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3 years ago

Which of the following is algebraically equivalent to the sum of and ?

Mathematics

1 answer:

Naddika [18.5K]3 years ago

4 0

What is the question marks value?

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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

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

8 0

2 years ago

A jacket cost £70 but is reduced by 12% in a sale. What is its new price

klemol [59]

100% = 70
1% = .7 (divide by 100)
12% = 8.4 (Multiply 1% by 12)
70 - 8.4 = 61.6 (New Price)
Hope this helped! Got any questions just ask!

8 0

3 years ago

GEOMETRY HELP ASAP!!!!!!!!!!!!!!!!!!!

vovangra [49]

Area of equilateral triangle = a^2/4 * √3 so side of triangle = a

but if area of equilateral triangle = area of square multiplied by √3 then area of square = a^2 / 4 so side of square = a/2

the ratio length of side triangle to length side of square = a: a/2 that means the side of triangle is doubled the side of square

answer
a) 2:1

6 0

3 years ago

Which ordered pair (x, y) satisfies the system of equations? 1/2 x − 1/4 y = 10 1/8 x − 1/8 y = 19

zlopas [31]

Answer:

-36,-192

Step-by-step explanation:

5 0

2 years ago

The school is planting a circular garden. If the

Tatiana [17]

Answer:

<u>The area of the circular garden is 28.3 square feet</u>

Step-by-step explanation:

Let's recall that the area of a circle is π * r², therefore if the diameter of the circular garden is 6 feet, the area is:

Diameter = 6 feet ⇒ radius = (6/2) = 3 feet

Area of the circular garden = π * 3²

Area of the circular garden = 3.1416 * 9

Area of the circular garden = 28.2744

<u>Area of the circular garden = 28.3 square feet</u>

8 0

3 years ago