This Question: 1 pt 6 of 9 This Quiz: 9 pts possible lood\'s uirect, a major I V

Question

This Question: 1 pt 6 of 9 This Quiz: 9 pts possible lood's uirect, a major I V salos chain neadquartered in Now Urleans, is about to open its hirst outiet in MoDile, Aabama, and wants to select a site that will prace 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 101 102 103 104 105 106 107 Population in Census Tract 1,800 5,200 9,500 6,800 10,400 18,000 12,000 ?, Y Map Coordinates (24.45) (26 ,24) (57 48) (52,18) (84,48) (68 22) (96 28) a) The center-of-gravity coordinates for the location of the proposed outiet in Mobile, Alabama should be: (round your response to two decimal places). y»» (round your response to two decimal places). b) Census tracts 103 and 105 are each pro ected to grow by 20% n the next year. The new center of a ty co rdnates for the location of the proposed outlet n Mobile, Alabama should be: x. (round your response to two decimal places). y·? (round your response to two decimal places). Enter your answer in each of the answer boxes

Explanation / Answer

Answer to question a :

Let location of the proposed outlet in Mobile = P, Q

Therefore ,

Sum of population in census tract x P = Sum ( Population in census tract x Corresponding X coordinate )

Or,

( 1800 + 5200 + 9500 + 6800 + 10400 + 18000 + 12000) . P = 1800 x 24 + 5200 x 26 + 9500 x 57 + 6800 x 52 + 10400 x 84 + 18000 x 68 + 12000 x 96

Or, 63700. P = 43200 + 135200 + 541500 + 353600 + 873600 + 1224000 + 1152000

Or, 63700.P = 4323100

Or, P = 67.87 ( rounded to 2 decimal places )

Similarly ,

Sum of population in census tract x Q = Sum ( Population in census tract x Corresponding X coordinate )

Or,

( 1800 + 5200 + 9500 + 6800 + 10400 + 18000 + 12000) . Q = 1800 x 45 + 5200 x 24 + 9500 x 48 + 6800 x 18 + 10400 x 48 + 18000 x 22 + 12000 x 28

Or, 63700. Q = 81000 + 124800 + 456000 + 122400+ 499200 + 396000 + 336000

Or, 63700.Q = 2015400

Or, Q = 31.64 ( rounded to 2 decimal places )

X = 67.87

Y = 31.64

Answer to question b :

Revised population of census tract 103 = 9500 x 1.20 = 11400

Revised population o census tract 105 = 10400 x 1.20 = 12480

The revised calculations for P and Q accordingly as follows :

Sum of population in census tract x P = Sum ( Population in census tract x Corresponding X coordinate )

Or,

( 1800 + 5200 + 11400 + 6800 + 12480 + 18000 + 12000) . P = 1800 x 24 + 5200 x 26 + 11400x 57 + 6800 x 52 + 12480 x 84 + 18000 x 68 + 12000 x 96

Or, 67680 . P = 43200 + 135200 + 649800 + 353600 + 1048320 + 1224000 + 1152000

Or, 67680.P = 4606120

Or, P = 68.06 ( rounded to 2 decimal places )

Similarly ,

Sum of population in census tract x Q = Sum ( Population in census tract x Corresponding X coordinate )

Or,

( 1800 + 5200 + 11400 + 6800 + 12480 + 18000 + 12000) . Q = 1800 x 45 + 5200 x 24 + 11400 x 48 + 6800 x 18 + 12480 x 48 + 18000 x 22 + 12000 x 28

Or, 67680. Q = 81000 + 124800 + 547200 + 122400+ 599040 + 396000 + 336000

Or, 67680.Q = 2206440

Or, Q = 32.60 ( rounded to 2 decimal places )

X = 68.06

Y = 32.60

X = 67.87

Y = 31.64

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