The difference between the number of students who got an F grade in the first and the second quarter is [tex]\frac{1}{30} .[/tex]
Step-by-step explanation:
Step 1:
First, we need to determine how many of the students got an F in the first quarter.
The number of students who got the grades A, B, C, and D is given. The remaining of the students got an F. So we need to add the values of the students who got grades other than F.
The students who got grades A, B, C, and D in the first quarter:[tex]\frac{2}{5} +\frac{1}{3} +\frac{1}{30} +\frac{1}{10} = \frac{12+10+1+3}{30} =\frac{26}{30}[/tex].
The students who got an F grade in the first quarter: [tex]1 - \frac{26}{30}= \frac{30-26}{30} = \frac{4}{30} .[/tex]
Step 2:
Now we determine the number of students who got an F in the second quarter.
We do the same and add the number of students who got grades other than F in the second quarter.
The students who got grades A, B, C, and D in the second quarter:[tex]\frac{1}{6} +\frac{1}{3} +\frac{7}{30} +\frac{1}{10} = \frac{5+10+7+3}{30} =\frac{25}{30}[/tex].
The students who got an F grade in the second quarter: [tex]1 - \frac{25}{30}= \frac{30-25}{30} = \frac{5}{30} .[/tex]
Step 3:
The difference in students who got an F grade in both terms = [tex]\frac{5}{30} -\frac{4}{30} =\frac{1}{30}[/tex].
So the difference between the number of students who got an F grade in the first and the second quarter is [tex]\frac{1}{30} .[/tex]
