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Let X be a set of finite (positive) measure. Let C be the collection of all finite subsets of X and their complements in X. Is C an algebra of sets? Is C a σ-algebra? Explain.
Find the radius of convergence and the interval of convergence of this taylor series.
Also, if the variables in an equation were reversed, what would happen to the graph of the equation? This was the example I was given, how would the graph of y = x² relate to the graph of x = y²?
Define a Markov chain with r+1 classes and find its transition probability matrix.
An electric charge is distributed throughout 3-space with density inversely proportional to the distance from the origin. Show that the total charge inside a sphere of radius R is proportional to R^2.
Calculate the probability that a person for whom the test result is positive has the disease
Please show me how to complete these problems correctly with the actual graph. Solve each absolute value equation and graph the solution set.
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 35 liters per minute. There are 500 liters in the pond to start.
A student claims that anything that can be accomplished by a translation can be accomplished by a reflection. She claims that if A' is the image of A under a translation, then A' can be obtained by a reflection in the line(which is the perpendicul..
Suppose that V is a complex (i.e. F = C) inner-product space. Prove that if N, an element of L(V), is normal and nilpotent, then N = 0.
Find the directional derivative at P(-2,2,-1) in the direction of Q(18,-2,4). Find the direction of maximum decrease at P. (your answer does not have to be unit vector.) What is the maximum rate of decrease?
At a particular University students must receive one of the following grades: A, B, C, D and F. What is the minimum number of students required in a course to ensure that at least 5 will receive the same grade?
What happens to the circumference of a circle if you double the radius? What happens if you double the diameter? What happens if you triple the radius?
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