To calculate your final weighted average, we'll use the formula for the weighted average, which is:
[tex]\[ \text{Weighted Average} = \frac{\sum (x \cdot w)}{\sum w} \][/tex]
where:
- [tex]\( x \)[/tex] represents each individual grade,
- [tex]\( w \)[/tex] represents the corresponding weight for each grade,
- [tex]\(\sum (x \cdot w)\)[/tex] is the sum of the products of each grade and its respective weight,
- [tex]\(\sum w\)[/tex] is the sum of the weights.
In this problem:
- Your midterm exam grade [tex]\( x_1 \)[/tex] is 95, and its weight [tex]\( w_1 \)[/tex] is 45% or 0.45.
- Your final exam grade [tex]\( x_2 \)[/tex] is 75, and its weight [tex]\( w_2 \)[/tex] is 55% or 0.55.
Using the formula, we can compute the weighted average step-by-step:
1. Calculate the product of each grade and its respective weight:
[tex]\[ x_1 \cdot w_1 = 95 \cdot 0.45 = 42.75 \][/tex]
[tex]\[ x_2 \cdot w_2 = 75 \cdot 0.55 = 41.25 \][/tex]
2. Sum these products:
[tex]\[ \sum (x \cdot w) = 42.75 + 41.25 = 84.0 \][/tex]
3. Sum the weights (in this case, the weights should sum to 1 since they represent percentages that add up to 100%):
[tex]\[ \sum w = 0.45 + 0.55 = 1.0 \][/tex]
4. Apply the weighted average formula:
[tex]\[ \text{Weighted Average} = \frac{84.0}{1.0} = 84.0 \][/tex]
5. To find the final rounded weighted average, round 84.0 to the nearest integer. Hence, the rounded weighted average is 84.
Therefore, your final weighted average is [tex]\( 84 \)[/tex].
