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How many weighings of a balance scale are needed to find a lighter counterfeit coin among four coins? Describe an algorithm to describe the lighter coin using this number of weighings.
Show that the mass, momentum, and energy are constants of motion (invariants) for the KdV equation by direct differentiation with respect to time.
Prove that the element K=k1+k2+....km is the center of the group ring R[G]. Let K1,....Kr be the conjugacy classes of G and for each Ki let Ki be the element of R[G] that is the sum of the members of Ki.
Is the multiplication of complex numbers similar to multiplication of polynomials? Is it possible to apply the FOIL method when multiplying complex numbers?
A baseball manager has decided who his 5 starting hitters are to be, but not the order in which they will bat. How many possibilities are there?
Probability: High Risk Apartments. In a local town, there are three separate apartment blocks, A, B and C. Block A contains 10 apartments, of which two contain "High Risk" inhabitants.
Find the break-even points and the maximum revenue.
Find the probability that a student selected at random failed the test?
Objective questions based on regression
A function f is given by the following table: Approximate the area between the x-axis and y=f (x) from x=0 to x=4 using Simpson's Rule.
Let I be the ring of integral Hamilton Quaternions and define N: I ->Z by N(a+bi+cj+dk) = a^2 +b^2 +c^2+d^2
The group of even permutations of n symbols is denoted by A_n and is called the alternating group of degree n. Show that A_8 contains an element of order 15.
Find the rate of change.
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