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Rudiy27
2 years ago
12

10/8c - 4/8 = 6/8 + 5/8c​

Mathematics
1 answer:
siniylev [52]2 years ago
5 0

Answer: c = 2

Step-by-step explanation: Solve for c by simplifying both sides of the equation, then isolating the variable.

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Find the number of elements in A 1 ∪ A 2 ∪ A 3 if there are 200 elements in A 1 , 1000 in A 2 , and 5, 000 in A 3 if (a) A 1 ⊆ A
lina2011 [118]

Answer:

a. 4600

b. 6200

c. 6193

Step-by-step explanation:

Let n(A) the number of elements in A.

Remember, the number of elements in A_1 \cup A_2 \cup A_3 satisfies

n(A_1 \cup A_2 \cup A_3)=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)

Then,

a) If A_1\subseteq A_2, n(A_1 \cap A_2)=n(A_1)=200, and if A_2\subseteq A_3, n(A_2\cap A_3)=n(A_2)=1000

Since A_1\subseteq A_2\; and \; A_2\subseteq A_3, \; then \; A_1\cap A_2 \cap A_3= A_1

So

n(A_1 \cup A_2 \cup A_3)=\\=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\=200+1000+5000-200-200-1000-200=4600

b) Since the sets are pairwise disjoint

n(A_1 \cup A_2 \cup A_3)=\\n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\200+1000+5000-0-0-0-0=6200

c) Since there are two elements in common to each pair of sets and one element in all three sets, then

n(A_1 \cup A_2 \cup A_3)=\\=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\=200+1000+5000-2-2-2-1=6193

8 0
3 years ago
Which is a stretch of an exponential decay function?
jeyben [28]

Answer:

c

Step-by-step explanation:

for the most recent your daddy

4 0
3 years ago
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Is 4 meters bigger than 450 centimeters
Reptile [31]
No.

4 meters is 400 centimeters, so is smaller than 450 centimeters.
8 0
3 years ago
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What is the value of the expression (2)^6?
Mumz [18]
The value of the expression (2)^6 is 64.
6 0
3 years ago
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write an equation using ''x'' and then solve the equation. on the new year eve there were 7,580 tons of cargo loaded in the morn
vovikov84 [41]

Answer:  12,997 - 7,580 = x

x= 5417

Step-by-step explanation: 12,997 - 7580 = 5417

Hope this helps

8 0
3 years ago
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