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Irina18 [472]
3 years ago
15

M5-3/2x less than or equal to 1/3

Mathematics
1 answer:
Zepler [3.9K]3 years ago
8 0

Answer: choice A

Step-by-step explanation:

by rearranging the initial inequality you’ll get

\frac{3}{2} x\leq 5-\frac{1}{3}

which equals

\frac{3}{2} x\leq\frac{14}{3}

then multiply both sides by 2/3

x\leq \frac{28}{9}

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A survey was conducted of 42 students who take math, Eng lish, or history. In the survey, 15 students said they take math and hi
strojnjashka [21]

Answer:

16 students take only English or only Math.

Step-by-step explanation:

We can solve this problem by treating these values as sets, and building the Venn Diagram.

I am going to say that:

A is the number of students who take Math.

B is the number of students who take English.

C is the number of students who take History.

We have that:

A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)

In which a is the number of students that only take Math, A \cap B is the number of students who take both Math and English, A \cap C is the number of students that take both Math and History, and A \cap B \cap C is the number of students that take all these classes.

By the same logic, we have:

B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)

C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)

This diagram has the following subsets:

a,b,c,(A \cap B), (A \cap C), (B \cap C), (A \cap B \cap C)

There were 42 students suveyed. This means that:

a + b + c + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 42

We start finding the values from the intersection of three sets.

12 students said they take math, English, and history. This means that:

A \cap B \cap C = 12

18 students said they take English and history. This also takes into account those who take math, english and history. So:

(B \cap C) + (A \cap B \cap C) = 18

B \cap C = 6

17 students said they take math and English.

(A \cap B) + (A \cap B \cap C) = 17

A \cap B = 5

15 students said they take math and history

(A \cap C) + (A \cap B \cap C) = 15

A \cap C = 3

2 students said they only take history.

c = 2

How many students take only English or only math?

This is a + b, that we can find by the following formula:

a + b + c + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 42

a + b + 2 + 5 + 3 + 6 + 12 = 42

a + b = 16

16 students take only English or only Math.

4 0
3 years ago
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