Todd's Direct, a major TV sales chain headquartered in New$$ Orleans, is about to open its first outlet in$$ Mobile, Alabama, and wants to select a site that will place the new outlet in the center of$$ Mobile's population base. Todd examines the seven census tracts in$$ Mobile, plots the coordinates of the center of each from a$$ map, and looks up the population base in each to use as a weighting. The information gathered appears in the following table.

$$

Census Tract

Population in Census Tract

$$X$,$ Y Map Coordinates

$101$

$1,800$

$(24,45)$

$102$

$5,000$

$(24,26)$

$103$

$9,500$

$(55,42)$

$104$

$7,000$

$(50,18)$

$105$

$10,200$

$(76,50)$

$106$

$18,000$

$(70,22)$

$107$

$15,000$

$(84,28)$

$$a$)$ The$$ center$-$of$-$gravity coordinates for the location of the proposed outlet in$$ Mobile, Alabama should$$ be:

Part $2$

x$=$ enter your response here $($round your response to two decimal$$ places$).$

Part $3$

y$=$ enter your response here $($round your response to two decimal$$ places$).$

Part $4$

$$b$)$ Census tracts $103$ and $105$ are each projected to grow by $20\%$ in the next year. The new$$ center$-$of$-$gravity coordinates for the location of the proposed outlet in$$ Mobile, Alabama should$$ be:

Part $5$

x$=$ enter your response here $($round your response to two decimal$$ places$).$

Part $6$

y$=$ enter your response here $($round your response to two decimal$$ places$).$