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4 years ago

15

The point (2, 3) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ

?

1 answer:

Ganezh [65]4 years ago

8 0

(2,3) so x=2, y=3 and h=(2^2+3^2)^(1/2)=√13

sina=3/√13, cosa=2/√13, tana=3/2

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According to the MIT Airline Data Project, American Airlines controlled 15.5% of the domestic market during a recent year. A ran

andrey2020 [161]

Answer:

$P(20$

And we can use the z score given by:

$z = \frac{x-\mu}{\sigma}$

And if we find the z score for 20 and 25 we got:

$z = \frac{20-19.375}{4.046}=0.154$

$z = \frac{25-19.375}{4.046}=1.390$

And we have the probability given by:

$P(20$

And we can find this probbaility with this difference:

$P(0.154< Z$

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:

$X \sim Binom(n=125, p=0.155)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

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

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

We need to check the conditions in order to use the normal approximation.

$np=125*0.155=19.375 \geq 10$

$n(1-p)=125*(1-0.155)=105.625 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=125*0.155=19.375$

$\sigma=\sqrt{np(1-p)}=\sqrt{125*0.155(1-0.155)}=4.046$

So then we can approximate the random variable like this:

$X\sim N(\mu = 19.375 , \sigma=4.046)$

And we are interested on this probability:

$P(20$

And we can use the z score given by:

$z = \frac{x-\mu}{\sigma}$

And if we find the z score for 20 and 25 we got:

$z = \frac{20-19.375}{4.046}=0.154$

$z = \frac{25-19.375}{4.046}=1.390$

And we have the probability given by:

$P(20$

And we can find this probbaility with this difference:

$P(0.154< Z$

4 0

3 years ago

HELP! <br> What is the measure of angle BGC??

sp2606 [1]

Answer:

90 degrees

Explanation:

I’m not 100% sure, but it’s opposite to a 90 degree.

3 0

3 years ago

There are 1,000 meters in 1 kilometer. Convert 5,000 meters to kilometers. A) 0.5 km B) 5 km C) 50 km D) 500 km

Sergeu [11.5K]

Answer:

5,000 meters * 1 kilometer / 1,000 meters = 5 kilometers answer is B

Step-by-step explanation:

7 0

4 years ago

Read 2 more answers

75 is 20% of what number?

katrin [286]

Answer:
37.5
you need to convert 75 divided by 200 which will give you 37.5

8 0

3 years ago

The 8th term of a GP is -7/32 find its common ratio if its first term is 28

Ugo [173]

<h2>Common ratio = -1/2</h2>

Step-by-step explanation:

$\text{8}^{th}$ term of a Geometric progression is given as $\dfrac{-7}{32}$ . The first term is given as $28$ .

Any general Geometric progression can be represented using the series $a,ar,ar^{2},ar^{3},ar^{4}...\text{ }ar^{n-1}$ .

The first term in such a GP is given by $a$ , common ratio by $r$ , and the $n^{th}$ term is given by $ar^{n-1}$ .

In the given GP, $a=28;t_{8}=ar^{7}=\dfrac{-7}{32}\\\\28r^{7}=\dfrac{-7}{32}\\\\r^{7}=\dfrac{-1}{128}\\\\r=\dfrac{-1}{2}$

∴ Common ratio is $\dfrac{-1}{2}$ .

5 0

3 years ago