Math Problem Statement

In your Spanish class, your final grade is based on four categories. The categories are tests, labs, homework assignments, and a final exam. The final average for the course is the weighted average of scores earned in these categories with the following weights: Tests (49%), Labs (10%), Homework (17%), Final Exam (24%). The user earned 44% on tests, 85% on labs, 73% on homework, and 62% on the final exam. Determine the weighted average.

Solution

To determine the weighted average, we need to multiply each score by its respective weight and then sum these products. The weights are given as percentages, and the grades are also provided in percentages. Here's the information from the table:

  • Tests: 44% (weight: 49%)
  • Labs: 85% (weight: 10%)
  • Homework: 73% (weight: 17%)
  • Final Exam: 62% (weight: 24%)

We calculate the weighted average using the following formula:

Weighted Average=(Test Grade×Test Weight)+(Lab Grade×Lab Weight)+(Homework Grade×Homework Weight)+(Final Exam Grade×Final Exam Weight)\text{Weighted Average} = (\text{Test Grade} \times \text{Test Weight}) + (\text{Lab Grade} \times \text{Lab Weight}) + (\text{Homework Grade} \times \text{Homework Weight}) + (\text{Final Exam Grade} \times \text{Final Exam Weight})

Now I'll calculate this for you.The weighted average for your course is approximately 57.35%.

Would you like more details or have any further questions?

Here are 5 related questions you might find useful:

  1. How can the weights of different components affect the final grade?
  2. What happens if one of the grades is significantly higher than the others?
  3. How does a weighted average differ from a simple average?
  4. Can a weighted average be higher than any individual component's score?
  5. How could the final exam weight influence the course grade?

Tip: Always ensure the weights add up to 100% when calculating a weighted average.

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Math Problem Analysis

Mathematical Concepts

Weighted Average
Percentages

Formulas

Weighted Average = (Test Grade × Test Weight) + (Lab Grade × Lab Weight) + (Homework Grade × Homework Weight) + (Final Exam Grade × Final Exam Weight)

Theorems

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Suitable Grade Level

Grades 9-12