NYC Sanitation wants to build a centrally located waste processing facility to serve the five boroughs' current recycling locations. The five locations have the properties listed in the following table. What is the approximate center of gravity of these five locations? $$\begin{array} { | c | c | c | c | }
\hline \text { Location } & \text { X-coordinate } & \text { Y-coordinate } & \text { Tonnage } \
\hline \text { Brooklyn } & 5 & 5 & 50 \
\hline \text { Bronx } & 6 & 9 & 50 \
\hline \text { Manhattan } & 4 & 7 & 45 \
\hline \text { Queens } & 8 & 5 & 35 \
\hline \text { Staten Island } & 2 & 2 & 20 \
\hline
\end{array}$$
A) 1,050, 1,230
B) 25, 28
C) 5.25, 6.15
D) 5.00, 5.60

Question

NYC Sanitation wants to build a centrally located waste processing facility to serve the five boroughs' current recycling locations. The five locations have the properties listed in the following table. What is the approximate center of gravity of these five locations? $$\begin{array} { | c | c | c | c | } 
\hline \text { Location } & \text { X-coordinate } & \text { Y-coordinate } & \text { Tonnage } \
\hline \text { Brooklyn } & 5 & 5 & 50 \
\hline \text { Bronx } & 6 & 9 & 50 \
\hline \text { Manhattan } & 4 & 7 & 45 \
\hline \text { Queens } & 8 & 5 & 35 \
\hline \text { Staten Island } & 2 & 2 & 20 \
\hline
\end{array}$$
A) 1,050, 1,230
B) 25, 28
C) 5.25, 6.15
D) 5.00, 5.60

Quizplus · Accepted Answer

To find the center of gravity, calculate the weighted average of the X and Y coordinates, using tonnage as the weight. For the X-coordinate: $\frac{(5*50) + (6*50) + (4*45) + (8*35) + (2*20)}{50+50+45+35+20} = 5.25$. For the Y-coordinate: $\frac{(5*50) + (9*50) + (7*45) + (5*35) + (2*20)}{50+50+45+35+20} = 6.15$.

NYC Sanitation Wants to Build a Centrally Located Waste Processing