A figure is translated four units to the left and seven units up. Which rule represents this translation? (x, y) → (x + 4, y + 7)
(x, y) → (x + 4, y − 7)
(x, y) → (x − 4, y + 7)
(x, y) → (x − 4, y − 7)

Step-by-step explanation:

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(x, y) --> (x-4, y+7)

Step-by-step explanation:

When translating along the x-axis, the x coordinate is changed by the amount with respect to the direction you're moving it in. Moving to the left means you need to subtract from x, moving to the right means you need to add. Since you're moving to the left by 4 in this problem, you need to subtract 4 from the x coordinate.

Similarly, when translating along the y-axis, the y coordinate is changed by an amount with respect to the direction it is moving in. Moving up means you need to add to the y coordinate, moving down means you need to subtract. Since you're moving up by 7 in this problem you need to add 7 to the y coordinate.

Combining these two ideas gives you the translated coordinates (x+4, y+7)

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