To determine the expected profits for the pizza parlor if it sells 325 pizzas, we need to use the given linear regression equation:
[tex]\[ y = 4.009x - 77.531 \][/tex]
Here, [tex]\( y \)[/tex] represents the profits in dollars, and [tex]\( x \)[/tex] represents the number of pizzas sold. Given that [tex]\( x = 325 \)[/tex], we can substitute 325 into the equation for [tex]\( x \)[/tex] and solve for [tex]\( y \)[/tex].
1. Substitute [tex]\( x = 325 \)[/tex] into the equation:
[tex]\[ y = 4.009 \times 325 - 77.531 \][/tex]
2. Perform the multiplication:
[tex]\[ 4.009 \times 325 = 1302.925 \][/tex]
3. Subtract 77.531 from the result:
[tex]\[ 1302.925 - 77.531 = 1225.394 \][/tex]
So, the expected profit when 325 pizzas are sold is approximately [tex]\( y = 1225.394 \)[/tex] dollars.
Given the possible answers:
A. [tex]$\$[/tex] 1150[tex]$
B. $[/tex]\[tex]$ 1375$[/tex]
C. [tex]$\$[/tex] 1300[tex]$
D. $[/tex]\[tex]$ 1225$[/tex]
The closest (and correct) answer to the calculated profit of \[tex]$1225.394 is:
D. $[/tex]\[tex]$ 1225$[/tex]
