To find the weighted average of the numbers -3 and 5 with [tex]\(\frac{3}{5}\)[/tex] of the weight on the first number and [tex]\(\frac{2}{5}\)[/tex] on the second number, follow these steps:
1. Identify the numbers and their corresponding weights.
- The first number is -3, and its weight is [tex]\(\frac{3}{5}\)[/tex].
- The second number is 5, and its weight is [tex]\(\frac{2}{5}\)[/tex].
2. Multiply each number by its respective weight to find the weighted contributions.
- The contribution of the first number: [tex]\(-3 \cdot \frac{3}{5} = -\frac{9}{5}\)[/tex].
- The contribution of the second number: [tex]\(5 \cdot \frac{2}{5} = 2\)[/tex].
3. Add the weighted contributions to get the weighted average.
- Weighted average = [tex]\(-\frac{9}{5} + 2\)[/tex].
4. Convert these fractions and perform the addition.
- [tex]\(-\frac{9}{5} = -1.8\)[/tex]
- 2 remains as it is.
Thus, we have:
- Weighted average = [tex]\(-1.8 + 2 = 0.2\)[/tex].
Therefore, the weighted average of the numbers -3 and 5 with the given weights is [tex]\(0.2\)[/tex].
The correct answer is:
[tex]\[ \boxed{0.2} \][/tex]
