Answer:
To write the information in a cardinal diagram, we need to find the number of students who passed in mathematics and science separately. Let x be the number of students who passed in science only and y be the number of students who passed in mathematics only. Then we have:
x + y + 20 = 100 - 40 (total number of students who passed in at least one subject)
y = 2x (number of students who passed in mathematics is two times the number of students who passed in science)
Solving these equations, we get x = 13.33 and y = 26.67. However, since x and y must be integers, we can round them to x = 13 and y = 27. This means that one student who passed in both subjects is counted twice, so we need to subtract one from the total number of students who passed in at least one subject. Therefore, the cardinal diagram looks like this:
|---------------------|---------------------|
| | |
| Science | Mathematics |
| | |
| | |
| 13 | 20 | 27
| | |
| | |
|---------------------|---------------------|
| | |
| Failed | Failed |
| | |
| 40 | | 40
| | |
|---------------------|---------------------|
To find out how many students failed in mathematics, we need to add the number of students who failed in both subjects and the number of students who passed in science only. That is, 40 + 13 = 53.
To find out how many students passed in only one of the subjects, we need to add the number of students who passed in science only and the number of students who passed in mathematics only. That is, 13 + 27 = 40.
Explanation: