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Complete the sentences with the correct preposition or phrase. Also, answer the math question about modal height.

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Here are the answers to the questions:

  1. Children are generally supposed to have a fondness ....... toys. The correct preposition to use with "fondness" is "for".

    • A. for
  2. Fathers are fond ....... their daughters. The correct preposition to use with "fond" is "of".

    • B. of
  3. It is important to emphasize ....... your main points in a presentation. The verb "emphasize" does not require a preposition.

    • C. none
  4. It took me all night to draw ....... a programme for today's meeting. The phrasal verb "draw up" means to prepare or draft. * D. up

  5. Old Major, the hardworking horse, died ....... harness. The idiom "to die in harness" means to die while still working. * D. in

  6. The heights (in feet) of seven boys are 4.5, 3.5, 4.8, 5.1, 4.5, 5.0, and 4.5. What is the modal height?

  1. List the given heights.

    $$
    4.5, 3.5, 4.8, 5.1, 4.5, 5.0, 4.5
    $$
    
  2. Identify the frequency of each height.

    • 3.5 appears 1 time.
    • 4.5 appears 3 times.
    • 4.8 appears 1 time.
    • 5.0 appears 1 time.
    • 5.1 appears 1 time.
  3. The mode is the value that appears most frequently.

    The height 4.5 appears 3 times, which is more than any other height.
    *   **A. 4.5**
    

    103. The marks of seven students in mathematics examinations are 50, 45, 65, 70, 82, 75, 60. What is the median mark?

  4. Arrange the marks in ascending order.

    $$
    45, 50, 60, 65, 70, 75, 82
    $$
    
  5. Identify the number of data points, nn.

    There are 7 marks, so $n=7$.
    
  6. Calculate the position of the median.

    For an odd number of data points, the median is the $\left(\frac{n+1}{2}\right)$-th value.
    $$
    \text{Median position} = \frac{7+1}{2} = \frac{8}{2} = 4
    $$
    
  7. Find the mark at the calculated position.

    The 4-th value in the ordered list is 65.
    *   **D. 65**
    

    104. A student got an average of 48 marks from three subjects. How many marks should he obtain in the fourth subject if the average pass mark is 50%?

  8. Calculate the total marks from the first three subjects.

    $$
    \text{Total marks for 3 subjects} = \text{Average} \times \text{Number of subjects}
    $$
    $$
    \text{Total marks for 3 subjects} = 48 \times 3 = 144
    $$
    
  9. Determine the required total marks for an average of 50% across four subjects.

    Assuming the average pass mark of 50% refers to the average across all four subjects.
    $$
    \text{Required total marks for 4 subjects} = \text{Required average} \times \text{Number of subjects}
    $$
    $$
    \text{Required total marks for 4 subjects} = 50 \times 4 = 200
    $$
    
  10. Calculate the marks needed in the fourth subject.

    $$
    \text{Marks in 4th subject} = \text{Required total marks} - \text{Total marks from 3 subjects}
    $$
    $$
    \text{Marks in 4th subject} = 200 - 144 = 56
    $$
    *   **C. 56**
    

    105. The average marks of 40 males and 60 females are 75 and 82 respectively. What is the average mark of all the students?

  11. Calculate the total marks for males.

    $$
    \text{Total marks for males} = \text{Number of males} \times \text{Average mark of males}
    $$
    $$
    \text{Total marks for males} = 40 \times 75 = 3000
    $$
    
  12. Calculate the total marks for females.

    $$
    \text{Total marks for females} = \text{Number of females} \times \text{Average mark of females}
    $$
    $$
    \text{Total marks for females} = 60 \times 82 = 4920
    $$
    
  13. Calculate the total marks for all students.

    $$
    \text{Total marks for all students} = \text{Total marks for males} + \text{Total marks for females}
    $$
    $$
    \text{Total marks for all students} = 3000 + 4920 = 7920
    $$
    
  14. Calculate the total number of students.

    $$
    \text{Total number of students} = \text{Number of males} + \text{Number of females}
    $$
    $$
    \text{Total number of students} = 40 + 60 = 100
    $$
    
  15. Calculate the average mark of all students.

    $$
    \text{Average mark of all students} = \frac{\text{Total marks for all students}}{\text{Total number of students}}
    $$
    $$
    \text{Average mark of all students} = \frac{7920}{100} = 79.2
    $$
    *   **C. 79.2**
    
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