Grades A student has scores of 72%, 74%, and 78% on three exams. What percent score does he need on the last exam to earn a grade of no less than B (80%)?We know three scores. We are to find what the student must score on the last exam to earn a grade of B or higher.We can let x = the score on the fourth (and last) exam. To find the average grade, we add the four scores and divide by 4.To earn a grade no less than B, the student's average must be greater than or equal to 80%.The average ofthe four gradesmust be no less than 80.72 + 74 + 78 + x804We can solve the inequality for x.+ X> 80Combine like terms in the numerator: 72 + 74 + 78 = 224.4+ X> 4(80) To clear the inequality of the fraction, multiply both sides by 4.4224 + x 2Simplify each side.To isolate x, undo the addition of 224 by subtracting 224 from both sides.To earn a B, the student must score 96% or better on the last exam. Assuming the student cannot score higher than 100% on the exam, the solution set is written as[96, 100]. The graph is shown below.9293 94 9596 97 98 99 100Pick some numbers in the interval, and verify that the average of the four scores will be 80% or greater.

Given: A student has scores 72%,74% and 78% To find : The percent score needed on the last exam to…

Answered: student has scores of 72%, 74 ee…

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student has scores of 72%, 74 ee scores. We are to find what = the score on the fourth (and

Algebra and Trigonometry (6th Edition)

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra

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Concept explainers

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

Grades A student has scores of 72%, 74%, and 78% on three exams. What percent score does he need on the last exam to earn a grade of no less than B (80%)?
We know three scores. We are to find what the student must score on the last exam to earn a grade of B or higher.
We can let x = the score on the fourth (and last) exam. To find the average grade, we add the four scores and divide by 4.
To earn a grade no less than B, the student's average must be greater than or equal to 80%.
The average of
the four grades
must be no less than 80.
72 + 74 + 78 + x
80
4
We can solve the inequality for x.
+ X
> 80
Combine like terms in the numerator: 72 + 74 + 78 = 224.
4
+ X
> 4(80) To clear the inequality of the fraction, multiply both sides by 4.
4
224 + x 2
Simplify each side.
To isolate x, undo the addition of 224 by subtracting 224 from both sides.
To earn a B, the student must score 96% or better on the last exam. Assuming the student cannot score higher than 100% on the exam, the solution set is written as
[96, 100]. The graph is shown below.
92
93 94 95
96 97 98 99 100
Pick some numbers in the interval, and verify that the average of the four scores will be 80% or greater.

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