Question

1. tracy made a venn diagram to compare the numbers of students in her english and history classes. which of the following conjectures is not supported by the venn diagram?

tracy has more friends in her history class.
there are 22 people in tracys history class.
there are fewer students in tracys english class.
there are 36 students in tracys english and history classes.

Explanation:

Step1: Calculate the number of students in English class

The number of students in English class is \(14 + 7=21\).

Step2: Calculate the number of students in History class

The number of students in History class is \(7+15 = 22\).

Step3: Calculate the total number of students in both classes

The total number of students in both classes is \(14 + 7+15=36\).

Answer:

Tracy has more friends in her history class (since \(22>21\)), there are \(22\) people in Tracy’s history class (\(7 + 15\)), there are fewer students in Tracy’s English class (\(21<22\)), and there are \(36\) students in Tracy’s English and history classes (\(14+7 + 15\)). So, all the statements except “Tracy has more friends in her history class” (assuming the numbers represent students, not friends - if we assume the problem is about students) might be wrong. But if we assume the numbers are about students:
The number of students in English is \(21\), in History is \(22\), total \(36\).
If we assume the options:

• For “Tracy has more friends in her history class” (if we assume the numbers are about students, this is wrong as we don’t know about friends). But if we assume the problem has a typo and it's about students:

If we check each option:

• Number of students in History: \(7 + 15=22\)
• Number of students in English: \(14 + 7=21\)
• Total students: \(14+7 + 15=36\)

If we assume the first option “Tracy has more friends in her history class” (assuming the data is about students, not friends - a wrong - worded option). But if we go by pure calculation:
If we assume all options are about students:
The number of students in English \(=14 + 7=21\), in History \(=7+15 = 22\), total \(=14+7+15=36\)
So the conjecture “Tracy has more friends in her history class” (assuming it should be students) is a wrong - statement as we are given data about students.

But if we follow the calculation - based on student numbers:
The answer is “Tracy has more friends in her history class” (assuming a mis - word in the option, should be students). But if we assume the options as they are:
Since we have no information about friends (only student numbers in classes), the conjecture “Tracy has more friends in her history class” is not supported by the Venn - diagram (as the Venn - diagram shows student numbers in classes, not friendship status).