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To calculate a weighted average, use the formula [tex]\text{weighted average} = \frac{\sum xw}{\sum w}[/tex], where:

- [tex]w[/tex] is the weight of the piece of data,
- [tex]x[/tex] is the value of the piece of data,
- [tex]\sum xw[/tex] is the sum of the products of each piece of data multiplied by its weight,
- [tex]\sum w[/tex] is the sum of the weights.

Suppose that your final grade for a course is determined by a midterm exam and a final exam. The midterm exam is worth [tex]40\%[/tex] of your grade, and the final exam is worth [tex]60\%[/tex]. If your midterm grade is [tex]83[/tex] and your final exam grade is [tex]73[/tex], calculate your final weighted average.

Your final weighted average is [tex]\boxed{\phantom{0}}[/tex] (Round to the nearest integer as needed).

Sagot :

GinnyAnswer
To calculate your final weighted average, we need to consider the weights and grades of both the midterm and final exams.

Here is the detailed, step-by-step solution:

1. Identify the weights and grades for each exam:
- The midterm exam is worth 40% of your grade.
- The final exam is worth 60% of your grade.
- Your midterm grade is 83.
- Your final exam grade is 73.

2. Convert the percentages into decimal form for calculation:
- Midterm weight: 40% = 0.4
- Final weight: 60% = 0.6

3. Calculate the contribution of each exam to your final score:
- Midterm contribution: [tex]\( 83 \times 0.4 = 33.2 \)[/tex]
- Final exam contribution: [tex]\( 73 \times 0.6 = 43.8 \)[/tex]

4. Add the contributions to find the total weighted average:
- Total weighted average: [tex]\( 33.2 + 43.8 = 77.0 \)[/tex]

5. Round the weighted average to the nearest integer:
- Final weighted average: 77

Therefore, your final weighted average is 77 (rounded to the nearest integer).
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