To calculate how a 48% score on a quiz will affect a 71% overall grade, you'll need to know the weight of the quiz in relation to the overall grade.
Let's assume the quiz is worth \( W \) percent of the overall grade. The calculation can be expressed as follows:
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Calculate the current weighted score: \[ \text{Current Grade Contribution} = 71 \times (1 - W) \]
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Calculate the new grade contribution from the quiz: \[ \text{Quiz Contribution} = 48 \times W \]
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The new overall grade would then be: \[ \text{New Overall Grade} = \text{Current Grade Contribution} + \text{Quiz Contribution} \]
Substituting the formulas gives: \[ \text{New Overall Grade} = 71 \times (1 - W) + 48 \times W \] \[ \text{New Overall Grade} = 71 - 71W + 48W \] \[ \text{New Overall Grade} = 71 - 23W \]
You would need to plug in the weight \( W \) (as a decimal, where 100% = 1.0) to find the new grade.
For example:
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If the quiz is worth 10% of the overall grade (W = 0.1), then: \[ \text{New Overall Grade} = 71 - 23(0.1) = 71 - 2.3 = 68.7% \]
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If it is worth 20% (W = 0.2): \[ \text{New Overall Grade} = 71 - 23(0.2) = 71 - 4.6 = 66.4% \]
You can use this formula to determine the new grade based on the weight of the quiz. Please provide the weight of the quiz if you want a specific calculation.
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