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Pani-rosa [81]
3 years ago
6

How to figure out the pattern , filling in the blank

Mathematics
1 answer:
zaharov [31]3 years ago
8 0
Show me the pattern first

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there are 6 times as many ways to arrange the letters in the word "sleeplessness" as there are to arrange the letters in the wor
EastWind [94]

Using arrangements of words, it is found that the statement is true.

------------------

  • Suppose a word has n letters.
  • Considering that m of these letters are repeating, each n_1,n_2,...,n_m times.
  • The number of distinct ways the word can be arranged is given by:

N = \frac{n!}{n_1\times n_2 \times ... n_m}

------------------

  • The word "sleeplessness" has 13 letters.
  • s repeats 5 times.
  • e repeats 4 times.
  • l repeats 2 times.

Thus, the number of ways to arrange the letters is given by:

N_1 = \frac{13!}{5!4!2!}

------------------

  • The word "senselessness" has 13 letters.
  • s repeats 6 times.
  • e repeats 4 times.
  • n repeats 2 times.

Thus, the number of ways to arrange the letters is given by:

N_2 = \frac{13!}{6!4!2!}

------------------

Finding the ratio of N_2 to N_1:

\frac{N_2}{N_1} = \frac{\frac{13!}{5!4!2!}}{\frac{13!}{6!4!2!}} = \frac{13!}{5!4!2!} \times \frac{6!4!2!}{13!} = \frac{6!}{5!} = 6

Thus, since the ratio is 6, the statement is true.

A similar problem is given at brainly.com/question/16790460

8 0
3 years ago
Read 2 more answers
Find the value of x.
Ksenya-84 [330]

Answer:

x=15

Step-by-step explanation:

Radius is 8 since thee short leg is 8 and it is from the center to the ed of the circle. 9 is the length of the hypotenuse from the tip of the triangle to the edge of the circle. The rest is equivalent to the radius which is 8. So hypotenuse  is 17, short leg is 8. Now we have what we need to find x. We can do this by using the formula A^2+B^2=C^2.

8^2=64 C^2=289

289-64=225

225 square root is 15

so x=15

Hope this was helpful!

3 0
3 years ago
3 + 4ab+ 4ab - 5b + m
Rainbow [258]

Answers:  

  • Number of terms: 5
  • Coefficients:  4, 4, -5 and 1
  • Constant term:  3

===================================================

Explanation:

Each term is separated by a plus sign or a minus sign. We could rewrite the 4ab-5b portion as 4ab + (-5b) to help get everything separated by a plus sign.

The five terms are

  • 3
  • 4ab
  • 4ab
  • -5b
  • m

The coefficients are the numbers just to the left of the variable. For a term like 4ab, the coefficient is 4. For the term "m", we can think of it as 1m so we can see it has a coefficient of 1.

The constant term is the term that doesn't have any variable attached to it. That would be the "3" as the first term.

5 0
2 years ago
What is the total vertical distance (both up and down) traveled by the ball when it stops bouncing? (Hint: Add the total distanc
storchak [24]
The total verticle distance is 8
8 0
3 years ago
Write an equation to represent the following statement. j is 7times as large as 6 .
Romashka-Z-Leto [24]
6=j-7, sorry if it’s wrong
3 0
3 years ago
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