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lapo4ka [179]
2 years ago
6

Please help!! I have tried it on my own and I am stuck

Mathematics
1 answer:
elena55 [62]2 years ago
8 0

Answer:

1. 23.59 feet

2. 32.9°

Step-by-step explanation:

1. See the diagram attached.

The man is 11 feet distance from the bottom of the tree.

And the angle of elevation from the man to the top of the tree is 65°.

Now, we need to approximate the height of the tree,

Using the trigonometry, we can write  

\tan 65^{\circ} = \frac{\textrm {Height of the Tree}}{\textrm {Base Distance}} = \frac{h}{11}

⇒ h = 11 tan 65° = 23.59 feet (Approx.) (Answer)

2. See the diagram attached.

From the given right triangle the hypotenuse is 25 feet and the base is 21 feet.

And the angle between the hypotenuse and the base is the pitch of the ram of a NASCAR turn.

Using trigonometry, we can write  

\cos \theta = \frac{\textrm {Base}}{\textrm {Hypotenuse}} = \frac{21}{25}

⇒ \theta = \cos^{-1}(\frac{21}{25}) = 32.9^{\circ} (Answer)

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13. Supplementary angles are two angles that add up to 180 degrees.

3x + x = 180

Combine like terms:
4x = 180

4x divided by 4 = x

180 divided by 4 = 45

x = 45

Equation:
3(45) + 45 = 180

135 + 45 = 180 (TRUE STATEMENT)

Angle A = 135 degrees
Angle B = 45 degrees

This is correct as 135 + 45 adds up to 180 (making it a supplementary angle) AND 135 is 3 times bigger than 45 so it fits the answer’s standard.

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2 years ago
In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. In addition, there
lesya692 [45]

Answer:

15.87% probability that a random sample of 16 people will exceed the weight limit

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums, the theorem can be applied, with mean n*\mu and standard deviation s = \sqrt{n}*\sigma

In this problem, we have that:

n = 16, \mu = 16*150 = 2400, s = \sqrt{16}*27 = 108

If a random sample of 16 persons from the campus is to be taken, what is the chance that a random sample of 16 people will exceed the weight limit

This is 1 subtracted by the pvalue of Z when X = 2508. So

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

By the Central Limit Theorem

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

Z = \frac{2508 - 2400}{108}

Z = 1

Z = 1 has a pvalue of 0.8413

1 - 0.8413 = 0.1587

15.87% probability that a random sample of 16 people will exceed the weight limit

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Notice the picture below

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\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
(y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\
\boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}}) }\\
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\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\
-----------------------------\\\\

\bf \begin{cases}
p=-1\\
h=-2\\
k=5
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\\\\\\
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