Question

1. solve the equation.

4(2x + 3) = 2x - 4

1. write an equation in point - slope form to represent the table. then explain the meaning of the slope.
2. identify the function family, domain,
3. solve the system by substitution.

range, and intercepts.
3x - 8y = - 7
function family:
x = - 2y
domain:
range:
intercepts:

1. 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 regression model is \(y=5.957x + 12.3\). Substitute \(x = 5\) into it:
\(y=5.957\times5+12.3\)
First, calculate \(5.957\times5\): \(5.957\times5=(6 - 0.043)\times5=30-0.215 = 29.785\)
Then, \(y=29.785+12.3=42.085\)

Step2: Calculate the residual

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

Answer:

The predicted mean weight is \(42.085\) lbs. The residual value is \(-2.085\). Since the residual is negative (\(e=-2.085<0\)), it indicates an over - estimate. The predicted value (\(42.085\) lbs) is greater than the actual value (\(40\) lbs).