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Suppose the linear regression line [tex]y = 2.009x - 37.131[/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 275 pizzas?

A. [tex]\[tex]$550[/tex]
B. [tex]\$[/tex]515[/tex]
C. [tex]\$585[/tex]
D. [tex]\$480[/tex]

Sagot :

GinnyAnsweridn
To determine the pizza parlor's expected profit when 275 pizzas are sold, we use the given linear regression equation [tex]\( y = 2.009x - 37.131 \)[/tex], where [tex]\( x \)[/tex] represents the number of pizzas sold and [tex]\( y \)[/tex] represents the profit in dollars.

Step-by-step:

1. Substitute [tex]\( x = 275 \)[/tex] into the equation:
[tex]\[ y = 2.009 \times 275 - 37.131 \][/tex]

2. Perform the multiplication:
[tex]\[ 2.009 \times 275 = 552.475 \][/tex]

3. Subtract the constant term from the result:
[tex]\[ 552.475 - 37.131 = 515.344 \][/tex]

Thus, the expected profit when 275 pizzas are sold is approximately [tex]\(\$515\)[/tex].

Therefore, the correct answer is:
B. \$515
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