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Maslowich
3 years ago
5

New Mexico has an area of 121,298 square miles. California has an area of 155,779 square miles. How many greater is the area in

square miles, of California than the area of New Mexico? show your work and explain how you know the answer is reasonable
Mathematics
1 answer:
makkiz [27]3 years ago
3 0
34,481 is the correct answer
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Using properties of sets show that : a) A ∩ (A’ U B) = A ∩ B b) A ∩ (A U B )’ = Ф
asambeis [7]

Answer:

a) From A ∩ A' = ∅, we have;

A ∩ (A' ∪ B) = A ∩ B

b) From A ∩ (A' ∩ B') = (A ∩ A') ∩ B' and A ∩ A' = ∅, we have;

A ∩ (A ∪ B)' = ∅

Step-by-step explanation:

a) By distributive law of sets, we have;

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

From the complementary law of sets, we have;

A ∩ A' = ∅

Therefore, for A ∩ (A' ∪ B) = A ∩ B, we have

A ∩ (A' ∪ B) = (A ∩ A') ∪ (A ∩ B) (distributive law of sets)

A ∩ A' = ∅ (complementary law of sets)

Therefore;

(A ∩ A') ∪ (A ∩ B) = ∅ ∪ (A ∩ B)  = (A ∩ B) (Addition to zero identity property)

∴  A ∩ (A' ∪ B) = A ∩ B

b) By De Morgan's law

(A ∪ B)' = A' ∩ B'

Therefore, A ∩ (A ∪ B)' = A ∩ (A' ∩ B')

By associative law of sets, we have;

A ∩ (A' ∩ B') = (A ∩ A') ∩ B'

A ∩ A' = ∅ (complementary law of sets)

Therefore, (A ∩ A') ∩ B' = ∅  ∩ B' = ∅

Which gives;

A ∩ (A ∪ B)' = ∅.

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3 years ago
Baker's Service Station Charges $38 For An Oil Change. Last Week The Cost Of The Oil Change Was 20% Off. What Was The cost of th
Katena32 [7]
38 divided by .20. to get the answer
8 0
2 years ago
The ratio of in-state to out-of-state visitors to the amusement park was 4 to 3. If there were 14,000 visitors to the park, how
exis [7]

Answer:

<em>6000 people</em>

Step-by-step explanation:

Given the ratio of in-state to out-of-state visitors to the amusement park was 4 to 3, the total ratio will be 4+3 = 7

Total visitors in the park = 14,000 visitors

Number of people that were out of state = 3/7 * 14000

Number of people that were out of state = 3 * 2000

Number of people that were out of state = 6000

<em>Hence there were 6000 people out of state.</em>

8 0
2 years ago
3. Buildings A and B are across the street from each other, 35m apart. From a point on the roof of Building A
FrozenT [24]

Answer:

The answer Building B

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2 years ago
50 POINTS PLEASE HELP FAST!!!!!
zavuch27 [327]

Answer:

this is 25 not 50

Step-by-step explanation:

give me brain 62 minus 14 is 48 divided by 2 is 24

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2 years ago
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