To determine how many sections of Alaina's spinner represent students who did not have homework, we first need to find the total number of students surveyed and then calculate the proportion of students who did not have homework.
From the data provided in the two-way table:
- Students who had homework: 8
- Students who did not have homework: 4
Now, we can find the total number of students: Total students = Students who had homework + Students who did not have homework Total students = 8 + 4 = 12
Next, we find the proportion of students who did not have homework: Proportion of students who did not have homework = (Students who did not have homework) / (Total students) Proportion of students who did not have homework = 4 / 12 = 1 / 3
Alaina's spinner has 6 congruent sections. To find out how many sections represent students who did not have homework, we multiply the total sections of the spinner by the proportion of students who did not have homework: Number of sections for no homework = Total sections × Proportion of students who did not have homework Number of sections for no homework = 6 × (1 / 3) = 2
Therefore, 2 sections of Alaina's spinner represent students who did not have homework.
The answer is 2.