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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]$750
B. $[/tex]675
C. [tex]$900
D. $[/tex]825



Answer :

GinnyAnswer
To determine the expected profits for the pizza parlor if it sells 275 pizzas, we use the given linear regression equation [tex]\( y = 3.009x - 77.131 \)[/tex].

Here’s a step-by-step solution:

1. Identify the given information:
- The linear regression equation: [tex]\( y = 3.009x - 77.131 \)[/tex]
- The number of pizzas sold, [tex]\( x = 275 \)[/tex]

2. Substitute [tex]\( x = 275 \)[/tex] into the equation to calculate the expected profits [tex]\( y \)[/tex].

3. Perform the calculation:

Start by plugging in the value of [tex]\( x \)[/tex]:

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

4. Simplify the expression:

First, multiply 3.009 by 275:

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

5. Next, subtract 77.131 from the result:

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

6. Therefore, the expected profits [tex]\( y \)[/tex] are approximately [tex]\( 750.344 \)[/tex] dollars.

Now, compare this value to the provided options:
A. [tex]\( \$750 \)[/tex]
B. [tex]\( \$675 \)[/tex]
C. [tex]\( \$900 \)[/tex]
D. [tex]\( \$825 \)[/tex]

The closest value to [tex]\( 750.344 \)[/tex] dollars is option A: [tex]\( \$750 \)[/tex].

Hence, if the pizza parlor sells 275 pizzas, it can expect the profits to be about [tex]\( \$750 \)[/tex]. The correct answer is:

A. [tex]\( \$750 \)[/tex]

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