Question

on a number line, coordinate -2 has a weight of 2 and coordinate 15 has a weight of 5. which expression can be used to find the weighted average?
-2(2)+15(5)
\frac{-2 + 15}{7}
-2(5)+15(2)
\frac{-2(2)+15(5)}{7}

Explanation:

Step1: Recall the weighted - average formula

The formula for the weighted average of two numbers \(x_1\) and \(x_2\) with weights \(w_1\) and \(w_2\) is \(\frac{w_1x_1 + w_2x_2}{w_1+w_2}\).
Here, \(x_1=-2\), \(w_1 = 2\), \(x_2 = 15\), and \(w_2=5\).

Step2: Substitute the values into the formula

First, calculate the numerator: \(w_1x_1+w_2x_2=-2\times2 + 15\times5\).
Then, calculate the denominator: \(w_1 + w_2=2 + 5=7\).
So the weighted - average formula gives \(\frac{-2(2)+15(5)}{7}\).

Answer:

\(\frac{-2(2)+15(5)}{7}\) (the fourth option)