Question

Points A=7 and B=21 are on a number line. If A is weighted at 60% and B at 40%, what is the weighted average?(1 point)

Answer 1

To calculate the weighted average of points A and B, you can use the formula:

\[
\text{Weighted Average} = \frac{(A \times w_A) + (B \times w_B)}{w_A + w_B}
\]

where \( w_A \) and \( w_B \) are the weights for points A and B respectively.

Here, \( A = 7 \), \( B = 21 \), \( w_A = 0.6 \) (for A), and \( w_B = 0.4 \) (for B).

Now, plug the values into the formula:

\[
\text{Weighted Average} = \frac{(7 \times 0.6) + (21 \times 0.4)}{0.6 + 0.4}
\]

Calculating the numerator:

\[
7 \times 0.6 = 4.2
\]
\[
21 \times 0.4 = 8.4
\]

Adding these results together:

\[
4.2 + 8.4 = 12.6
\]

The denominator:

\[
0.6 + 0.4 = 1
\]

So, the weighted average is:

\[
\text{Weighted Average} = \frac{12.6}{1} = 12.6
\]

Thus, the weighted average is **12.6**.