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wel
3 years ago
11

In a certain year the price of gasoline rose by 20% during January, fell by 20% during February, rose by 25% in March, and fell

by x% in April. The price of gasoline at the end of April was the same as it had been at the beginning of January. Find the value of x.
Mathematics
1 answer:
zavuch27 [327]3 years ago
8 0

Answer:

Fell by 25%

Step-by-step explanation:

+20% January

-20% February (20-20 is zero, so we're back to the original price we started at here)

+25% March

?? April

Currently, we are 25% more than what we had, so to get back to normal, the price needs to go down by 25 percent. This will put us back to zero. Put another way...

+20%-20%+25%-25%=0% (Original Price)

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ANEK [815]

Step-by-step explanation:

We have to prove both implications of the affirmation.

1) Let's assume that A \ B and C \ D are disjoint, we have to prove that A ∩ C ⊆ B ∪ D.

We'll prove it by reducing to absurd.

Let's suppose that A ∩ C ⊄ B ∪ D. That means that there is an element x that belongs to A ∩ C but not to B ∪ D.

As x belongs to A ∩ C, x ∈ A and x ∈ C.

As x doesn't belong to B ∪ D, x ∉ B and x ∉ D.

With this, we can say that x ∈ A \ B and x ∈ C \ D.

Therefore, x ∈ (A \ B) ∩ (C \ D), absurd!

It's absurd because we were assuming that A \ B and C \ D were disjoint, therefore their intersection must be empty.

The absurd came from assuming that A ∩ C ⊄ B ∪ D.

That proves that A ∩ C ⊆ B ∪ D.

2) Let's assume that A ∩ C ⊆ B ∪ D, we have to prove that A \ B and C \ D are disjoint (i.e.  A \ B ∩ C \ D is empty)

We'll prove it again by reducing to absurd.

Let's suppose that  A \ B ∩ C \ D is not empty. That means there is an element x that belongs to  A \ B ∩ C \ D. Therefore, x ∈ A \ B and x ∈ C \ D.

As x ∈ A \ B, x belongs to A but x doesn't belong to B.  

As x ∈ C \ D, x belongs to C but x doesn't belong to D.

With this, we can say that x ∈ A ∩ C and x ∉ B ∪ D.

So, there is an element that belongs to A ∩ C but not to B∪D, absurd!

It's absurd because we were assuming that A ∩ C ⊆ B ∪ D, therefore every element of A ∩ C must belong to B ∪ D.

The absurd came from assuming that A \ B ∩ C \ D is not empty.

That proves that A \ B ∩ C \ D is empty, i.e. A \ B and C \ D are disjoint.

7 0
3 years ago
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The answer is choice D:
exponents are listed from highest to lowest.
8 0
3 years ago
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Firstly, we have to find out what 10% of $25000 is. To do this, multiply $25000 by 0.1 (10% in decimal form): \$25000 \times 0.1=\$2500 . <em>$2500 is the 10% raise.</em>

Next, to find your first new salary, add $25000 and $2500 together: \$25000+\$2500=\$27500 . <u>$27500 is your new salary after the 10% raise.</u>

Next, we need to find 10% of $27500. It's a similar process as to finding 10% of $25000. \$27500 \times 0.1=\$2750 . <em>$2750 is your 10% cut.</em>

Next, since this is a cut, subtract $2750 from $27500. \$27500-\$2750=\$24750 . <u>$24750 is your new salary after the 10% cut.</u>

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Answer:

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Step-by-step explanation:

Since there is 12 months in a year, divide 12 by 3.

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Now, multiply 4 by 2.

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This gives you the answer of 8 months.

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