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3 years ago

I am so confused! Can anyone help me with this trig problem?

Mathematics

1 answer:

Dominik [7]3 years ago

4 0

$\frac{5\pi }{4}$ or $\frac{7\pi }{4}$

divide both sides by 2

sinΘ = - $\frac{\sqrt{2} }{2}$

Since the sin ratio is negative then Θ is in third / fourth quadrants

Θ = $sin^{- 1}$ ( $\frac{\sqrt{2} }{2}$ ) = $\frac{\pi }{4}$ related acute angle

Θ = ( π + $\frac{\pi }{4}$ ) = $\frac{5\pi }{4}$

or Θ = ( 2π - $\frac{\pi }{4}$ ) = $\frac{7\pi }{4}$

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For what value of x do the expressions 2x+3 and 3x+-6 have the same value?

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g An urn contains 150 white balls and 50 black balls. Four balls are drawn at random one at a time. Determine the probability th

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Answer:

With replacement, 0.2109 = 21.09% probability that there are 2 black balls and 2 white balls in the sample.

Without replacement, 0.2116 = 21.16% probability that there are 2 black balls and 2 white balls in the sample.

Step-by-step explanation:

For sampling with replacement, we use the binomial distribution. Without replacement, we use the hypergeometric distribution.

Binomial probability distribution

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The probability of x sucesses is given by the following formula:

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In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

Sampling with replacement:

I consider a success choosing a black ball, so $p = \frac{50}{150+50} = \frac{50}{200} = 0.25$

We want 2 black balls and 2 white, 2 + 2 = 4, so $n = 4$ , and we want P(X = 2).

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

$P(X = 2) = C_{4,2}.(0.25)^{2}.(0.75)^{2} = 0.2109$

With replacement, 0.2109 = 21.09% probability that there are 2 black balls and 2 white balls in the sample.

Sampling without replacement:

150 + 50 = 200 total balls, so $N = 200$

Sample of 4, so $n = 4$

50 are black, so $k = 50$

We want P(X = 2).

$P(X = 2) = h(2,200,4,50) = \frac{C_{50,2}*C_{150,2}}{C_{200,4}} = 0.2116$

Without replacement, 0.2116 = 21.16% probability that there are 2 black balls and 2 white balls in the sample.

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