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For the functions:
f(x)=4-x^2
g(x)=e^(-x)
a. Sketch both graphs. Find and label the intersection points.
b. Find the area between the graphs using integration. Give the full integral, including limits, in proper notation.
Let G be finite abelian group with this property: For each positive integer m such that m | |G|, there are exactly m elements in G with order dividing m. Prove that G is cyclic.
In each of the attached cases show that the set U is linearly independent subset of the vector space V. Give, with justification, a basis of V which contains the set U.
Suppose someone offers to pay you $100 if you draw 3 cards from a standard deck of 52 cards and all the cards are clubs. What should you pay for the chance to win
Determine the equation of the Straight line from the given data - Find the equation of the indicated curve, subject to the given conditions, Sketch the curve
How do you find (and what is it) the principal branch of the following complex powers:
Write as a system of 2 equations in 2 unknowns. Solve each system by substitution and show each step. Perimeter of a rectangle : the length of a rectangular swimming pool is 15 feet longer than the width.
Provide Description of Card Probability. What is the probability that exactly one suit is represented among these 8 cards? Exactly 2 suits?
Statistical Probability: Emergency Call Rates. Let sample mean = 70 and the sample variance = 36 and assume the data is normally distributed. Use ths information to answer the following:
for the remaining 30% you choose randomly among the 5 answers. What percent of the answers should you expect to get right? learning about conditional probability and independence
Show that if f:A->R is Lipschitz then it is uniformly continuous on A. Is the converse statement true? Are all uniformly continuous functions necessarily Lipschitz?
Find the average value of the function in the given region. The average value of f(x)=1/x over [1,10] is______.
Let n >= 2 be a number. Define the graph L2(n) as follows: Vertices are ordered pairs from the set {1, ..., n}. Two vertices are adjacent if they have the same first coordinate, or the same second coordinate (but not both).
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