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An element e of a monoid M is called an idempotent if e^2 = e. If M is finite, show that some positive power of every element is an idempotent.
Identify the definite integral that represents the volume of the solid formed by revolving the region bounded by y=x^3, y=1, and x=2 about the line y=10.
ABCD is a cross-section of a uniform rectangular block of mass 20kg. AB is 0.75m and BC is 1m. The block rests with A on rough horizontal ground with AB at 20 degrees to the horizontal.
Let x, y be elements in the Boolean algebra B. Prove that x = y if and only if xy + xy = 0. How many rows are needed to construct the (function) table for a Boolean function of n variables?
What happens if the first shot is intentionally missed? What is the better strategy shooting the deadliest one or the weakest one?
Calculation of a Laplace Transform from first principles
Using standard partition Pn (0,1) where n greater or equal to 4 and deduce that f is intergrable on (0,1) and evaluate (intergral sign with 1 at top and 0 at bottom) of f
Calculate the mode
Probability Sampling Without Replacement Card Hands. A hand of 4 cards contains one card of each suit
For solving a system of equations, is there a difference between using an algebraic method and using the graphical method? Explain why or why not
What route will take the least amount of time?
Solve the average cost function.
Show that the positive integers less than 11, except 1 and 10, can be split into pairs of integers such that each pair consists of integers that are inverses of each other modulo 11.
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