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2 years ago

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

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

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

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

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3 years ago

Which is a stretch of an exponential decay function?

jeyben [28]

Answer:

Step-by-step explanation:

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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.

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3 years ago

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Mumz [18]

The value of the expression (2)^6 is 64.

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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

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3 years ago

10/8c - 4/8 = 6/8 + 5/8c​

10/8c - 4/8 = 6/8 + 5/8c