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Maksim231197 [3]
3 years ago
9

Does the following situation describe opposite quantities combining to make zero? Explain.Tanya makes 2 cups of cleaning solutio

n and puts it into a spray bottle. She uses all the solution to clean her house. *
Yes, because the amount of cleaning solution in the bottle after Tanya uses the solution is not the same as before Tanya makes the solution.
Yes, because the amount of cleaning solution in the bottle after Tanya uses the solution is the same as before Tanya makes the solution.
No, because the amount of cleaning solution in the bottle after Tanya uses the solution is more than before Tanya makes the solution.
No, because the amount of cleaning solution in the bottle after Tanya uses the solution is less than before Tanya makes the solution.
Mathematics
1 answer:
Andreyy893 years ago
5 0

Answer:

Yes, because the amount of cleaning solution in the bottle after Tanya uses the solution is the same as before Tanya makes the solution.

Step-by-step explanation:

Tanya makes 2 cups then uses 2 cups.

2-2=0

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At a school with 100? students, 33 were taking? Arabic, 32 ?Bulgarian, and 40 Chinese. 9 students take only? Arabic, 12 take onl
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Answer: The answer is 4 and 32.

Step-by-step explanation: Let "A", "B" and "C" represents the set of students who were taking Arabic, Bulgarian and Chinese respectively.

The, according to the given information, we have

n(A)=33,~~n(B)=32,~~n(C)=40,~~n(A\cap B)=14.

Let 'p' represents the number of students who take all the three languages, then

n(A\cap B\cap C)=p.

Also,

n(A)-n(A\cap B)-n(A\cap C)+n(A\cap B\cap C)=9\\\\\Rightarrow n(A\cap B)+n(A\cap C)=24+p~~~~~~~~~~~~~~(a),\\\\n(A\cap B)+n(B\cap C)=20+p~~~~~~~~~~~~~~(b),\\\\n(B\cap C)+n(A\cap C)=20+p~~~~~~~~~~~~~~~(c).

From here, we get after subtracting equation(c) from (b) that

n(A\cap B)=n(A\cap C)=14.

Therefore,

p=14+14-24=4, and from equation (a), we find

n(B\cap C)=24-14=10.

Thus,

n(A\cap B\cap C)=4 and

n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)\\\\\Rightarrow n(A\cap B\cap C)=33+32+40-9-12-20+4\\\\\Rightarrow n(A\cap B\cap C)=68.

Thus, the number of students who take all the three languages is 4 and the number of students who take none of the languages is 100-68 = 32.

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Step-by-step explanation:

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