Certainly! Let's solve the given linear regression equation step-by-step to determine the expected profit when 275 pizzas are sold.
The linear regression equation we're given is:
[tex]\[ y = 2.009x - 37.131 \][/tex]
Here, [tex]\( x \)[/tex] is the number of pizzas sold, and [tex]\( y \)[/tex] is the profit in dollars. We need to find the profit [tex]\( y \)[/tex] when [tex]\( x = 275 \)[/tex].
Substitute [tex]\( x = 275 \)[/tex] into the equation:
[tex]\[ y = 2.009(275) - 37.131 \][/tex]
First, calculate the product of 2.009 and 275:
[tex]\[ 2.009 \times 275 = 552.475 \][/tex]
Next, subtract 37.131 from this product:
[tex]\[ 552.475 - 37.131 = 515.344 \][/tex]
Therefore, the expected profit [tex]\( y \)[/tex] when 275 pizzas are sold is:
[tex]\[ y \approx 515.344 \][/tex]
Now we can compare this result to the options given:
A. [tex]$515$[/tex]
B. [tex]$550$[/tex]
C. [tex]$585$[/tex]
D. [tex]$480$[/tex]
The closest option to the calculated profit of [tex]$515.344 is:
A. $[/tex]515[tex]$
Hence, the pizza parlor can expect a profit of approximately \$[/tex]515 if it sells 275 pizzas.
