To find the weighted average, we use the formula:
\[ \text{Weighted Average} = \frac{(w_1 \cdot x_1) + (w_2 \cdot x_2)}{w_1 + w_2} \]
where \(w_1\) is the weight on the first number, \(x_1\) is the first number, \(w_2\) is the weight on the second number, and \(x_2\) is the second number.
In this case:
- \(x_1 = -3\)
- \(x_2 = 5\)
- \(w_1 = \frac{3}{5}\)
- \(w_2 = \frac{2}{5}\)
Now, substitute the values into the formula:
\[ \text{Weighted Average} = \frac{\left(\frac{3}{5} \cdot (-3)\right) + \left(\frac{2}{5} \cdot 5\right)}{\frac{3}{5} + \frac{2}{5}} \]
Calculating the numerator:
\[ \frac{3}{5} \cdot (-3) = -\frac{9}{5} \]
\[ \frac{2}{5} \cdot 5 = \frac{10}{5} = 2 \]
Thus, the numerator becomes:
\[ -\frac{9}{5} + 2 = -\frac{9}{5} + \frac{10}{5} = \frac{1}{5} \]
Now, calculate the denominator:
\[ \frac{3}{5} + \frac{2}{5} = \frac{5}{5} = 1 \]
So, the weighted average is:
\[ \text{Weighted Average} = \frac{\frac{1}{5}}{1} = \frac{1}{5} = 0.2 \]
Therefore, the weighted average of the numbers -3 and 5 is 0.2.