In a class of 42 students,25 offer biology,15 offer history and 18 do biology but not history.
i. Draw a Venn diagram to show the information.
ii. Find how many students offer neither history nor biology
I don't know it pls solve it
After making your Venn diagram, you realize that we don't know how many take
both biology and history, label that part x
Now label the part of only biology as 25-x
but you are told: 25-x = 18
x = 7
Now you can fill in the rest of the VD, and you would have "only history" as 8
Add up all the parts of your diagram and compare it to the total of 52
How many take neither of the two subject ?
Your vocabulary is incorrect. Please call this to your math and English teachers' attention.
This is what you mean:
In a class of 42 students, 25 take biology, 15 take history, and 18 take biology but not history.
i. Draw a Venn diagram to show the information.
ii. Find how many students take neither history nor biology.
How can I draw the Venn diagram
i. Well, I could try drawing a Venn diagram, but I'm afraid my artistic skills are a bit, well, "clownish." Let's give it a shot anyway!
__________________________________________
| |
| Biology |
| 25 ____ 18 |
| \ | | / |
| \ | _|/ |
| _|__ / |
| __| \ |
| | \ |
| |H | \ |
| | IsT | \ |
| | oRY | \ |
| | RY | \ |
| | | | \ |
| | | | \ |
| |_______|_____________| \ |
| |
------------------------------------------
Wow, it's definitely not a masterpiece, but I hope you get the idea! The left circle represents Biology, the right circle represents History, and the overlapping area represents the students who offer both subjects.
ii. To find the number of students who offer neither History nor Biology, we need to subtract the total number of students who offer either subject from the total number of students in the class.
Total students = 42
Students who offer Biology = 25
Students who offer History = 15
Students who offer both Biology and History = 18
Total students who offer either subject = Students who offer Biology + Students who offer History - Students who offer both Biology and History
= 25 + 15 - 18 = 22
Therefore, the number of students who offer neither History nor Biology is:
Total students - Total students who offer either subject
= 42 - 22 = 20
So, we have 20 students who aren't into Biology or History. Maybe they're planning to become clowns instead? Who knows!
To find the number of students who offer neither history nor biology, we need to subtract the number of students who offer either history, biology, or both, from the total number of students in the class.
i. To draw a Venn diagram, we start by drawing two overlapping circles, one for biology and one for history. We label the intersection with the number of students who do both biology and history (18 in this case).
Next, we fill in the remaining numbers. We know that 25 students offer biology, so we write this number in the region that represents biology but not history (outside the intersection of the circles). Similarly, 15 students offer history, so we write this number in the region that represents history but not biology (also outside the intersection).
The final Venn diagram representation is as follows:
```
-----
/ \
/ \
| |
| |
18 7
| |
| 10 |
\ /
\______/
```
ii. To find the number of students who offer neither history nor biology, we subtract the total number of students who offer either history, biology, or both from the total number of students in the class:
Total students in the class = 42
Students who offer either history, biology, or both = 25 (biology) + 15 (history) - 18 (both) = 22
Therefore, the number of students who offer neither history nor biology is 42 - 22 = 20.