Question

question 1-5 on the number line below, point a has a weight of 26% and point b has a weight of 74%. what is the weighted average of points a and b? number line with a at -6, b at 7

Explanation:

Step1: Identify values of A and B

From the number line, point A is at -6 and point B is at 7. The weights are \( w_A = 0.26 \) (26%) and \( w_B = 0.74 \) (74%).

Step2: Apply weighted average formula

The weighted average formula is \( \bar{x} = w_A \cdot x_A + w_B \cdot x_B \).
Substitute \( x_A = -6 \), \( w_A = 0.26 \), \( x_B = 7 \), \( w_B = 0.74 \):
\( \bar{x} = 0.26 \times (-6) + 0.74 \times 7 \)

Step3: Calculate each term

First term: \( 0.26 \times (-6) = -1.56 \)
Second term: \( 0.74 \times 7 = 5.18 \)

Step4: Sum the terms

\( \bar{x} = -1.56 + 5.18 = 3.62 \)

Answer:

3.62