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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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15 stepsHere are the answers to the questions:
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Children are generally supposed to have a fondness ....... toys. The correct preposition to use with "fondness" is "for".
- A. for
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Fathers are fond ....... their daughters. The correct preposition to use with "fond" is "of".
- B. of
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It is important to emphasize ....... your main points in a presentation. The verb "emphasize" does not require a preposition.
- C. none
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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
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Old Major, the hardworking horse, died ....... harness. The idiom "to die in harness" means to die while still working. * D. in
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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?
List the given heights.
$$ 4.5, 3.5, 4.8, 5.1, 4.5, 5.0, 4.5 $$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.
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?
Arrange the marks in ascending order.
$$ 45, 50, 60, 65, 70, 75, 82 $$Identify the number of data points, .
There are 7 marks, so $n=7$.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. $$ \text{Median position} = \frac{7+1}{2} = \frac{8}{2} = 4 $$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%?
Calculate the total marks from the first three subjects.
$$ \text{Total marks for 3 subjects} = \text{Average} \times \text{Number of subjects} $$ $$ \text{Total marks for 3 subjects} = 48 \times 3 = 144 $$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. $$ \text{Required total marks for 4 subjects} = \text{Required average} \times \text{Number of subjects} $$ $$ \text{Required total marks for 4 subjects} = 50 \times 4 = 200 $$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?
Calculate the total marks for males.
$$ \text{Total marks for males} = \text{Number of males} \times \text{Average mark of males} $$ $$ \text{Total marks for males} = 40 \times 75 = 3000 $$Calculate the total marks for females.
$$ \text{Total marks for females} = \text{Number of females} \times \text{Average mark of females} $$ $$ \text{Total marks for females} = 60 \times 82 = 4920 $$Calculate the total marks for all students.
$$ \text{Total marks for all students} = \text{Total marks for males} + \text{Total marks for females} $$ $$ \text{Total marks for all students} = 3000 + 4920 = 7920 $$Calculate the total number of students.
$$ \text{Total number of students} = \text{Number of males} + \text{Number of females} $$ $$ \text{Total number of students} = 40 + 60 = 100 $$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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