Question

question 3 of 5 sydney earned 91, 93, 93, 94, and 96 points on the 5 essays—each out of a total of 100 points—given so far this semester. how many points must she earn on her sixth essay, which is also out of 100 points, to average 90 points for the six essays assigned this semester? a 73 b 80 c 86 d 90

Explanation:

Step1: Calculate the total points needed

The average of 6 essays should be 90 points. The formula for the average $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 6$ and $\bar{x}=90$, so the total points needed for 6 essays is $90\times6=540$ points.

Step2: Calculate the sum of the first 5 - essay points

The points of the first 5 essays are 91, 93, 93, 94, and 96. The sum of these points is $91 + 93+93+94+96=467$ points.

Step3: Calculate the points needed on the sixth essay

Let the points on the sixth essay be $x$. We know that $467 + x=540$. Solving for $x$, we get $x=540 - 467=73$ points.

Answer:

A. 73