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

Sagot :

GinnyAnsweridn
To determine the expected profits for the pizza parlor when they sell 275 pizzas, we can use the given linear regression equation:

[tex]\[ y = 2.009 x - 37.131 \][/tex]

Here, [tex]\( y \)[/tex] represents the profits in dollars and [tex]\( x \)[/tex] represents the number of pizzas sold. We need to calculate [tex]\( y \)[/tex] when [tex]\( x = 275 \)[/tex].

Substitute [tex]\( x = 275 \)[/tex] into the equation:

[tex]\[ y = 2.009(275) - 37.131 \][/tex]

Now, calculate step by step:

1. Multiply [tex]\( 2.009 \)[/tex] by [tex]\( 275 \)[/tex]:
[tex]\[ 2.009 \times 275 = 552.475 \][/tex]

2. Subtract [tex]\( 37.131 \)[/tex] from [tex]\( 552.475 \)[/tex]:
[tex]\[ 552.475 - 37.131 = 515.344 \][/tex]

Therefore, the expected profit when selling 275 pizzas is \[tex]$515. Hence, the correct answer is: D. \$[/tex]515
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