A county wants to build one centrally-located processing facility to serve the county's four recycling drop-off locations. The four drop-offs have characteristics as given in the table below. What is the approximate center of gravity of these four locations?
A) (4.75, 6.04)
B) (17.00, 24.00)
C) (4.25, 6.00)
D) (4.90, 5.85)
E) (490, 585)

Question

A county wants to build one centrally-located processing facility to serve the county's four recycling drop-off locations. The four drop-offs have characteristics as given in the table below. What is the approximate center of gravity of these four locations? 
A) (4.75, 6.04) 
B) (17.00, 24.00) 
C) (4.25, 6.00) 
D) (4.90, 5.85) 
E) (490, 585)

Quizplus · Accepted Answer

To find the center of gravity, we need to calculate the weighted average of the x-coordinates and the y-coordinates.

The formula for the x-coordinate is (sum of (weight * x-coordinate)) / (sum of weights).

Using this formula, we get:
((200 * 4) + (150 * 6) + (100 * 4) + (50 * 4)) / (200 + 150 + 100 + 50) ≈ 4.90

Similarly, the formula for the y-coordinate is:
((200 * 5) + (150 * 7) + (100 * 5) + (50 * 3)) / (200 + 150 + 100 + 50) ≈ 5.85

Therefore, the approximate center of gravity is (4.90, 5.85), which is choice D.

A County Wants to Build One Centrally-Located Processing Facility to Serve