To find the student’s overall average, we use the weights provided for each component of the class:

• Midterm exam: 40% of the final grade.
• Homework: 20% of the final grade.
• Final exam: 40% of the final grade.

Step 1: Calculate the weighted average

The formula for the overall average is:

$\text{Overall average} = (\text{Midterm score} \times 0.40) + (\text{Homework score} \times 0.20) + (\text{Final exam score} \times 0.40)$

Substitute the given scores:

$\text{Overall average} = (87 \times 0.40) + (88 \times 0.20) + (83 \times 0.40)$

Now, I'll calculate that.

$87 \times 0.40 = 34.8$ $88 \times 0.20 = 17.6$ $83 \times 0.40 = 33.2$

Now sum these values:

$34.8 + 17.6 + 33.2 = 85.6$

The student’s overall average is 85.6%.

Step 2: Determine if it is possible to get a 4.0 (92% or higher)

Next, we want to know what score the student would need on the final exam to achieve an overall average of 92%. The midterm and homework scores remain the same, so we can set up an equation where $x$ is the final exam score:

$\text{Overall average} = (87 \times 0.40) + (88 \times 0.20) + (x \times 0.40)$

We want the overall average to be 92:

$92 = (87 \times 0.40) + (88 \times 0.20) + (x \times 0.40)$

We already know that:

$(87 \times 0.40) + (88 \times 0.20) = 34.8 + 17.6 = 52.4$

So the equation becomes:

$92 = 52.4 + (x \times 0.40)$

Now solve for $x$:

$92 - 52.4 = x \times 0.40$ $39.6 = x \times 0.40$ $x = \frac{39.6}{0.40} = 99$

So the student would have needed to score 99% on the final exam to get a 4.0 in the class.

Conclusion:

• The student’s overall average is 85.6%.
• The score needed on the final exam to get a 4.0 is 99%.

Let me know if you'd like more details, or if you have any questions!

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Here are 5 related questions:

1. What if the student’s midterm score was 90? How would that change their final grade?
2. How would the overall average change if homework were worth 30% instead of 20%?
3. What is the impact on the final grade if the final exam score were 5 points higher?
4. How could improving homework scores affect the overall average in a different scenario?
5. What would the student’s grade be if only the midterm and final exams were considered?

Tip: Always check the weight of each component in your course to understand how it affects your final grade!