From the given list, identify the proper fractions.
, 
, 
, 
, 
A. 
, 
B. 
, 
, 
C. 
, 
, 
D. 
, 
, 
Answer: A
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Integrate the function f over the given region.f(x, y) = 
over the square 4 ? x ? 6, 4 ? y ? 6
A. ln 
B. 
2
C. 
2
D. 
Approximate the integral 
using
(a) the Trapezoid rule with n = 6 . (b) Simpson’s rule with n = 6 .
Solve the problem.An office manager is buying used filing cabinets. Each small file cabinet costs $4, takes up 5 square feet of floor space, and holds 8 cubic feet of files. Each large file cabinet costs $12, takes up 10 square feet of floor space, and holds 14 cubic feet of files. The total cost cannot exceed $60, and the office has no more than 60 square feet of floor space available for the cabinets. How many of each file cabinet should the manager buy to maximize storage capacity? What is the maximum storage capacity?
A. 3 small file cabinets and 6 large file cabinets; 132 cubic feet B. 9 small file cabinets and 0 large file cabinets; 72 cubic feet C. 0 small file cabinets and 9 large file cabinets; 126 cubic feet D. 6 small file cabinets and 3 large file cabinets; 90 cubic feet
Suppose that the consumer expenditure E (in dollars) depends on the market price p per unit (in dollars) according to 
. Graph this equation with a graphing utility and the range
BecauseErepresents consumer expenditure, only values
of 
have meaning. Determine the values ofpfor which .
? ?
A. 
B. 
C. 
D. 
E. 