second draw if the first one is not put back in the box after it is drawn?
The equation x - 3 ln x = 2 has exactly two solutions A and B, with 0
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