According to the history 202 syllabus, the first paper is worth 25% of the course grade, the second paper is worth 20% of the course grade, and the final exam is worth 55% of the overall course grade. inara earns a 74% on the first term paper, an 99% on the second term paper, and the final exam has not happened yet. what is the lowest grade that inara would need on the final exam in order to earn at least an 80% in the course?

  76%

Step-by-step explanation:

Let f represent the score on the final. Then Inara wants the final grade to be ...

  0.25·74 +0.20·99 +0.55·x ≥ 80

  38.3 +0.55x ≥ 80

  0.55x ≥ 41.7

  x ≥ 41.7/0.55 ≈ 75.82

Inara needs a final exam grade of 76% or better to earn at least 80% in the course.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x