question 1(multiple choice worth 1 points)\n(linear models mc)\ndata were collected from several hospitals…

question 1(multiple choice worth 1 points)\n(linear models mc)\ndata were collected from several hospitals about the charge for medical procedures and the popularity of the procedures. the results were used to calculate the model ŷ = -58.25x + 927, where x represents the cost of the procedure in thousands of dollars and ŷ represents the predicted number of procedures performed. using the model, how much would a procedure cost that is predicted to be performed 600 times?\n$561\n$3,402\n$5,614\n$34,023

question 1(multiple choice worth 1 points)\n(linear models mc)\ndata were collected from several hospitals about the charge for medical procedures and the popularity of the procedures. the results were used to calculate the model ŷ = -58.25x + 927, where x represents the cost of the procedure in thousands of dollars and ŷ represents the predicted number of procedures performed. using the model, how much would a procedure cost that is predicted to be performed 600 times?\n$561\n$3,402\n$5,614\n$34,023

Answer

Explanation:

Step1: Substitute $\hat{y}$ value

We are given $\hat{y} = 600$ and the model $\hat{y}=-58.25x + 927$. Substitute $\hat{y}$ into the equation: $600=-58.25x + 927$.

Step2: Isolate the term with $x$

Subtract 927 from both sides: $600 - 927=-58.25x$, so $- 327=-58.25x$.

Step3: Solve for $x$

Divide both sides by - 58.25: $x=\frac{-327}{-58.25}\approx5.614$. Since $x$ is in thousands of dollars, the cost is $x\times1000 = 5.614\times1000 = 5614$ dollars.

Answer:

$5,614$ dollars (corresponding to the third option)