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Oksanka [162]
3 years ago
10

How do you solve an equation by completing the square? Example:

D-8" id="TexFormula1" title=" x^{2}+6x=-8" alt=" x^{2}+6x=-8" align="absmiddle" class="latex-formula">
Mathematics
2 answers:
Serga [27]3 years ago
7 0
X²+6x+8=0
x²+2*3x+9-1=0
(x+3)²-1=0
(x+3)²-1²=0
(x+3-1)(x+3+1)=0
(x+2)(x+4)=0
x₁=-2
x₂=-4
Answer: x₁=-2,  x₂=-4
bixtya [17]3 years ago
7 0
x^2+6x=-8\\
x^2+6x+9=1\\
(x+3)^2=1\\
x+3=1 \vee x+3=-1\\
x=-2 \vee x=-4
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d = ra * 2.4                        d = rb 4

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3 years ago
A computer is used to generate passwords made up of numbers 0 through 9 and lowercase letters. The computer generates 400 passwo
tamaranim1 [39]

The prediction for the number of passwords in which the first character is a vowel is 56 passwords.

<h3>How to find that a given condition can be modelled by binomial distribution?</h3>

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

X \sim B(n,p)

The probability that out of n trials, there'd be x successes is given by

P(X =x) = \: ^nC_xp^x(1-p)^{n-x}

The expected value and variance of X are:

E(X) = np\\

Given that the characters that can be used are numbers 0 through 9 and lowercase letters. Therefore, a total of 36 different characters are available.

Since we need to know the passwords made with vowels, therefore, the probability of a password in which the first character will be a, e, i, o, u is (5/36).

Now as the computer produces 400 passwords, therefore, the predicted value can be written as,

E = np = 400 \times \dfrac{5}{36} = 55.5556 \approx 56

Hence, the prediction for the number of passwords in which the first character is a vowel is 56 passwords.

Learn more about Binomial Distribution:

brainly.com/question/14565246

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