To find the weighted average of the numbers 1 and 6, with a weight of [tex]\(\frac{2}{3}\)[/tex] on the first number and [tex]\(\frac{1}{3}\)[/tex] on the second number, we follow these steps:
1. Identify the values and their respective weights:
- First number ([tex]\(num1\)[/tex]): 1
- Second number ([tex]\(num2\)[/tex]): 6
- Weight of the first number ([tex]\(weight1\)[/tex]): [tex]\(\frac{2}{3}\)[/tex]
- Weight of the second number ([tex]\(weight2\)[/tex]): [tex]\(\frac{1}{3}\)[/tex]
2. Multiply each number by its respective weight:
- [tex]\(num1 \times weight1 = 1 \times \frac{2}{3} = \frac{2}{3}\)[/tex]
- [tex]\(num2 \times weight2 = 6 \times \frac{1}{3} = 2\)[/tex]
3. Add the weighted values to find the weighted average:
- Weighted average = [tex]\(\frac{2}{3} + 2\)[/tex]
4. Convert the fractions to a common denominator, if necessary, and sum:
- [tex]\(\frac{2}{3} = \frac{2}{3}\)[/tex]
- [tex]\(2 = \frac{6}{3}\)[/tex]
- Add the fractions: [tex]\(\frac{2}{3} + \frac{6}{3} = \frac{8}{3}\)[/tex]
5. Simplify the result, if possible:
- [tex]\(\frac{8}{3} \approx 2.6666666666666665\)[/tex]
Therefore, the weighted average of the numbers 1 and 6, with given weights, is approximately [tex]\(2.67\)[/tex].
By identifying the choices, the closest value to our calculated weighted average is [tex]\(2.7\)[/tex].
So, the correct choice is [tex]\(2.7\)[/tex].
Answer: [tex]\(2.7\)[/tex]
