Answer: The average of the next five quizzes = 83.
Step-by-step explanation:
Given : After taking 4 quizzes your average is 74 points out of 100.
Let q be the average of the next five quizzes.
Then , the total number of quizzes = 4+5=9
Since , [tex]\text{Average}=\dfrac{\text{Sum of observations}}{\text{Number of observations}}[/tex]
Sum of observations = (Average) x (Number of observations)
i.e. Sum of first four quizzes = 74 (4)
Sum of next five quizzes = 5q
According to the question , we have
[tex]79=\dfrac{74(4)+5q}{9}[/tex]
[tex]\Rightarrow\ 711=296+5q\\\\\Rightarrow\ 5q=711-296\\\\\Rightarrow\ 5q=415\\\\\Rightarrow\ q=\dfrac{415}{5}\\\\\Rightarrow\ q=83[/tex]
Hence, the average of the next five quizzes = 83.
