1. **Problem 18:** Boyo had a mean score of 80 in two subjects. When the mark of a third subject was added, the mean dropped by 2. Find the third mark.
2. The mean of two subjects is 80, so the total marks for two subjects is:
$$\text{Total} = 2 \times 80 = 160$$
3. When the third subject is added, the mean drops by 2, so the new mean is:
$$80 - 2 = 78$$
4. The total marks for three subjects with the new mean is:
$$3 \times 78 = 234$$
5. To find the third mark, subtract the total of the first two subjects from the total of all three:
$$\text{Third mark} = 234 - 160 = 74$$
6. **Answer for problem 18:** The third mark is **74**.
7. **Problem 19:** The table shows the scores of students in a mental mathematics competition with five questions. Find the fraction of students who scored 80% or more.
8. Scoring 80% or more means scoring at least 4 out of 5 questions correctly.
9. From the table, frequencies for scores 4 and 5 are:
- Score 4: 10 students
- Score 5: 6 students
10. Total students who scored 80% or more:
$$10 + 6 = 16$$
11. Total number of students is the sum of all frequencies:
$$2 + 3 + 4 + 5 + 10 + 6 = 30$$
12. The fraction of students scoring 80% or more is:
$$\frac{16}{30} = \frac{8}{15}$$
13. **Answer for problem 19:** The fraction is **\frac{8}{15}**.
Mean Score Fraction F1Bb71
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.