Answer:
Laura will need to grade more than 80 in the final exam to earn a B
Step-by-step explanation:
Average Value
The mean or average of a data set is found by adding all numbers and then dividing by the number of values in the set. Written as a formula:
[tex]\displaystyle \bar x=\frac{\sum x_i}{n}[/tex]
Where xi is the value of each data and n is the total number of values.
Laura has the grades of 70, 86, 81, and 83 in computer applications class. If we call x to the grade on the final exam, then the sum of her grades is:
[tex]\sum x_i=70+86+81+83+x[/tex]
[tex]\sum x_i=320+x[/tex]
The average of her grades is:
[tex]\displaystyle \bar x=\frac{320+x}{5}[/tex]
For Laura to earn a B the average must be greater than or equal to 80 and less than 90. Thus:
[tex]\boxed{\displaystyle 80\le \frac{320+x}{5} < 90}[/tex]
This is the inequality that must be satisfied. Now we solve it.
Multiply by 5:
[tex]5*80\le 320+x < 5*90[/tex]
Operating:
[tex]400\le 320+x < 450[/tex]
Subtracting 320:
[tex]80\le x < 120[/tex]
Laura will need to grade more than 80 in the final exam to earn a B
