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MArishka [77]
3 years ago
6

A statue is mounted on top of a 21 foot hill. From the base of the hill to where you are standing is 57feet and the statue subte

nds an angle of 7.1° to where you are standing. Find the height of the statue.

Mathematics
1 answer:
AleksandrR [38]3 years ago
3 0

Please find the attached diagram for a better understanding of the question.

As we can see from the diagram,

RQ = 21 feet = height of the hill

PQ = 57 feet = Distance between you and the base of the hill

SR= h=height of the statue

\angle SPR=Angle subtended by the statue to where you are standing.

\angle x=\angle RPQ= which is unknown.

Let us begin solving now. The first step is to find the angle \angle x which can be found by using the following trigonometric ratio in \Delta PQR :

tan(x)=\frac{RQ}{PQ} =\frac{21}{57}

Which gives \angle x to be:

\angle x=tan^{-1}(\frac{21}{57})\approx20.22^{0}

Now, we know that\angle x and \angle SPR can be added to give us the complete angle \angle SPQ in the right triangle \Delta SPQ.

We can again use the tan trigonometric ratio in \Delta SPQ to solve for the height of the statue, h.

This can be done as:

tan(\angle SPQ)=\frac{SQ}{PQ}

tan(7.1^0+20.22^0)=\frac{SR+RQ}{PQ}

tan(27.32^0)=\frac{h+21}{57}

\therefore h+21=57tan(27.32^0)

h\approx8.45 ft

Thus, the height of the statue is approximately, 8.45 feet.

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Answer:

The p-value is significantly low(<0.01), which means that the data provides convincing evidence that the true mean advertisement length is longer than 45 seconds.

Step-by-step explanation:

An online streaming service providing television programs claims that a 30-minute program will stream with advertisements that average 45 seconds. Test if the true mean advertisement length is longer than 45 seconds.

At the null hypothesis, we test if the mean time is of 45 seconds, that is:

H_0: \mu = 45

At the alternate hypothesis, we test if the mean is more than 45 seconds, that is:

H_1: \mu > 45

The test statistic is:

t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

45 is tested at the null hypothesis:

This means that \mu = 45

They recorded the times of 21 randomly selected advertisements. The mean and standard deviation for these times are 46.67 and 2.78.

This means that n = 21, X = 46.67, s = 2.78

Value of the test-statistic:

t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}

t = \frac{46.67 - 45}{\frac{2.78}{\sqrt{21}}}

t = 2.75

P-value of the test and decision:

The p-value of the test is the probability of finding a sample mean above 46.67, which is a right-tailed test, with t = 2.75 and 21 - 1 = 20 degrees of freedom.

With the help of a calculator, this p-value is of 0.0062.

The p-value is significantly low(<0.01), which means that the data provides convincing evidence that the true mean advertisement length is longer than 45 seconds.

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C - 9.5 ≤ 9.5 + 9.5 ≤ + 9.5 C ≤ 19.0
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Answer:

D

Step-by-step explanation:

A coin has two sides. A side tagged the head and the order side tagged the tail.

By mathematical and probabilistic standards, a fair coin is a coin which has equal value of probabilities for head turning up as well as tail turning up.

what we are saying here is that for a fair coin, P(H) = P(T) = 0.5 or 1/2

Any option or value short of this will make the coin unfair. Whenever we are having the probability of the head greater than the probability of the tail or vice versa, then the coin in question has become unfair.

Now back to the options, by observation, expressing each of the options to the smallest numbers will yield 7/10.

Let’s have a decimal value of each go drive home the point;

7/10 = 0.7

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700/1000 = 0.7

Thus the probability of the head which is meant to be 0.5 is now given as 0.7 which shows that the coin is unfair in all three options since in the real sense they are all same numbers written in different form which of course is not the 0.5 value we should have for a fair coin for probability of getting a head

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The top left is the correct answer, because the sides are parallel.

Hope this helps!
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