Find the average value of the function f over the given region.f(x, y) = e4x over the square 0 ? x ? 
, 0 ? y ? 
.
A. 2e - 1
B. e - 1
C. 
D. 
Answer: B
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Use Chebyshev's theorem to solve the problem.Find the least possible fraction of numbers in a data set lying within 5 standard deviations of the mean.
A. 
B. 
C. 
D. 
Identify the numerator and the denominator of the fraction.
A. Numerator 2
Denominator 7
B. Numerator 7
Denominator 2
C. Numerator 9
Denominator 1
D. Numerator 
Denominator 7
Mark as true any statement that is always true. Mark as false any statement that is never true or that is not necessarily true. Be able to justify your answers.
1. The surface area of a rectangular prism is the sum of the areas of the six rectangles which form its faces. 2. The volume of any pyramid is the product of one-half the area of the base and its height. 3. The volume of a sphere is the product of and four times the cube of the radius. 4. The volume of a right pyramid is 1/3 of the volume of a right prism with the same height and the same base. 5. The volume of a sphere is 1/3 of the volume of a right circular cylinder with the same diameter.
Simplify.
A. 1
B. 
C. 
D. 12