Solve the compound inequality. Other than ∅, use interval notation to express the solution set and graph the
solution set on a number line.
-On the first four exams, your grades are $75,89,60$, and 76 . You are hoping to earn a $C$ in the course. This will occur if the average of your five exam grades is greater than or equal to 70 and less than 80 . What range of grades on the fifth exam will result in earning a $C$ ?
A) $[ 50,100 )$
B) $( 50,100 ]$
C) $[ 40,90 )$
D) $( 40,90 ]$

Question

Quizplus · Accepted Answer

To find the range of grades on the fifth exam that will result in earning a C, we first calculate the total points needed to achieve an average between 70 and 80 over five exams. The total points from the first four exams are $75 + 89 + 60 + 76 = 300$. For an average of 70 over five exams, the total points needed are $70 \times 5 = 350$. For an average of 80, the total points needed are $80 \times 5 = 400$. Therefore, the fifth exam score must make the total fall between 350 and 400 points. Subtracting the current total of 300 from these values gives us the range for the fifth exam score: $350 - 300 = 50$ and $400 - 300 = 100$. Thus, the fifth exam score must be in the range $[50, 100)$ to achieve a C.

Solve the Compound Inequality 75,89,6075,89,6075,89,60 , and 76 You Are Hoping to Earn A Use

Solve the Compound Inequality $75,89,60$ , and 76 You Are Hoping to Earn A Use