To find the weighted average of the numbers 1 and 5, where [tex]\(\frac{1}{4}\)[/tex] of the weight is on the first number and [tex]\(\frac{3}{4}\)[/tex] of the weight is on the second number, follow these detailed steps:
1. Identify the numbers and their respective weights:
- The first number is [tex]\(1\)[/tex] with a weight of [tex]\(\frac{1}{4}\)[/tex].
- The second number is [tex]\(5\)[/tex] with a weight of [tex]\(\frac{3}{4}\)[/tex].
2. Express the weights as decimals:
- The weight [tex]\(\frac{1}{4}\)[/tex] can be written as [tex]\(0.25\)[/tex].
- The weight [tex]\(\frac{3}{4}\)[/tex] can be written as [tex]\(0.75\)[/tex].
3. Multiply each number by its corresponding weight:
- For the first number: [tex]\(1 \times 0.25 = 0.25\)[/tex].
- For the second number: [tex]\(5 \times 0.75 = 3.75\)[/tex].
4. Add the weighted values together to find the weighted average:
- Sum: [tex]\(0.25 + 3.75 = 4.0\)[/tex].
So, the weighted average of the numbers 1 and 5, with [tex]\(\frac{1}{4}\)[/tex] of the weight on the first number and [tex]\(\frac{3}{4}\)[/tex] on the second number, is [tex]\(4.0\)[/tex].
