Question

1. solve the equation. 4(2x + 3) = 2x - 4
2. write an equation in point - slope form to represent the table. then explain the meaning of the slope.
3. identify the function family, domain, range, and intercepts. function family: domain: range: intercepts:
4. solve the system by substitution. 3x - 8y = - 7 x = - 2y
5. the mean weight of boys ages 2 - 12 is displayed in the table. the linear regression model y = 5.957x + 12.3 represents the data. use the model to predict the mean weight of boys age 5. the actual mean weight of boys age 5 is 40. determine the residual value for boys age 5. does this value indicate an overestimate or underestimate? explain.

Explanation:

Step1: Substitute \(x = 5\) into the regression model

The linear regression model is \(y=5.957x + 12.3\).
Substitute \(x = 5\) into the equation:
\(y=5.957\times5+12.3\)

$$
LATEXBLOCK0
$$

Step2: Calculate the residual

The formula for the residual \(e\) is \(e = \text{actual value}-\text{predicted value}\).
The actual value \(y_{actual}=40\), and the predicted value \(y_{predicted} = 42.085\).
\(e=40 - 42.085=- 2.085\)

Answer:

The predicted mean weight of 5 - year - old boys is \(42.085\) lbs. The residual value is \(-2.085\). Since the residual \(e=-2.085<0\), the regression model overestimates the mean weight of 5 - year - old boys.