Two rectangular picture frames have the same area of 45 square inches but have different side lengths. Frame A has a length of 6 3/4 inches, and Frame B has a length of 7 1/2 inches. Without calculating, predict which frame has the shorter width. Explain your reasoning

Frame B has the shorter width.

Step-by-step explanation:

The area of a rectangle is given by length×width. If the two have a maintained area of 45 in², then length and width are inversely proportional, meaning if one goes up, the other must go down. Since Frame B has a larger length than Frame A and both frames have the same area, Frame B must have a shorter width to accommodate for its larger length.

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0