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On the first four​ exams, Steve's grades are 72​, 75​, 88​, and 93. There is still one more exam and he is hoping to earn a B in the course. This will occur if the average of his first five exam grades is greater than or equal to 75 and less than 95. What range of grades on the fifth exam will result in earning a​ B? The range of grades on the fifth exam that results in earning a B is nothing. If the highest grade is​ 100, then nothing. ​(Type your answers in interval​ notation.)

Respuesta :

Answer:[tex]47\leq x\leq 100[/tex]

Step-by-step explanation:

Given

Steve's grade are 72, 75, 88, and 93

Steve's wish to earn Grade B in the course and this can occur when average of first five exam grades is greater than or equal to 75 and less than to 95

Suppose x be the score of last exam

average of 5 exams [tex]P_{avg} =\frac{72+75+88+93+x}{5}=\frac{328+x}{5}[/tex]

[tex]75\leq P_{avg}< 95[/tex]

[tex]75\leq \frac{328+x}{5}[/tex]

[tex]375-328\leq x[/tex]

[tex]47\leq x[/tex]

and [tex]\frac{328+x}{5} <95[/tex]

[tex]x <475-328[/tex]

[tex]x <147[/tex]

but highest grade is 100

therefore [tex]x \leq 100[/tex]

thus belongs to [tex]47\leq x\leq 100[/tex]

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