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2 years ago

7

Un globo busca aterrizar en medio de dos ciudades A y B, cuya distancia entre si es de 200 km. Si se mide el ángulo de elevación

desde cada casa hasta el punto C en el que se ubica el globo en un instante dado, se obtienen 27° y 36° . ¿Cuál es la altura aproximada del globo?

1 answer:

scoundrel [369]2 years ago

7 0

Answer:

$h \approx 59.898\,km$

Step-by-step explanation:

El diagrama trigonométrico que representa el enunciado es incluido abajo como adjunto. Las siguientes relaciones trigonométricas describen la localización del globo. (The trigonometric diagram representing the statement is included below as attachment. The following trigonometric relations describes the location of the balloon):

$\tan 27^{\circ} = \frac{h}{x}$

$\tan 36^{\circ} = \frac{h}{200-x}$

A continuación, se obtiene la distancia horizontal: (The horizontal distance is obtained hereafter):

$x \cdot \tan 27^{\circ} = (200-x)\cdot \tan 36^{\circ}$

$x \cdot (\tan 27^{\circ} + \tan 36^{\circ})= 200\cdot \tan 36^{\circ}$

$x = \frac{200\cdot \tan 36^{\circ}}{\tan 27^{\circ}+ \tan 36^{\circ}}$

$x \approx 117.557\,km$

La altura aproximada del globo es (The approximated height of the globe is):

$h = x\cdot \tan 27^{\circ}$

$h \approx 59.898\,km$

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Suppose a continuous probability distribution has an average of μ=35 and a standard deviation of σ=16. Draw 100 times at random

yulyashka [42]

Answer:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

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, we have that the mean is $\mu*n$ and the standard deviation is $s = \sigma \sqrt{n}$

In this problem, we have that:

$\mu = 100*35 = 3500, \sigma = \sqrt{100}*16 = 160$

This probability is the pvalue of Z when X = 4000 subtracted by the pvalue of Z when X = 3000.

X = 4000

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

By the Central Limit Theorem

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

$Z = \frac{4000 - 3500}{160}$

$Z = 3.13$

$Z = 3.13$ has a pvalue of 0.9991

X = 3000

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

$Z = \frac{3000 - 3500}{160}$

$Z = -3.13$

$Z = -3.13$ has a pvalue of 0.0009

0.9991 - 0.0009 = 0.9982

So the correct answer is:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

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Tyler wants to use $300 he has saved to buy a new guitar and join a music club. The guitar costs $140. The music club has a $25

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Answer:

ok __?__ is 11 and ___ is 3.55

Step-by-step explanation:

so first you subtract the 140 and 25 from the 300 then divide by 11.95, which gives you 11, then you multiply 11 times 11.95 and subtract that answer from 135.

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Alex

Answer:

$\frac{\pi }{2}$

Step-by-step explanation:

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We use the trinomial theorem to answer this question. Suppose we have a trinomial (a + b + c)ⁿ, we can determine any term to be:

[n!/(n-m)!(m-k)!k!] a^(n-m) b^(m-k) c^k

In this problem, the variables are: x=a, y=b and z=c. We already know the exponents of the variables. So, we equate this with the form of the trinomial theorem.

n - m = 2
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Since we know k, we can determine m. Once we know m, we can determine n. Then, we can finally solve for the coefficient.

m - 10 = 5
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