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3 years ago

In right triangle DEF, ∠E is a right angle, m∠D=26∘, and DF=4.5.

Mathematics

1 answer:

jok3333 [9.3K]3 years ago

3 0

Answer:

The measurement of EF is 1.98 units

Step-by-step explanation:

In Δ DEF

∵ m∠E = 90°

∴ FD is the hypotenuse of the triangle

∵ m∠D = 26°

∵ EF is opposite to angle D

- We can use the sine ratio to find it

∵ sin D = $\frac{EF}{FD}$ ⇒ (opposite side / hypotenuse)

∵ FD = 4.5 units

∴ sin(26) = $\frac{EF}{4.5}$

- Multiply both sides by 4.5

∴ 4.5 sin(26) = EF

∵ sin 26° ≈ 0.44

∴ 4.5(0.44) = EF

∴ 1.98 = EF

The measurement of EF is 1.98 units

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2 years ago

A computer is used to generate passwords made up of numbers 0 through 9 and lowercase letters. The computer generates 400 passwo

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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,

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