The given equation for predicting $y$ is:

$y = 0.72x + 34.55$

We are given that $x = 87$ and $y = 95$. To find the predicted value and residual, we will use the following steps:

Step 1: Calculate the Predicted Value

Substitute $x = 87$ into the equation:

$\text{Predicted } y = 0.72(87) + 34.55$ $\text{Predicted } y = 62.64 + 34.55 = 97.19$

So, the predicted value is 97.19.

Step 2: Calculate the Residual

The residual is given by:

$\text{Residual} = \text{Actual } y - \text{Predicted } y$ $\text{Residual} = 95 - 97.19 = -2.19$

So, the residual is -2.19.

Final Answers:

• Predicted: 97.19
• Residual: -2.19

Would you like further explanation or any additional details?

Here are five related questions you could explore:

1. How would the predicted value change if $x$ increased by 10?
2. What happens to the residual if the actual $y$ value increases?
3. How does changing the slope in the equation affect the predicted value?
4. Can a residual ever be positive, and if so, what does that imply?
5. How does rounding affect the accuracy of the residual?

Tip: Always check whether rounding instructions are provided, as it can influence final answers when dealing with decimals!