Solve the problem.One rope pulls a barge directly east with a force of 82 newtons, and another rope pulls the barge directly north with a force of 70 newtons. Find the magnitude of the resultant force acting on the barge.
A. 12 newtons
B. 108 newtons
C. 152 newtons
D. 5740 newtons
Answer: B
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Evaluate the line integral along the curve C.
ds , C is the path from (1, 1, 0) to (e10, e10, 1) given by:C1: r(t) = e10ti + e10tj, 0 ? t ? 1C2: r(t) = e10i + e10j + 7tk, 0 ? t ? 1
A. 
(e30 - 1) + e20 + 
e10
B. 
(e30 - 1) + 7e20 + 49e10
C. 
(e30 - 1)
D. 
(e30 - 1) + 7e20 + 
e10
Decide whether the statement makes sense. Explain your reasoning.The argument is weak, so its conclusion must be false.
What will be an ideal response?
Provide an appropriate response.The probability distribution for the random variable X is: 
What is the expected value of X?
A. 0.62 B. 0.26 C. 0.22 D. 0.50
Express the function in the form f(x) = a(x - h)2 + k and indicate the vertex.f(x) = x2 + 10x + 3
A. f(x) = (x + 5)2 - 22 vertex: (-5, -22) B. f(x) = (x + 5)2 - 72 vertex: (-5, -72) C. f(x) = (x - 10)2 + 203 vertex: (10, 203) D. f(x) = (x - 5)2 + 78 vertex: (5, 78)