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Sagot :
Let's go through the questions step-by-step:
### Part (a)
Question: If P, L, and I represent set of students who replied for Pokhara, Lumbini, and Ilam respectively, then write set of students in cardinality notation who replied for all places.
Answer:
In mathematical notation, the number of students who replied that all three places are appropriate (Pokhara, Lumbini, and Ilam) is represented as [tex]\( n(P \cap L \cap I) = 15 \)[/tex].
### Part (b)
Question: Represent the above information in a Venn diagram.
Answer:
To create the Venn diagram, let's use the following information:
- 40 students replied for Pokhara.
- 30 students replied for Lumbini.
- 45 students replied for Ilam.
- 15 students replied for all three places.
- 5 students did not express any view.
Since a Venn diagram can't be drawn here, I will describe its structure:
1. Draw three intersecting circles representing Pokhara (P), Lumbini (L), and Ilam (I).
2. Label the intersecting area of all three circles as 15.
3. The numbers specific to each place or intersection should ensure that the total count matches the 40 for Pokhara, 30 for Lumbini, and 45 for Ilam.
4. The intersections can be determined, considering the exclusive and shared counts.
### Part (c)
Question: How many students are studying in class 10 of Sharada Secondary School? Calculate.
Answer:
To calculate the total number of students:
- We have students who considered Pokhara, Lumbini, or Ilam suitable.
- Since 15 students considered all three places, this overlap needs to be subtracted twice.
- There are 5 students with no opinion that should be added to the total.
Let's summarize:
[tex]\[ 40 \text{ (Pokhara)} + 30 \text{ (Lumbini)} + 45 \text{ (Ilam)} - 2 \times 15 \text{ (All three)} + 5 \text{ (No opinion)} = 90 \][/tex]
Thus, the total number of students in class 10 is [tex]\( 90 \)[/tex].
### Part (d)
Question: If 5 students who did not express any view in the survey replied for Lumbini, what is the ratio of students who replied for Pokhara only and Lumbini only as the appropriate place?
Answer:
If the 5 students with no opinion decided for Lumbini, the new count for Lumbini becomes [tex]\( 30 + 5 = 35 \)[/tex].
- Students who replied only for Pokhara will be [tex]\( 40 - 15 = 25 \)[/tex].
- Students who replied only for Lumbini will be [tex]\( 35 - 15 = 20 \)[/tex].
The ratio of students who replied only for Pokhara to those who replied only for Lumbini is:
[tex]\[ \frac{25}{20} = 1.25 \][/tex]
Therefore, the ratio is [tex]\( 1.25 \)[/tex].
These are the detailed steps and explanations for the given questions based on the survey data of Sharada Secondary School's class 10 students regarding the suitable locations for an educational tour.
### Part (a)
Question: If P, L, and I represent set of students who replied for Pokhara, Lumbini, and Ilam respectively, then write set of students in cardinality notation who replied for all places.
Answer:
In mathematical notation, the number of students who replied that all three places are appropriate (Pokhara, Lumbini, and Ilam) is represented as [tex]\( n(P \cap L \cap I) = 15 \)[/tex].
### Part (b)
Question: Represent the above information in a Venn diagram.
Answer:
To create the Venn diagram, let's use the following information:
- 40 students replied for Pokhara.
- 30 students replied for Lumbini.
- 45 students replied for Ilam.
- 15 students replied for all three places.
- 5 students did not express any view.
Since a Venn diagram can't be drawn here, I will describe its structure:
1. Draw three intersecting circles representing Pokhara (P), Lumbini (L), and Ilam (I).
2. Label the intersecting area of all three circles as 15.
3. The numbers specific to each place or intersection should ensure that the total count matches the 40 for Pokhara, 30 for Lumbini, and 45 for Ilam.
4. The intersections can be determined, considering the exclusive and shared counts.
### Part (c)
Question: How many students are studying in class 10 of Sharada Secondary School? Calculate.
Answer:
To calculate the total number of students:
- We have students who considered Pokhara, Lumbini, or Ilam suitable.
- Since 15 students considered all three places, this overlap needs to be subtracted twice.
- There are 5 students with no opinion that should be added to the total.
Let's summarize:
[tex]\[ 40 \text{ (Pokhara)} + 30 \text{ (Lumbini)} + 45 \text{ (Ilam)} - 2 \times 15 \text{ (All three)} + 5 \text{ (No opinion)} = 90 \][/tex]
Thus, the total number of students in class 10 is [tex]\( 90 \)[/tex].
### Part (d)
Question: If 5 students who did not express any view in the survey replied for Lumbini, what is the ratio of students who replied for Pokhara only and Lumbini only as the appropriate place?
Answer:
If the 5 students with no opinion decided for Lumbini, the new count for Lumbini becomes [tex]\( 30 + 5 = 35 \)[/tex].
- Students who replied only for Pokhara will be [tex]\( 40 - 15 = 25 \)[/tex].
- Students who replied only for Lumbini will be [tex]\( 35 - 15 = 20 \)[/tex].
The ratio of students who replied only for Pokhara to those who replied only for Lumbini is:
[tex]\[ \frac{25}{20} = 1.25 \][/tex]
Therefore, the ratio is [tex]\( 1.25 \)[/tex].
These are the detailed steps and explanations for the given questions based on the survey data of Sharada Secondary School's class 10 students regarding the suitable locations for an educational tour.
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