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3 years ago

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A 15 ft. telephone pole has a wire that extends from the top of the pole to the ground. The wire and the ground form a 42° angle

. How long is the wire, and what is the distance from the base of the pole to the spot where the wire touches the ground?

1 answer:

Lorico [155]3 years ago

8 0

Answer:

Correct choice is A

Step-by-step explanation:

Consider right triangle ABC formed by the telephone pole (side AB) and ground (side BC). In this triangle AC is the length of the wire, BC is the distance from the base of the pole to the spot where the wire touches the ground and AB=15 ft, ∠ACB=42°.

Then

$\sin 42^{\circ}=\dfrac{AB}{AC}\Rightarrow AC=\dfrac{AB}{\sin 42^{\circ}}=\dfrac{15}{\sin 42^{\circ}}\approx 22.4\ ft.$
$\tan 42^{\circ}=\dfrac{AB}{BC}\Rightarrow BC=\dfrac{AB}{\tan 42^{\circ}}=\dfrac{15}{\sin 42^{\circ}}\approx 16.7\ ft.$

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A collection of 30 gems, all of which are identical in appearance, are supposedto be genuine diamonds, but actually contain 8 wo

levacccp [35]

Answer:

Step-by-step explanation:

From the given information:

There are 30 collections of gems, of which 8 are worthless;

Thus, the number of the genuine diamonds = 30 - 8 = 22.

Let X = random variable;

X consider the value as 0 (for 2 worthless stone selection),

X = 1200(1 worthless stone & 1 genuine stone)

X = 2400 (2 genuine stones selected)

However, the numbers of ways of selecting and chosen Gems can be estimated as:

$(^n_r) = (^{30}_2) \\ \\ \implies \dfrac{30!}{2!(30-2)!} \\ \\ \implies \dfrac{30!}{2!(28)!} \\ \\ \implies \dfrac{30*29*28!}{2!(28)!} \\ \\ \implies \dfrac{30*29}{2*1} \\ \\ \implies 435$

Thus;

$Pr (X = 0) = \dfrac{(^8_2)}{435}$

$Pr (X = 0) = \dfrac{\dfrac{8!}{2!(8-2)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8!}{2!(6)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8*7*6!}{2!(6)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8*7}{2*1}}{435} \\ \\ Pr (X = 0) = 0.0644$

$P(X =1200) = \dfrac{(^{8}_{1})(^{22}_{1})}{435}$

$P(X =1200) = \dfrac{ \dfrac{8!}{1!(8-1)!}) ( \dfrac{22!}{1!(22-1)!}) }{435}$

$P(X =1200) = \dfrac{ (8) ( 22) }{435}$

$P(X =1200) =0.4046$

$Pr (X = 2400) = \dfrac{(^{22}_2)}{435}$

$Pr (X = 2400) = \dfrac{\dfrac{22!}{2!(22-2)!}}{435} \\ \\ Pr (X = 2400) = \dfrac{\dfrac{22!}{2!(20)!}}{435} \\ \\ Pr (X = 2400) = \dfrac{\dfrac{22*21*20!}{2!(20)!}}{435} \\ \\ Pr (X =2400) = \dfrac{\dfrac{22*21}{2*1}}{435} \\ \\ Pr (X = 2400) = 0.5310$

To find E(X):

E(X) = (0 × 0.0644) + (1200 × 0.4046) + (2400 × 0.5310)

E(X) = 0 + 485.52 + 1274.4

E(X) = 1759.92

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1 year ago

You are constructing triangle ABC given the line segments AB and AC and ∠A. The first thing you do is copy segment AC. Next, you

kondaur [170]

Answer:

C) Copy AB

Step-by-step explanation:

The general idea is that you copy one segment, then the angle (so you know which direction the other segment goes), then the second segment. Finally, you connect the ends of the segments to complete the triangle.

The given description says you've done the first two parts of this, so you must mark off the length of segment AB in the direction you just constructed. That is, you must ...

Copy AB.

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Lisa [10]

Answer:

degree measure of arc AB = 120°

length of arc AB = 40π/3 in.

Step-by-step explanation:

arc AB has the same measure as its central angle. So, arc AB = 120°

120 is 1/3 of 360, Therefore, the length of arc AB is 1/3 of the circumference.

Therefore, the

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The heights of baby giraffe are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 100 b

ANEK [815]

Answer:

$P(\bar X$

And we can solve this using the following z score formula:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we use this formula we got:

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So we can find this probability equivalently like this:

$P( Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

$X \sim N(63.6,2.5)$

Where $\mu=63.6$ and $\sigma=2.5$

We select n =100. Since the distribution for X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

We want this probability:

$P(\bar X$

And we can solve this using the following z score formula:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we use this formula we got:

$z = \frac{63-63.6}{\frac{2.5}{\sqrt{100}}}= -2.4$

So we can find this probability equivalently like this:

$P( Z$

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3 years ago