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Ulleksa [173]
3 years ago
14

What are the ratios for sin A and cos A? The triangle is not drawn to scale.

Mathematics
1 answer:
dalvyx [7]3 years ago
7 0

Answer:

SinA = \frac{84}{85}  and  CosA=\frac{13}{85}

Step-by-step explanation:

The ratios of sine and cos are defined as follows:

Sin A = \frac{Opposite}{Hypotenuse} , and

CosA = \frac{Adjacent}{Hypotenuse}

The hypotenuse is always the side opposite of the 90 degree angle (for the given triangle, the hypotenuse is 85)

Since we are looking at the angle A, the opposite side with respect to A would be the side length of 84. That leaves the side 13 as the adjacent side.

Thus, we can now write:

Sin A = \frac{Opposite}{Hypotenuse}\\SinA = \frac{84}{85}

CosA = \frac{Adjacent}{Hypotenuse}\\CosA=\frac{13}{85}

The correct answer is  the first answer choice.

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A popular resort hotel has 300 rooms and is usually fully booked. About 7% of the time a reservation is canceled before the 6:00
kicyunya [14]

Answer:

8.69% probability that at least 285 rooms will be occupied.

Step-by-step explanation:

For each booked hotel room, there are only two possible outcomes. Either there is a cancelation, or there is not. So we use concepts of the binomial probability distribution to solve this question.

However, we are working with a big sample. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

A popular resort hotel has 300 rooms and is usually fully booked. This means that n = 300

About 7% of the time a reservation is canceled before the 6:00 p.m. deadline with no pen-alty. What is the probability that at least 285 rooms will be occupied?

Here a success is a reservation not being canceled. There is a 7% probability that a reservation is canceled, and a 100 - 7 = 93% probability that a reservation is not canceled, that is, a room is occupied.  So we use p = 0.93

Approximating the binomial to the normal.

E(X) = np = 300*0.93 = 279

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.93*0.07} = 4.42

The probability that at least 285 rooms will be occupied is 1 subtracted by the pvalue of Z when X = 285. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{285- 279}{4.42}

Z = 1.36

Z = 1.36 has a pvalue of 0.9131.

So there is a 1-0.9131 = 0.0869 = 8.69% probability that at least 285 rooms will be occupied.

8 0
3 years ago
Find the area of the figures by counting the squares
statuscvo [17]

Answer:

Six

six

nine

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6 0
2 years ago
Find the value of x in the isosceles triangle shown below. WILL MARK BRAINLIEST 18 POINTS!
julsineya [31]

Answer:

ur answer

and thank u for following me

4 0
3 years ago
Use proportion to find the answer.
prisoha [69]

<u>Answer</u>

\boxed {64}


<u>Detailed Explanation </u>

Let's set up a proportion.


\frac{3}{4.8} = \frac{40}{x}


Now that we have set up a proportion we would need to cross multiply.

3*x=3x

40*4.8= 192


Solve for x

3x=192


\frac{192}{3} = 64


Therefore, the answer would be 64.


5 0
3 years ago
Which of the following expressions is correct?
AysviL [449]

Answer:

-7.5x3+(20+2.5)=0

this one is equal to 0 ;)

8 0
2 years ago
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