Give the probability distribution for the indicated random variable.
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A fair coin is tossed three times, and we count the number of "runs" that occur. A "run" is defined as a sequence of one or more of the same letter (e.g., HTH is 3 runs, TTH is 2 runs, and TTT is 1 run).
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A. 
?
B. ?
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C. ?
?
D. ?
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E. ?
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Answer: E
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Compute the gradient of the function at the given point.
A. ?f = 4,782,969i + 1,062,882j + 4,782,969k B. ?f = 4,782,969i + 1,594,323j + 3,188,646k C. ?f = 1,594,323i + 1,594,323j + 354,294k D. ?f = 1,594,323i + 1,062,882j + 531,441k
Use the properties of exponents to simplify the expression. Write with positive exponents.(r1/5 ? s1/5)2
A. r1/25s1/25 B. r2/5s2/5 C. r1/10s1/10 D. r2s2
Solve the problem.Of the fifty states in the United States, 12 have at least one mountain higher than 12,000 feet. What fraction of states have at least one mountain higher than 12,000 feet? Write your answer in lowest terms.
A. 
B. 
C. 
D. 
Provide an appropriate response.Explain the error in the following: x2 + 2x - 15 = (x - 5)(x + 3)
What will be an ideal response?