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Yuri [45]
3 years ago
10

How to simplify 0.111111111 repeating as a fraction

Mathematics
2 answers:
antiseptic1488 [7]3 years ago
6 0
Any numerical repeating pattern can be rationalized...let x=0.111 then:

10x=1.111 and upon taking differences:

10x-x=1.111-0.111

9x=1  then divide both sides by 9

x=1/9

(This method works for converting any repeating numerical pattern to a rational number) 
arlik [135]3 years ago
5 0
Depending on how many times it repeats, and I used 9 1's from your question, the answer would be 1/9.
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For i≥1 , let Xi∼G1/2 be distributed Geometrically with parameter 1/2 . Define Yn=1n−−√∑i=1n(Xi−2) Approximate P(−1≤Yn≤2) with l
murzikaleks [220]

Answer:

The answer is "0.68".

Step-by-step explanation:

Given value:

X_i \sim \frac{G_1}{2}

E(X_i)=2 \\

Var (X_i)= \frac{1- \frac{1}{2}}{(\frac{1}{2})^2}\\

             = \frac{ \frac{2-1}{2}}{\frac{1}{4}}\\\\= \frac{ \frac{1}{2}}{\frac{1}{4}}\\\\= \frac{1}{2} \times \frac{4}{1}\\\\= \frac{4}{2}\\\\=2

Now we calculate the \bar X \sim N(2, \sqrt{\frac{2}{n}})\\

\to \frac{\bar X - 2}{\sqrt{\frac{2}{n}}}  \sim  N(0, 1)\\

\to \sum^n_{i=1}  \frac{X_i - 2}{n}  \times\sqrt{\frac{n}{2}}}  \sim  N(0, 1)\\\\\to  \sum^n_{i=1}  \frac{X_i - 2}{\sqrt{2n}}  \sim  N(0, 1)\\

\to Z_n = \frac{1}{\sqrt{n}} \sum^n_{i=1} (X_i -2) \sim N(0, 2)\\

\to P(-1 \leq X_n \leq 2)  = P(Z_n \leq Z) -P(Z_n \leq -1) \\\\

                               = 0.92 -0.24\\\\= 0.68

6 0
3 years ago
Out of 8 boys and 6 girls in a high school, a team of seven students is selected. What is the probability that three boys and fo
maria [59]
The probabitily is if they get selected  as a team of 7 aswell if they're playing a game of some sort.
 
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3 years ago
PLEASE ANSWER!!! <br> You don’t have to do number 25 *****
Ilia_Sergeevich [38]

Answer:

see explanation

Step-by-step explanation:

The directed lines have the form < x, y >

With the usual notation

right in x- direction → +

left in x- direction → -

up in y- direction → +

down in y- direction → -

21

EF = < 4, 1 >

22

FG = < 4, - 2 >

23

GH = < - 4, - 2 >

24

EH = < 4, - 3 >

8 0
3 years ago
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Alex_Xolod [135]

Answer:

1. .900+.020+.008, 2. .700+.030+.001, 3. 4.5, 4.56, 4.565656, 4.6

Step-by-step explanation:

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3 years ago
What is the Compound interest on a 10,000 investment the earns 6% compound monthlyfor5 years
Vlad1618 [11]

Answer:

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Step-by-step explanation:

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So to solve for the compound interest we would plug in our numbers in replacement for the letters

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2 years ago
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