Math Snap

STEP 1

Assumptions1. Emily's4 quiz scores are70,80,85, and85.
. Each quiz score contributes15% to the semester grade.
3. The final exam score contributes40% to the semester grade.
4. Emily wants to receive at least an82 for her semester grade.

STEP 2

First, we need to calculate the total contribution of the quiz scores to the semester grade. We can do this by multiplying each quiz score by its weight and then adding these up.
$$Quiz\, contribution = \sum_{i=1}^{4} Quiz\, score_i \\times Quiz\, weight$$

STEP 3

Now, plug in the given values for the quiz scores and their weights to calculate the quiz contribution.
$$Quiz\, contribution = (70 \\times15\%) + (80 \\times15\%) + (85 \\times15\%) + (85 \\times15\%)$$

STEP 4

Convert the percentages to decimal values.
$$15\% =0.15$$$$Quiz\, contribution = (70 \\times0.15) + (80 \\times0.15) + (85 \\times0.15) + (85 \\times0.15)$$

STEP 5

Calculate the quiz contribution.
$$Quiz\, contribution = (70 \\times0.15) + (80 \\times0.15) + (85 \\times0.15) + (85 \\times0.15) =48$$

STEP 6

Now that we have the quiz contribution, we can find the minimum final exam score Emily needs to get at least an82 for her semester grade. We can do this by subtracting the quiz contribution from the desired semester grade and then dividing by the weight of the final exam.
$$Final\, exam\, score = (Semester\, grade - Quiz\, contribution) / Final\, exam\, weight$$

STEP 7

Plug in the values for the semester grade, the quiz contribution, and the final exam weight to calculate the final exam score.
$$Final\, exam\, score = (82 -48) /40\%$$

STEP 8

Convert the percentage to a decimal value.
$$40\% =0.4$$$$Final\, exam\, score = (82 -48) /0.4$$

Calculate the minimum final exam score Emily needs.
$$Final\, exam\, score = (82 -48) /.4 =85$$Emily needs to score at least85 on her final exam to receive at least an82 for her semester grade.