Part 3 of 3 In the United States, the revenue (money taken from sales) at a "hull service restaurant is increasing at a faster rate than the revenue at a "Tast food restaurant. The data below represent the annual revenue in billions of dollars for each type of restaurant. Use the data to answer the three questions below. Let xD represent the year 1990. 1996 1999 2000 199 327 141 2001 150 154 159 Fast Food 113 115 117 2002 119 2003 121 164 123 Full Service 2004 104 a) Write a linear regression equation for the "full service restaurant y= 53.080 +7.46 (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.) b) Now write a linear regression equation for the "fast food" restaurant y-2.104-93.761 [Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.) c) Use the equations to approximate the year that the revenue from the two types of restaurants was the same. Round to the nearest year as needed.) Points: 1.33 of 4

Question

Part 3 of 3 In the United States, the revenue (money taken from sales) at a "hull service restaurant is increasing at a faster rate than the revenue at a "Tast food restaurant. The data below represent the annual revenue in billions of dollars for each type of restaurant. Use the data to answer the three questions below. Let xD represent the year 1990. 1996 1999 2000 199 327 141 2001 150 154 159 Fast Food 113 115 117 2002 119 2003 121 164 123 Full Service 2004 104 a) Write a linear regression equation for the "full service restaurant y= 53.080 +7.46 (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.) b) Now write a linear regression equation for the "fast food" restaurant y-2.104-93.761 [Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.) c) Use the equations to approximate the year that the revenue from the two types of restaurants was the same. Round to the nearest year as needed.) Points: 1.33 of 4

Answer 1

a) The linear regression equation for the "full service" restaurant is:

y = 53.080 + 7.46x

b) The linear regression equation for the "fast food" restaurant is:

y = -2.104 - 93.761x

c) To find the year when the revenue from the two types of restaurants was the same, we set the two equations equal to each other and solve for x:

53.080 + 7.46x = -2.104 - 93.761x

Combining like terms:

100.221x = -55.184

Divide both sides by 100.221 to isolate x:

x = -55.184 / 100.221

x ≈ -0.550 (rounded to the nearest thousandth)

Since x represents the number of years after 1990, we add 1990 to get the approximate year:

1990 - 0.550 ≈ 1989 (rounded to the nearest year)

Therefore, the revenue from the two types of restaurants was approximately the same in the year 1989.