Question
Find the weighted average of J=0 and K=8 with a ratio of 1:3.(1 point) Responses 8 8 6.5 6.5 4 4 6.25
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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 following formula for weighted averages:
\[
\text{Weighted Average} = \frac{(J \times w_1) + (K \times w_2)}{w_1 + w_2}
\]
Here, \( J = 0 \), \( K = 8 \), and the weights \( w_1 = 1 \) and \( w_2 = 3 \).
Now plug in the values:
\[
\text{Weighted Average} = \frac{(0 \times 1) + (8 \times 3)}{1 + 3}
\]
This simplifies to:
\[
\text{Weighted Average} = \frac{0 + 24}{4} = \frac{24}{4} = 6
\]
So the weighted average is \( 6 \).
Looking at the provided options, the response is not listed directly, but it seems there's a potential error or mismatch. The correct answer based on the calculation should be 6.
However, if we are to consider rounding decisions or looking closely at specific options of values presented (like 6.25, 6.5, etc.), note we do not have an exact match.
Thus, based on the calculation, the answer is 6 which is not included. If you had options or errors to reconsider, please provide that context.
In the absence of it, preferring rounding decisions might direct towards responses: 6.25 or 6.5, etc., if the route of approximation was part of your question intent.
\[
\text{Weighted Average} = \frac{(J \times w_1) + (K \times w_2)}{w_1 + w_2}
\]
Here, \( J = 0 \), \( K = 8 \), and the weights \( w_1 = 1 \) and \( w_2 = 3 \).
Now plug in the values:
\[
\text{Weighted Average} = \frac{(0 \times 1) + (8 \times 3)}{1 + 3}
\]
This simplifies to:
\[
\text{Weighted Average} = \frac{0 + 24}{4} = \frac{24}{4} = 6
\]
So the weighted average is \( 6 \).
Looking at the provided options, the response is not listed directly, but it seems there's a potential error or mismatch. The correct answer based on the calculation should be 6.
However, if we are to consider rounding decisions or looking closely at specific options of values presented (like 6.25, 6.5, etc.), note we do not have an exact match.
Thus, based on the calculation, the answer is 6 which is not included. If you had options or errors to reconsider, please provide that context.
In the absence of it, preferring rounding decisions might direct towards responses: 6.25 or 6.5, etc., if the route of approximation was part of your question intent.