Math Snap

STEP 1

Assumptions1. The weights for the categories are as follows Tests44%, Labs15%, Homework14%, Final Exam27%
. The grades earned in each category are as follows Tests45%, Labs83%, Homework91%, Final Exam56%
3. The final grade is a weighted average of the grades in each category

STEP 2

We need to calculate the weighted average. The formula for a weighted average is$$Weighted\, average = \frac{\sum (grade \times weight)}{\sum weight}$$However, since the sum of the weights is100%, we can simplify this to$$Weighted\, average = \sum (grade \times weight)$$

STEP 3

Now, we can plug in the grades and weights for each category into the formula.
$$Weighted\, average = (45\% \times44\%) + (83\% \times15\%) + (91\% \times14\%) + (56\% \times27\%)$$

STEP 4

Convert the percentages to decimal values.
$$Weighted\, average = (0.45 \times0.44) + (0.83 \times0.15) + (0.91 \times0.14) + (0.56 \times0.27)$$

STEP 5

Perform the multiplication for each category.
$$Weighted\, average =0.198 +0.1245 +0.1274 +0.1512$$

STEP 6

Add the results to get the weighted average.
$$Weighted\, average =0.198 +0.1245 +0.1274 +0.1512 =0.6011$$

Convert the decimal value back to a percentage.
$$Weighted\, average =0.6011 \times100\% =60.11\%$$The final course average is60.11%.