Provide an appropriate response.Let M be a 2 × 2 matrix. Which of the following statements are true?(i)I2 M = M(ii)I2 + M = M(iii)MI2 = I2(iv)MI2 = M
A. (i), (ii), (iii), (iv)
B. (i), (iv)
C. (ii), (iii)
D. (i), (iii), (iv)
Answer: B
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A mail truck must deliver packages to 5 different homes (A, B, C, D, and E). The trip must start and end at A. The graph below shows the distances (in miles) between locations. We want to minimize the total distance traveled.
How many different Hamilton circuits would we have to check if we use the brute-force algorithm? (Do not count the same circuit traveled backward.)
A. 60 B. 4 C. 12 D. 30 E. none of these
Figure (a) shows a vacant lot with a 100-ft frontage in a development. To estimate its area, we introduce a coordinate system so that the x-axis coincides with the edge of the straight road forming the lower boundary of the property, as shown in Figure (b). Then, thinking of the upper boundary of the property as the graph of a continuous function f over the interval [0, 100], we see that the problem is mathematically equivalent to that of finding the area under the graph of f on [0, 100]. To estimate the area of the lot using a Riemann sum, we divide the interval [0, 100] into five equal subintervals of length 20 ft. Then, using surveyor's equipment, we measure the distance from the midpoint of each of these subintervals to the upper boundary of the property. These measurements give the
values of f(x) at x = 10, 30, 50, 70, and 90. What is the approximate area of the lot?
?
?
?
A. 7,900 sq ft
B. 8,600 sq ft
C. 8,100 sq ft
D. 8,400 sq ft
Find the average of the numbers.What is the average of all integers between 5 and 26, inclusive of both?
A. 16.5 B. 341 C. 99 D. 15.5
If f is one-to-one, find an equation for its inverse.f(x) = 
, x ? 9
A. f-1(x) = 
B. Not a one-to-one function
C. f-1(x) = x2 + 9, x ? 0
D. f-1(x) = (x - 9)2