Final answer:
The student is anticipated to pass 72 percent of all quizzes throughout the school year after passing 60 percent of the initial 20 quizzes and an expected 80 percent of the remaining 30 quizzes.
Step-by-step explanation:
The subject of this question involves calculating the overall percentage of passed quizzes in mathematics. The student initially passed 60 percent of 20 quizzes, which amounts to 12 quizzes.
For the remaining 30 quizzes (50 quizzes in total minus the 20 already taken), the student is expected to pass 80 percent, which would be 24 quizzes (80 percent of 30). To find the overall pass percentage, you add the passed quizzes together (12 initially passed quizzes + 24 expected to be passed in the remaining quizzes = 36 passed quizzes) and divide by the total number of quizzes taken (50). Then you multiply by 100 to get the percentage.
The calculation is as follows: (36 passed quizzes / 50 total quizzes) × 100 = 72%. Therefore, the student will pass 72 percent of all the quizzes in the entire year.