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2 years ago

BRAINLIEST ASAP! PLEASE HELP ME :)

Mathematics

1 answer:

Likurg_2 [28]2 years ago

7 0

Answer:

$\large \boxed{41^{\circ}}$

Step-by-step explanation:

∠1 = ∠2

∠3 = ∠4

∠JKN = ∠1 + ∠2 = 8x + 2

∠MKN = ∠3

∠MKL = ∠4 = 3x + 5

So, ∠3 = 3x + 5

$\begin{array}{rcll}(\angle 1 + \angle 2) + \angle 3 + \angle 4 & = & 180 & \text{$\vec{KJ}$ and $\vec{KL}$ are opposite rays}\\8x + 2 + 3x + 5 + 3x + 5 & = & 180 & \text{Made the substitutions}\\14x + 12 & = & 180 & \text{Simplified}\\14x & = & 168 &\text{Subtracted 12 from each side}\\x & = & \mathbf{12} & \text{Divided each side by 14}\\\angle3 & = & 3x + 5 & \\& = & 3(12) + 5 & \\& = & 36 + 5 & \\& = & \mathbf{41} & \\\end{array}\\m\angle MKN = \large \boxed{\mathbf{41^{\circ}}}$

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Using the binomial distribution, it is found that there is a 0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.

For each die, there are only two possible outcomes, either a 3 or a 4 is rolled, or it is not. The result of a roll is independent of any other roll, hence, the <em>binomial distribution</em> is used to solve this question.

Binomial probability distribution

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

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p is the probability of a success on a single trial.

In this problem:

There are 9 rolls, hence $n = 9$ .

Of the six sides, 2 are 3 or 4, hence $p = \frac{2}{6} = 0.3333$

The desired probability is:

$P(X \geq 2) = 1 - P(X < 2)$

In which:

$P(X < 2) = P(X = 0) + P(X = 1)$

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$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{9,0}.(0.3333)^{0}.(0.6667)^{9} = 0.026$

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$P(X < 2) = P(X = 0) + P(X = 1) = 0.026 + 0.117 = 0.143$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.143 = 0.857$

0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.

For more on the binomial distribution, you can check brainly.com/question/24863377

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