Question
Two points are on a number line at 2 and 6. The original weighted average is 4, with a ratio of 1: 1. What will be the new weighted average if the ratio changes to 2: 1? (1 point)
1. 5
2. 3.3
3. 4
4. 2.67
1. 5
2. 3.3
3. 4
4. 2.67
Answers
GPT-4o mini
To find the new weighted average when the ratio changes from 1:1 to 2:1, we start by calculating the original weighted average.
Given the points are 2 and 6, and they are weighted equally (1:1), the original weighted average can be calculated as follows:
\[
\text{Weighted Average} = \frac{(1 \cdot 2) + (1 \cdot 6)}{1 + 1} = \frac{2 + 6}{2} = \frac{8}{2} = 4
\]
Now, we are asked to find the new weighted average with a ratio of 2:1. This means we will have:
- The number 2 with a weight of 2
- The number 6 with a weight of 1
The new weighted average is calculated as follows:
\[
\text{New Weighted Average} = \frac{(2 \cdot 2) + (1 \cdot 6)}{2 + 1} = \frac{4 + 6}{3} = \frac{10}{3} \approx 3.33
\]
Thus, the new weighted average is approximately 3.3.
The answer is:
**2. 3.3**
Given the points are 2 and 6, and they are weighted equally (1:1), the original weighted average can be calculated as follows:
\[
\text{Weighted Average} = \frac{(1 \cdot 2) + (1 \cdot 6)}{1 + 1} = \frac{2 + 6}{2} = \frac{8}{2} = 4
\]
Now, we are asked to find the new weighted average with a ratio of 2:1. This means we will have:
- The number 2 with a weight of 2
- The number 6 with a weight of 1
The new weighted average is calculated as follows:
\[
\text{New Weighted Average} = \frac{(2 \cdot 2) + (1 \cdot 6)}{2 + 1} = \frac{4 + 6}{3} = \frac{10}{3} \approx 3.33
\]
Thus, the new weighted average is approximately 3.3.
The answer is:
**2. 3.3**