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]
