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Suppose the linear regression line [tex]\( y = 3.009x - 77.131 \)[/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]$900
B. \$[/tex]675
C. \[tex]$825
D. \$[/tex]750

Sagot :

GinnyAnswer
To determine the expected profit when 275 pizzas are sold, we use the given linear regression equation:

[tex]\[ y = 3.009 x - 77.131 \][/tex]

Here:
- [tex]\( x \)[/tex] represents the number of pizzas sold.
- [tex]\( y \)[/tex] represents the pizza parlor's profits in dollars.

Given that 275 pizzas are sold, we substitute [tex]\( x = 275 \)[/tex] into the equation to find [tex]\( y \)[/tex]:

[tex]\[ y = 3.009 \times 275 - 77.131 \][/tex]

By performing the calculation step-by-step, we can find the profit:

1. Multiply 3.009 by 275:

[tex]\[ 3.009 \times 275 = 827.475 \][/tex]

2. Subtract 77.131 from the result:

[tex]\[ 827.475 - 77.131 = 750.344 \][/tex]

Therefore, the expected profit when 275 pizzas are sold is approximately \[tex]$750. So, the correct answer is: D. \$[/tex]750
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