Questions: In your calculus 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. Assignments Tests Labs Homework Final Exam --- --- --- --- --- Weights 50% 10% 17% 23% Suppose you earned the following grades on each of the categories; 64% on tests, 59% on labs, 62% on homework assignments, and 77% on the final exam. Determine your weighted average in the course. Record the average below as a percentage accurate to two decimal places. Course Average: %

In your calculus 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. Assignments Tests Labs Homework Final Exam --- --- --- --- --- Weights 50% 10% 17% 23% Suppose you earned the following grades on each of the categories; 64% on tests, 59% on labs, 62% on homework assignments, and 77% on the final exam. Determine your weighted average in the course. Record the average below as a percentage accurate to two decimal places. Course Average: %
Transcript text: In your calculus 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. \begin{tabular}{|l|c|c|c|c|} \hline Assignments & Tests & Labs & Homework & Final Exam \\ \hline Weights & $50 \%$ & $10 \%$ & $17 \%$ & $23 \%$ \\ \hline \end{tabular} Suppose you earned the following grades on each of the categories; 64\% on tests, 59\% on labs, 62\% on homework assignments, and $77 \%$ on the final exam. Determine your weighted average in the course. Record the average below as a percentage accurate to two decimal places. Course Average: $\square$ \%
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Solution

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Solution Steps

Step 1: Identify the weights and corresponding grades

The weights for each category are:

  • Tests: 50% (0.50)
  • Labs: 10% (0.10)
  • Homework: 17% (0.17)
  • Final Exam: 23% (0.23)

The corresponding grades are:

  • Tests: 64%
  • Labs: 59%
  • Homework: 62%
  • Final Exam: 77%
Step 2: Multiply each grade by its weight

Calculate the weighted contribution of each category:

  • Tests: \( 64 \times 0.50 = 32 \)
  • Labs: \( 59 \times 0.10 = 5.9 \)
  • Homework: \( 62 \times 0.17 = 10.54 \)
  • Final Exam: \( 77 \times 0.23 = 17.71 \)
Step 3: Sum the weighted contributions

Add the weighted contributions to find the total weighted average: \[ 32 + 5.9 + 10.54 + 17.71 = 66.15 \]

Step 4: Round the result to two decimal places

The weighted average is \( 66.15\% \).

Final Answer

\(\boxed{66.15\%}\)

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