Question
Find the weighted average of J=0 and K=8 with a ratio of 1:3.(1 point)
Answers
GPT-4o mini
To find the weighted average of \( J = 0 \) and \( K = 8 \) with a ratio of 1:3, you can use the formula for weighted average:
\[
\text{Weighted Average} = \frac{(J \cdot w_1) + (K \cdot w_2)}{w_1 + w_2}
\]
Here, \( w_1 \) and \( w_2 \) are the weights corresponding to \( J \) and \( K \) respectively. Given the ratio of 1:3, you can set:
- \( w_1 = 1 \) (for \( J \))
- \( w_2 = 3 \) (for \( K \))
Now substitute the values into the formula:
\[
\text{Weighted Average} = \frac{(0 \cdot 1) + (8 \cdot 3)}{1 + 3}
\]
Calculating this step by step:
1. Calculate \( 0 \cdot 1 = 0 \).
2. Calculate \( 8 \cdot 3 = 24 \).
3. Add the products: \( 0 + 24 = 24 \).
4. Calculate the sum of the weights: \( 1 + 3 = 4 \).
5. Divide the total by the sum of the weights:
\[
\text{Weighted Average} = \frac{24}{4} = 6
\]
Thus, the weighted average of \( J = 0 \) and \( K = 8 \) with a ratio of 1:3 is **6**.
\[
\text{Weighted Average} = \frac{(J \cdot w_1) + (K \cdot w_2)}{w_1 + w_2}
\]
Here, \( w_1 \) and \( w_2 \) are the weights corresponding to \( J \) and \( K \) respectively. Given the ratio of 1:3, you can set:
- \( w_1 = 1 \) (for \( J \))
- \( w_2 = 3 \) (for \( K \))
Now substitute the values into the formula:
\[
\text{Weighted Average} = \frac{(0 \cdot 1) + (8 \cdot 3)}{1 + 3}
\]
Calculating this step by step:
1. Calculate \( 0 \cdot 1 = 0 \).
2. Calculate \( 8 \cdot 3 = 24 \).
3. Add the products: \( 0 + 24 = 24 \).
4. Calculate the sum of the weights: \( 1 + 3 = 4 \).
5. Divide the total by the sum of the weights:
\[
\text{Weighted Average} = \frac{24}{4} = 6
\]
Thus, the weighted average of \( J = 0 \) and \( K = 8 \) with a ratio of 1:3 is **6**.