To solve this, let's define the problem variables clearly:

• Let the current Canvas grade be $79.9\%$, which accounts for all assignments except the fourth exam.
• The fourth exam is worth 15% of the total course grade.

Part 1: Highest course grade you can earn

The highest score you can achieve on the fourth exam is 100%. So, let's calculate the highest possible course grade:

• Let the current Canvas grade (before the fourth exam) represent 85% of the total course grade.
• The fourth exam will make up the remaining 15%.

Thus, the highest possible course grade $G$ can be calculated using the formula:

$G = 0.85 \times 79.9 + 0.15 \times 100$

Let's calculate this.

$G = 0.85 \times 79.9 + 0.15 \times 100 = 67.915 + 15 = 82.915\%$

So, the highest course grade you can earn is 82.92%.

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Part 2: Minimum score to earn a 73% course grade

To earn at least 73% in the course, the overall course grade should meet the threshold $G = 73\%$.

We can set up the equation as:

$0.85 \times 79.9 + 0.15 \times x = 73$

Where $x$ is the score needed on the fourth exam. Let's solve for $x$:

$67.915 + 0.15x = 73$

$0.15x = 73 - 67.915 = 5.085$

$x = \frac{5.085}{0.15} = 33.9$

So, you would need to score 34% on the fourth exam to earn at least a 73% overall.

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Part 3: Minimum score to earn an 83% course grade

To earn at least 83%, the course grade must be:

$0.85 \times 79.9 + 0.15 \times x = 83$

Solving for $x$:

$67.915 + 0.15x = 83$

$0.15x = 83 - 67.915 = 15.085$

$x = \frac{15.085}{0.15} = 100.57$

Since the maximum exam score is 100%, you would need to score 101%, which is impossible. Therefore, it's not possible to earn an 83% or higher.

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Part 4: Minimum score to earn a 93% course grade

To earn at least 93%, the course grade must be:

$0.85 \times 79.9 + 0.15 \times x = 93$

Solving for $x$:

$67.915 + 0.15x = 93$

$0.15x = 93 - 67.915 = 25.085$

$x = \frac{25.085}{0.15} = 167.23$

You would need 167.23% on the fourth exam, which is impossible. Therefore, it's also not possible to earn a 93% or higher.

Conclusion: Is it mathematically possible to get an A?

No, it is not mathematically possible to get an A given your current Canvas grade of 79.9%. You would need to score higher than 100% on the fourth exam, which is not feasible.

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Do you want details on any part of the explanation? Here are some related questions to practice:

1. If you need 85% on the fourth exam to earn a B in the course, what would be your final grade?
2. If the fourth exam counted for 20% instead of 15%, what would the new highest possible course grade be?
3. How would the required score change if you had 82% before the final exam?
4. What grade would you earn if you scored 75% on the fourth exam, given your current Canvas grade of 79.9%?
5. If the course had only three exams, how would the grading calculation change?

Tip: Always check how much weight each assignment or exam carries in your final grade to better predict your outcomes!