Question content area

Part $1$

$$Todd$\text{'}$s Direct, a major TV sales chain headquartered in New$$ 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

$101$

$1$ comma $800$

$(24,46)$

$102$

$5$ comma $000$

$(25,26)$

$103$

$10$ comma $500$

$(57,45)$

$104$

$6$ comma $800$

$(50,22)$

$105$

$10$ comma $200$

$(84,52)$

$106$

$20$ comma $000$

$(72,22)$

$107$

$15$ comma $000$

$(84,25)$

$$a$)$ The$$ 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$).$