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You might need: 囲 Calculator Jacob distributed a survey to his fellow students asking them how many hours they spent on the Internet in the past day. He also asked them to rate their mood on a scale from 0 to 10 , with 10 being the happiest. A line was fit to the data to model the relationship. Which of these linear equations best describes the given model? Choose 1 answer: (A) hat(y)=x+7.5 (B) hat(y)=-x+7.5 (c) hat(y)=-(1)/(2)x+7.5 Based on this equation, estimate the mood rating for a student that spent 5.5 hours online. ◻

You might need: 囲 Calculator\newlineJacob distributed a survey to his fellow students asking them how many hours they spent on the Internet in the past day. He also asked them to rate their mood on a scale from 00 to 1010 , with 1010 being the happiest. A line was fit to the data to model the relationship.\newlineWhich of these linear equations best describes the given model?\newlineChoose 11 answer:\newline(A) y^=x+7.5 \hat{y}=x+7.5 \newline(B) y^=−x+7.5 \hat{y}=-x+7.5 \newline(c) y^=−12x+7.5 \hat{y}=-\frac{1}{2} x+7.5 \newlineBased on this equation, estimate the mood rating for a student that spent 55.55 hours online.\newline□ \square

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Full solution

Q. You might need: 囲 Calculator\newlineJacob distributed a survey to his fellow students asking them how many hours they spent on the Internet in the past day. He also asked them to rate their mood on a scale from 00 to 1010 , with 1010 being the happiest. A line was fit to the data to model the relationship.\newlineWhich of these linear equations best describes the given model?\newlineChoose 11 answer:\newline(A) y^=x+7.5 \hat{y}=x+7.5 \newline(B) y^=−x+7.5 \hat{y}=-x+7.5 \newline(c) y^=−12x+7.5 \hat{y}=-\frac{1}{2} x+7.5 \newlineBased on this equation, estimate the mood rating for a student that spent 55.55 hours online.\newline□ \square
  1. Identify Equations: Identify the given equations: (A) y^=x+7.5 \hat{y} = x + 7.5 (B) y^=−x+7.5 \hat{y} = -x + 7.5 (C) y^=−12x+7.5 \hat{y} = -\frac{1}{2}x + 7.5
  2. Choose Correct Equation: Choose the correct equation: Since mood rating decreases with more hours online, the slope should be negative. Correct equation: (c) y^=−12x+7.5 \hat{y} = -\frac{1}{2}x + 7.5
  3. Calculate Mood Rating: Calculate the mood rating for 5.55.5 hours online: y^=−12(5.5)+7.5\hat{y} = -\frac{1}{2}(5.5) + 7.5
  4. Perform Multiplication: Perform the multiplication: −12(5.5)=−2.75-\frac{1}{2}(5.5) = -2.75
  5. Add Result: Add the result to 7.57.5: y^=7.5−2.75=4.75\hat{y} = 7.5 - 2.75 = 4.75

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