Management of a fast-food chain proposed the following regression model to predict sales at outlets: y = β0 + β1x1 + β2x2 + β3x3 + ε, where y = sales ($1000s) x1 = number of competitors within one mile x2 = population (in 1000s) within one mile x3 is 1 if a drive-up window is present, 0 otherwise The following estimated regression equation was developed after 20 outlets were surveyed: begin mathsize 14px style y with hat on top end style = 14.8 − 3.5x1 + 3.2x2 + 15.8x3 Use this equation to predict sales for a store with 3 competitors, a population of 5100 within one mile, and no drive-up window. Note: omit the $ symbol in your answer

y [ Expected Sales ] = 20.62 thousands

Step-by-step explanation:

Regression line : y = 14.8 − 3.5x1 + 3.2x2 + 15.8x3 ; where

y = sales (in 1000s), x1 = number of competitors within one mile, x2 =  population (in 1000s) within one mile, x3 = 1 (if a drive-up window is present) or x3 = 0 (if a drive-up window is not present)

x1 (competitors) = 3 , x2 (population) = 5100 = 5.1 thousands , x3 (no drive up window) = 0

y = 14.8 − 3.5 (3)  + 3.2 (5.1) + 15.8 (0)

y = 14.8 - 10.5 + 16.32

y [ Expected Sales ] = 20.62 thousands

4 & 3

step-by-step explanation:

factor of 108=2×2×3×3×3=2×2×3^3=the number is 4 because 2 only occurs 2 times and 2×2=4 and factor of 2187=3^3×3^3×3=the number is 3 because 3 onlyvoccur 1 time.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1