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jeka57 [31]
3 years ago
14

Please answer all the questions if possible, due 2morrow... also, is what I did for the top answer right?

Mathematics
1 answer:
geniusboy [140]3 years ago
8 0
1a. It does say y is "less than 8", which means 7, 6, 5, 4, etc. So it should be y < 8, with the arrow going from 8 to the the left. 
Everything else in 1 is correct. 

For 2, you're just picking out which of the given numbers satisfy the inequality, for example
a. 14, 15, 16 are solutions. 13 is not because it is less than 14.

3. Same thing as 1 
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When the members of a family discussed where their annual reunion should take​ place, they found that out of all the family​ mem
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The total number of family members is 21.

Step-by-step explanation:

To solve this problem, we must build the Venn's Diagram of these sets.

I am going to say that:

-The set A represents those that would not go to a park.

-The set B represents those who would not go to a beach.

-The set C represents those who would not go to the family cottage.

The value d represents those who would go to all three places.

We have that:

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

In which a are those that would only not go to a park, A \cap B are those who would not got to a park or to the beach, A \cap C are those who would not go to a park or to the famili cottage. And A \cap B \cap C are those that would not go to any of these places.

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 values:

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

The total number of family members is the sum of all these values:

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

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

5 would not go to a park or a beach or to the family​ cottage.

This means that A \cap B \cap C = 5

1 would go to all three places. This means that d = 1.

8 would go to neither a park nor the family​ cottage

This means that:

A \cap C + (A \cap B \cap C) = 8

A \cap C = 3

8 would go to neither a beach nor the family​ cottage

B \cap C + (A \cap B \cap C) = 8

B \cap C = 3

7 would go to neither a park nor a​ beach

A \cap B + (A \cap B \cap C) = 7

A \cap B = 2

15 would not go to the family​ cottage

C = 15

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

15 = c + 3 + 3 + 5

c = 4

12 would not go to a​ beach

B = 12

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

12 = b + 3 + 2 + 5

b = 2

11 would not go to a​ park

A = 11

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

11 = a + 2 + 3 + 5

a = 1

Now, we can find the total number of family members.

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

T = 1 + 2 + 4 + 1 + 2 + 3 + 3 + 5

T = 21

The total number of family members is 21.

5 0
3 years ago
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