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masha68 [24]
3 years ago
8

In the diagram, the measurements that are labeled are known, while the other measurements are unknown. Which measurement of acut

e triangle ABC can you find by direct substitution of the labeled measures in the Law of Sines?
A.c

B.m/_C

C.m/_B

D.none

Mathematics
1 answer:
andrew-mc [135]3 years ago
8 0
As the sine rule states,

A/sina = B/sinb = C/sinc .

in the diagram, there are two identified sides and if you use the sine rule, you can find the opposed angles easily.

there are:

side a, with angle â .
side b, with angle b.

so the answer is C.

if you input these into the sine rule, it would be:

a/ sin a = b/sin b
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Georgia [21]

Answer:

See the proof below.

Step-by-step explanation:

For this case we need to proof that: Let X_1, X_2, ...X_n \in R be independent random variables with a common CDF F_0. Let F_n be their ECDF and let F any CDF. If F \neq F_n then L(F)

Proof

Let z_a different values in the set {X_1,X_2,...,X_n}} and we can assume that n_j \geq 1 represent the number of X_i that are equal to z_j.

We can define p_j = F(z_j) +F(z_j-) and assuming the probability \hat p_j = \frac{n_j}{n}.

For the case when p_j =0 for any j=1,....,m then we have that the L(F) =0< L(F_n)

And for the case when all p_j >0 and for at least one p_j \neq \hat p_j we know that log(x) \leq x-1 for all the possible values x>0. So then we can define the following ratio like this:

log (\frac{L(F)}{L(F_n)}) = \sum_{j=1}^m n_j log (\frac{p_j}{\hat p_j})

log (\frac{L(F)}{L(F_n)}) = n \sum_{j=1}^m \hat p_j log(\frac{p_j}{\hat p_j})

log (\frac{L(F)}{L(F_n)}) < n\sum_{j=1}^m \hat p_j (\frac{p_j}{\hat p_j} -1)

So then we have that:

log (\frac{L(F)}{L(F_n)}) \leq 0

And the log for a number is 0 or negative when the number is between 0 and 1, so then on this case we can ensure that L(F) \leq L(F_n)

And with that we complete the proof.

8 0
3 years ago
Find the area of each segment, round to the nearest tenth
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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3 0
3 years ago
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
AleksandrR [38]

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.

3 0
3 years ago
What is the midpoint of the segment shown below?
Aneli [31]

Answer:

(1, -3/2)

Step-by-step explanation:

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The midpoint is

(1, -3/2)

5 0
3 years ago
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