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Avro1

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In summary, there are 75 girls who play exactly two sports, with a total of 315 girls playing at least one sport. Of those, 100 play a fall sport, 150 play a winter sport, and 200 play a spring sport. Using the formula provided, we can find that $|A\cap B\cap C| = 40$, meaning that 40 girls play all three sports.

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Avro1

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MarkFL

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MHB

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Hello, and welcome to MHB! (Wave)

I would begin by constructing a Venn diagram:

View attachment 9104

We've got 7 variables...can you construct equations involving these variables from the given information?

I would begin by constructing a Venn diagram:

View attachment 9104

We've got 7 variables...can you construct equations involving these variables from the given information?

- #3

Olinguito

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You can also use this formula for any sets $A$, $B$, $C$:

$$|A\cup B\cup C|\ =\ |A|+|B|+|C|-|A\cap B|-|B\cap C|-|C\cap A|+|A\cap B\cap C|.$$

So, in this problem, $A$ might be the set of girls playing fall sports, $B$ the set of those playing winter sports, and $C$ the set of those playing spring sports; then you want to find $|A\cap B\cap C|$. Also, note that while you are not given $|A\cap B|$, $|B\cap C|$ or $|C\cap A|$ separately, you

There are 315 girls who play at least one sport in the school.

This cannot be determined without knowing the total number of girls in the school.

This cannot be determined without knowing how many sports are offered in the school.

It is possible that there are girls who do not play sports in the school, but this information cannot be determined from the given information.

This cannot be determined without knowing the number of boys who play sports in the school.

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