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Let S be a set with an associative binary operation but with no identity. Choose an element 1 not belonging to S, write M = {1} or S, and define an operation on M by using the operation of S and 1s=s=s1 for all s belonging to S. Show that M is a monoid.
Evaluate the ratio of circumferences of inscribed and circumscribed circles in a regular hexagon
A ski jump is design to follow the path given by the equations: x=3.5t^2 and y=20.0+0.120t^4 - 3.00 sqrt(t^4+1) (0 less than or equal to (t) less than or equal to 4.00 s) ( x and y in m, t in s). Find the velocity and acceleration of a skier when ..
Prove Let D be a nontrivial connected digraph. Then D is Eulerian if and only if od(v)=id(v) for every vertex v of D. Od means the outdegree of a vertex v of a digraph D. (is the number of vertices of D that are adjacent from v.
Calculate the probability that the return for common stocks
Compare your approximation with the acutal value of the tangent of 1/4 radian as shown on a calculator.
Find a definite integral that represents the arc length of the curve over the indicated interval and observe that the length cannot be evaluated with the techniques studied so far
Probability that a player's pick wins the grand prize. In a certain lottery, k balls are chosen at random and without replacement from a bin containing N balls numbered 1 through N
Let G be a group (finite or infinite) and let a and b in G. Let o(a) represent the order of a. Suppose G is abelian and both a and b are of finite order. Show that ab is of finite order and o(ab) divides o(a)o(b).
What would you do if supply exceeded demand? What if demand exceeded supply?
Important information about Probability with dice, You roll a dice twice. What is the probability that you will roll each of the following pairs of numbers.
Solve the system of equation by matrix method - Use augmented matrices to solve the following 2 x 2 systems of equations.
Suppose demand is expressed as QD = 300 - 50P. If we want to make this equation consistent with the typical supply and demand diagram, this equation must be stated as:
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