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3 years ago

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Determine whether the given triangles are similar. Justify your answer. If they are similar write a similarity statement. How do

you do this?

1 answer:

zimovet [89]3 years ago

3 0

8/6 = 12/9

8/6 x 9/9 = 72/54
12/9 x 6/6 = 72/54

72/54 = 72/54

They are similar.

Triangle ABC is similar to triangle PQR

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Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose t

worty [1.4K]

Answer:

a) $P(X \leq 100) = 1- e^{-0.01342*100} =0.7387$

$P(X \leq 200) = 1- e^{-0.01342*200} =0.9317$

$P(100\leq X \leq 200) = [1- e^{-0.01342*200}]-[1- e^{-0.01342*100}] =0.1930$

b) $P(X>223.547) = 1-P(X\leq 223.547) = 1-[1- e^{-0.01342*223.547}]=0.0498$

c) $m = \frac{ln(0.5)}{-0.01342}=51.65$

d) $a = \frac{ln(0.05)}{-0.01342}=223.23$

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

$P(X=x)=\lambda e^{-\lambda x}$

Solution to the problem

For this case we have that X is represented by the following distribution:

$X\sim Exp (\lambda=0.01342)$

Is important to remember that th cumulative distribution for X is given by:

$F(X) =P(X \leq x) = 1-e^{-\lambda x}$

Part a

For this case we want this probability:

$P(X \leq 100)$

And using the cumulative distribution function we have this:

$P(X \leq 100) = 1- e^{-0.01342*100} =0.7387$

$P(X \leq 200) = 1- e^{-0.01342*200} =0.9317$

$P(100\leq X \leq 200) = [1- e^{-0.01342*200}]-[1- e^{-0.01342*100}] =0.1930$

Part b

Since we want the probability that the man exceeds the mean by more than 2 deviations

For this case the mean is given by:

$\mu = \frac{1}{\lambda}=\frac{1}{0.01342}= 74.516$

And by properties the deviation is the same value $\sigma = 74.516$

So then 2 deviations correspond to 2*74.516=149.03

And the want this probability:

$P(X > 74.516+149.03) = P(X>223.547)$

And we can find this probability using the complement rule:

$P(X>223.547) = 1-P(X\leq 223.547) = 1-[1- e^{-0.01342*223.547}]=0.0498$

Part c

For the median we need to find a value of m such that:

$P(X \leq m) = 0.5$

If we use the cumulative distribution function we got:

$1-e^{-0.01342 m} =0.5$

And if we solve for m we got this:

$0.5 = e^{-0.01342 m}$

If we apply natural log on both sides we got:

$ln(0.5) = -0.01342 m$

$m = \frac{ln(0.5)}{-0.01342}=51.65$

Part d

For this case we have this equation:

$P(X\leq a) = 0.95$

If we apply the cumulative distribution function we got:

$1-e^{-0.01342*a} =0.95$

If w solve for a we can do this:

$0.05= e^{-0.01342 a}$

Using natural log on btoh sides we got:

$ln(0.05) = -0.01342 a$

$a = \frac{ln(0.05)}{-0.01342}=223.23$

5 0

3 years ago

What is the answer to the q's

TEA [102]

Answer:

1.TRUE

2.TRUE

3.FALSE

4.TRUE

4 0

3 years ago

Ten members of a wedding party are lining up in a row for a photograph. How many ways are there to line up the ten people? How m

svp [43]

Answer:

(a) 10!

(b) 9!

(c) 2!9!

Step-by-step explanation:

(a)

Total number of members = 10

We need to line up the ten people.

Total number of ways to arrange n terms is n!. Similarly, total number of ways to line up the ten people is

$\text{Total ways} =10!$

Therefore the total number of ways to line up the ten people is 10!.

(b)

Let groom is immediate left of the bride it means both will sit together. So we need to arrange peoples for total 9 places (8 of others and 1 of bride and groom).

$\text{Total ways} =9!1!1!=9!$

Therefore the number of ways to line up the ten people if the groom must be to the immediate left of the bride in the photo is 9!.

(c)

Let groom is immediate left of the bride it means both will sit together. So we need to arrange peoples for total 9 places (8 of others and 1 of bride and groom).

Bride and groom can interchange there sits.

Total number of ways to arrange bride and groom = 2!

$\text{Total ways} =9!2!$

Therefore the number of ways to line up the ten people if the groom must be next to the bride (either on her left to right side) is 9!2!.

3 0

3 years ago

Read 2 more answers

The area of a parallelogram is found using the formula bh, where b represents the length of the base and h represents the length

Alborosie

Answer:

120 square centimeters

Step-by-step explanation:

The question says the formula already.

Area = bh

b = base length b = 10

h = height length h = 12

Area = 10 · 12

Area = 120 square centimeters

8 0

3 years ago

Read 2 more answers

Twelve less than a number is 50.

Katen [24]

Answer:

62

Step-by-step explanation:

another way to write this is

x - 12 = 50

the answer is 62

62 - 12 = 50

7 0

3 years ago