To predict the weight of a 10-foot-tall elephant, we'll use the given line of best fit equation:
[tex]\[
\hat{y} = 0.823x - 0.344
\][/tex]
Here [tex]\( \hat{y} \)[/tex] is the predicted weight in tons, and [tex]\( x \)[/tex] is the height in feet. We need to substitute [tex]\( x = 10 \)[/tex] feet into this equation to find the predicted weight.
So, substitute [tex]\( x = 10 \)[/tex] into the equation:
[tex]\[
\hat{y} = 0.823 \times 10 - 0.344
\][/tex]
Now perform the multiplication and subtraction:
[tex]\[
\hat{y} = 8.23 - 0.344
\][/tex]
Finally, subtract 0.344 from 8.23:
[tex]\[
\hat{y} = 7.886
\][/tex]
Therefore, the predicted weight of a 10-foot-tall elephant is 7.886 tons.
So, the correct answer is:
[tex]\[
\hat{y} = 0.823x - 0.344; \ a \ 10 \text{-foot-tall elephant is predicted to weigh } 7.886 \text{ tons}
\][/tex]
