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Stolb23 [73]
3 years ago
7

A class of 10 students hang up their coats when they arrive at school. Just before recess, the teacher hands one coat selected a

t random to each child. What is the expected number of children who get his or her own coat?
Mathematics
1 answer:
Fittoniya [83]3 years ago
6 0

Answer:

0.1274

Step-by-step explanation:

Let X be the random variable that measures the number of children who get their own coat.

Then, the expected value of X is

E[X] = 1P(X=1) + 2P(X=2)+3P(X=3)+...+10P(X=10)

The probability that a child gets her or his coat is

P(X=1) = 1/10

To compute the probability that 2 children get their own coat, we notice that there are 10! possible permutations of coats. The two children can get their coat in only one way, the other 8 coats can be arranged in 8! different positions, so the probability that 2 children get their own coat is

P(X=2) = 8!/10! = 1/(10*9)  and

2P(X=2) = 2/(10*9)

Similarly, we can see that the probability that 3 children get their own coat is

P(X=3) = 7!/10! = 1/(10*9*8) and  

3P(X=3) = 3/(10*9*8*7)

and the expected value of X would be

E[X] = 1/10 + 2/(10*9) + 3/(10*9*8)+...+10/10! = 0.1274

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dybincka [34]

Answer:

150,595

Step-by-step explanation:

First, convert miles to feet:

4.1 mi × (5280 ft/mi) = 21648 ft

The area that the crowd takes up is:

2 × 8 ft × 21648 ft = 346368 ft²

The number of people is:

346368 ft² × (1 person / 2.3 ft²) = 150594.8

Rounding to the nearest integer, there are approximately 150,595 people in the crowd.

7 0
3 years ago
The graph of the function f(x)=-|5x| is translated 3 units up. Write the equation of the transformed function.
bija089 [108]

Answer:

f(x) = -|5x|+3

Step-by-step explanation:

When doing transformations that go up or down, the number always goes all the way on the right, separate from the x. When its being translated up its positive, when its being translated down, its negative.

4 0
3 years ago
Find the sum of the first 35 terms in this geometric series <br><br> 8 - 12 + 18
Alex777 [14]

Answer: 13

Step-by-step explanation:

4 0
3 years ago
Given the two expressions shown below:
AlladinOne [14]
\sqrt3\ is\ irrational\\\\\sqrt2\ is\ irrational\\\\\sqrt6\ is\ irrational\\\\therefore\\\\A.\ \sqrt3+\sqrt2\ is\ irrational\ and\ B.\ \sqrt3+\sqrt6\ is\ irrational
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3 0
3 years ago
Ayudeme a resolver y poner signo positivo y negativo
Lina20 [59]

Debido a restricciones de extensión y la características del ejercicio, recomendamos leer la explicación de esta pregunta para mayores detalles sobre la adición de números <em>enteros</em>.

<h3>¿Cuáles son los resultados de cada suma?</h3>

En este ejercicio tenemos un grupo de sumas con números <em>enteros</em> <em>positivos</em> y <em>negativos</em>, en las cuales se prueba la capacidad del estudiante para realizar varias operaciones en serie (adición, sustracción) y comprender las diferencias entre números <em>positivos</em>, <em>negativos</em> y <em>neutros</em>. Ahora procedemos a determinar el resultado de cada una de las expresiones:

20 + 50 + 30 + 7 = 107

30 + 5 + 2 = 37

- 200 - 50 - 70 - 8 = - 328

- 500 + 100 - 20 + 50 = - 370

10 - 5 = 5

20 + 50 - 25 - 10 = 35

- 100 + 20 = - 80

- 30 + 5 + 4 - 20 + 8 = - 33

- 258 + 8 = - 250

- 10 + 20 + 520 - 100 + 8 = 438

- 20 - 5 - 42 + 3 = - 64

1000 - 200 + 50 + 30 - 45 + 75 - 87 + 90 + 50 - 100 + 50 - 10 = 903

- 400 + 500 - 200 - 50 + 48 + 8 - 47 - 50 = - 191

300 + 20 - 50 + 30 - 84 + 35 - 7 + 20 - 40 + 10 - 45 + 65 + 8 - 55 = 207

800 + 50 - 69 + 8 - 35 + 85 - 54 + 40 + 85 + 74 - 32 - 8 + 65 - 27 = 982

Para aprender más sobre sumas: brainly.com/question/1456841

#SPJ1

4 0
1 year ago
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