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KatRina [158]
3 years ago
14

Many newspapers carry a certain puzzle in which the reader must unscramble letters to form words. how many ways can the letters

of wsilutawsiluta be​ arranged? identify the correct​ unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters.
Mathematics
1 answer:
Shtirlitz [24]3 years ago
5 0
<span>The letters wsilutawsiluta have 87178291200 unique combinations. Which we can find via the factorial rule (14x13x12... ect). There are no 14 letter words in english that contain this combination of letters (we can narrow the search by looking for 14 letter words with two W's of which none contain the same combination of letters). Ergo we can conclude the correct unscrambling is more than one word. The letters unscramble to spell 'lawsuit' twice. this is the only correct unscrambling (unless we allow the archaic word williwau). Thus there is a 1 in 87178291200 possibility of randomly unscrambling the letters</span>
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julia-pushkina [17]

A irrational number is a number that can't be expressed as a ratio of two whole numbers. That's it.

For examples (in increasing order of difficulty)

1 is a rational number because it is 1/1

0.75 is a rational number because it is equal to 3/4

2.333... (infinite number of digits, all equal to three) is rational because it is equal to 7/3.

sqrt(2) is not a rational number. This is not completely trivial to show but there are some relatively simple proofs of this fact. It's been known since the greek.

pi is irrational. This is much more complicated and is a result from 19th century.

As you see, there is absolutely no mention of the digits in the definition or in the proofs I presented.

Now the result that you probably hear about and wanted to remember (slightly incorrectly) is that a number is rational if and only if its decimal expansion is eventually periodic. What does it mean ?

Take, 5/700 and write it in decimal expansion. It is 0.0057142857142857.. As you can see the pattern "571428" is repeating in the the digits. That's what it means to have an eventually periodic decimal expansion. The length of the pattern can be anything, but as long as there is a repeating pattern, the number is rational and vice versa.

As a consequence, sqrt(2) does not have a periodic decimal expansion. So it has an infinite number of digits but moreover, the digits do not form any easy repeating pattern.

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2 years ago
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alina1380 [7]

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Step-by-step explanation:

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3 years ago
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Kruka [31]

Answer:

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Step-by-step explanation:

Inequalities like these are solved the same way equations are solved, except when multiplying both sides you flip the less than/greater than sign:

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3x > -x -16

3x + x > -x -16 + x     add x to both sides

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In this case the inequality sign did not have to be flipped since we never multiply both sides by a negative number.

3 0
2 years ago
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Answer:

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Step-by-step explanation:

The given angles are vertically opposite and congruent , then

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7x = 35 ( divide both sides by 7 )

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