Explain how to estimate 498÷12

Mathematics

2 answers:

PSYCHO15rus [73]3 years ago

8 0

498 is approximately 500

12 is approximately 10

500/10 = 50

So, 498/12 is approximately 50.

exis [7]3 years ago

8 0

Round 498 to the hundreds place making it 500. Then round the twelve to a 10 because you have to follow the rule that if the digit you are rounding is below five you go back if it is above five you round to the next place. The problem would then become 500/10 which is equal to 50

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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,

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