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3 years ago

What is the value of sinC ?

Mathematics

2 answers:

Sever21 [200]3 years ago

8 0

Answer:

$sin \:C =\frac{8}{17}$

Step-by-step explanation:

In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse.

$sin \:x =\frac{O}{H}$

From the formula above we know that the sine of an angle is the opposite side divided by the hypotenuse. The opposite side is AB and has a length of 8. The hypotenuse is AC with a length of 17. So we can write

$sin \:C =\frac{8}{17}$

Vlada [557]3 years ago

7 0

SinC=(8/17)
solve for C = arcsin(8/17)

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a) $P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

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Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

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Where (nCx) means combinatory and it's given by this formula:

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

Part a

$P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

Part b

The expected value is givn by:

$E(X) = np = 4*0.75=3$

Part c

For the standard deviation we have this:

$Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

Part d

For this case the sample size needs to be higher or equal to 9. Since we need a value such that:

$P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

We can verify this using the following code:

"=1-BINOM.DIST(3,9,0.75,TRUE)" and we got 0.99 and the condition is satisfied.

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