Solve the problem.The time to failure t, in hours, of a certain machine can often be assumed to be exponentially distributed with probability density function f(t) = ke-kt, 0 ? t < ?, where k = 
and a is the average amount of time that will pass before a failure occurs. Suppose the average amount of time that will pass before a failure occurs is 80 hours. What is the probability that a failure will occur in 49 hours or less?
A. 0.5496
B. 0.4580
C. 0.3435
D. 0.3664
Answer: B
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Use the half-angle formulas to simplify the given expression.
A. 2
cos 1.6?
B. 2
cos 0.4?
C. 2 cos 0.4?
D. 4 cos 0.4?
Solve the given differential equation. (The form of yp is given.)D2y + 6Dy + 5y = 2 + ex (Let yp = A + Bex.)
A. y = c1e-5x + c2e-x - 
+ 
ex
B. y = c1e5x + c2ex + 
+ 
ex
C. y = c1e-5x + c2e-x + 
- 
ex
D. y = c1e-5x + c2e-x + 
+ 
ex
Solve the problem.A collection of dimes is arranged in a triangular array, with 15 coins in the base row, 14 in the next, 13 in the next, and so forth. Find the value of the collection.
A. $1.20 B. $12.00 C. $24.00 D. $6.00
Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.f(x) = 3(x + 1)2 - 2
A. 
B. 
C. 
D. 