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Suppose the linear regression line [tex] y = 4.009x - 77.531 [/tex] predicts a pizza parlor's profits based on the number of pizzas sold. If [tex] x [/tex] represents the number of pizzas sold and [tex] y [/tex] represents the pizza parlor's profits in dollars, about how much can the pizza parlor expect in profits if it sells 325 pizzas?

A. [tex]$\$[/tex]1150[tex]$
B. $[/tex]\[tex]$1375$[/tex]
C. [tex]$\$[/tex]1300[tex]$
D. $[/tex]\[tex]$1225$[/tex]

Sagot :

GinnyAnsweridn
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]
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