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Let f be a non-negative monotone continuous function defined on the interval (0 <). Suppose that the improper integral f(x)dx integrated is convergent. Prove that f is bounded on (0<) and the limit as x goes to infinity of f(x) is 0.
If A and B are normal subgroups of G such that G/A and G/B are abelian, prove that G/(A intersect B) is abelian
Calculating the probability that the player wins in a game of craps. The dice game craps is played as follows. The player throws two die, and if the sum is seven or eleven then she wins. If the sum is two, three, or twelve, then she loses
Determine the kernel and range of each of the following linear transformations from R3 into R3. (a) L(x) = (x3, x2, x1)^T
Probability of speeding violations, A sample of 2000 licensed drivers revealed the following number of speeding violations
35% of a store's computers come from factory A and the remainder come from factory B.2% of computers from factory A are defective while 1% of computers from factory B are defective.
Probability values.
Solve the average cost function.
Prove that the set of all onto mapping from A to A is closed under composition of mappings. Prove that the set of all one-to-one mappings from A to A is closed under mapping composition.
Augmented matrices to solve the word problem
Assume that the spinner cannot land on a line. Determine the probability that the spinner lands on (a) red, (b) green, (c) yellow, (d) green. The spinner is divided into 8 halves. There are (a) red = 4, (b) green = 1, (c) yellow = 1, and (d) blue = ..
Find the slope of the line 2x + y = 4. Find the point of intersection of the lines x + y = 5 and 3x - y = 7. Graph the pair of lines.
Explain why a decision maker might feel uncomfortable with the expected value approach, and decide to use a non-probabilistic approach even when probabilities are available.
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