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4 years ago

Prove the divisibility of the following numbers: 5^23−5^21 by 24

2 answers:

6 0

5^23 - 5^21 = 5^(21+2) - 5^21
5^23 - 5^21 = 5^21*5^2 - 5^21*1
5^23 - 5^21 = 5^21*(5^2 - 1)
5^23 - 5^21 = 5^21*(25 - 1)
5^23 - 5^21 = 5^21*24
5^23 - 5^21 = 24*5^21
5^23 - 5^21 = 24*k

The original number is in the form 24k where k = 5^21, so this proves that the original number is a multiple of 24

Serga [27]4 years ago

4 0

5^21 is the answer to the question.

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Global Airlines operates two types of jet planes: jumbo and ordinary. On jumbo jets, 25% of the passengers are on business while

MArishka [77]

Answer:

The probability is $P(J|B) = 0.36$

Step-by-step explanation:

B =business

J=jumbo

Or =ordinary

From the question we are told that

The proportion of the passenger on business in the ordinary jet is $P(B| Or) = 0.25$

The proportion of the passenger on business in the jumbo jet is $P(B|J) = 0.30$

The proportion of the passenger on jumbo jets is $P(j) = 0.40$

The proportion of the passenger on ordinary jets is evaluated as

$1 - P(J) = 1- 0.40 = 0.60$

According to Bayer's theorem the probability a randomly chosen business customer flying with Global is on a jumbo jet is mathematically represented as

$P(J|B) = \frac{P(J) * P(B|J)}{P(J ) * P(B|J) + P(Or ) * P(B|Or)}$

substituting values

$P(J|B) = \frac{ 0.4 * 0.25}{0.4 * 0.25 + 0.6 * 0.3}$

$P(J|B) = 0.36$

Step-by-step explanation:

8 0

3 years ago

name the lengths of the sides of three rectangles with a perimeter of 12 units use only whole numbers

AysviL [449]

The perimeter of a rectangle is 2(w+l)
We can find the lengths by setting the equation equal to 12.
12=2(w+l)
12÷2=(2(w+l))÷2
6=w+l
6=1+5
6=2+4
6=3+3
These are the lengths of the sides of three rectangles with a perimeter of 12 units.
You're probably wondering why the third one has two of the same number, because that's usually how the lengths of sides of squares are, not rectangles.
Well, there's this wonderful thing about the rules of shapes.
<em>Squares ARE rectangles.
</em>Because they follow the rules for a rectangle, squares are also classified as rectangles.
So, the rectangle side lengths are as follows:
1 unit by 5 units
2 units by 4 units
3 units by 3 units
<em />

8 0

3 years ago

0.18(y-9)+0.06y=0.04y-0.9

Ksju [112]

Simplify both sides then isolate the variable and it gives you y=3.6

7 0

3 years ago

Principal, $3000; Annual interest rate, 5.4%; time, 4 years<br> The Balance after 4 years is?

Neporo4naja [7]

Answer: 777600

Step-by-step explanation:

you times 12 by 4 then you times 3000 by 5.4 and add the two answers

3 0

3 years ago

Round 248,739 to the nearest hundred

vampirchik [111]

Look at your hundredth spot which is where the 7 is. So…

248, 739

Since 3 is not 5 or higher you cant round 7 up to 8. So your correct answer is 248,700

Hope this helps!

7 0

3 years ago