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vladimir1956 [14]
3 years ago
14

What is the value of x in the diagram below?

Mathematics
1 answer:
Tanzania [10]3 years ago
7 0

Answer:

The answer to your question is: x = 100

Step-by-step explanation:

It's a polygon of 7 sides

The sum of internal angles in a polygon equals 180(n-2), where n = # of sides

                 

            Internal angles = 180(7-2)

                                      = 180(5)

                                     = 900°

      (x + 50) + (x + 50) + (x + 50) + x + x + x + (x + 50) = 900

      4(x + 50) + 3x = 900

      4x + 200 + 3x = 900

      7x = 900 - 200

      7x = 700

      x = 700 / 7

      x = 100

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Birds arrive at a birdfeeder according to a Poisson process at a rate of six per hour.
m_a_m_a [10]

Answer:

a) time=10 \frac{1}{6}=\frac{10}{6}=1.67 hours

b) P(T\geq 0.25h)=e^{-(6)0.25}=0.22313

c) P(T\leq 0.0833)=1-e^{-(6)0.0833}=0.39347

Step-by-step explanation:

Definitions and concepts

The Poisson process is useful when we want to analyze the probability of ocurrence of an event in a time specified. The probability distribution for a random variable X following the Poisson distribution is given by:

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

And the parameter \lambda represent the average ocurrence rate per unit of time.

The exponential distribution is useful when we want to describ the waiting time between Poisson occurrences. If we assume that the random variable T represent the waiting time btween two consecutive event, we can define the probability that 0 events occurs between the start and a time t, like this:

P(T>t)= e^{-\lambda t}

a. What is the expected time you would have to wait to see ten birds arrive?

The original rate for the Poisson process is given by the problem "rate of six per hour" and on this case since we want the expected waiting time for 10 birds we have this:

time=10 \frac{1}{6}=\frac{10}{6}=1.67 hours

b. What is the probability that the elapsed time between the second and third birds exceeds fifteen minutes?

Assuming that the time between the arrival of two birds consecutive follows th exponential distribution and we need that this time exceeds fifteen minutes. If we convert the 15 minutes to hours we have 15(1/60)=0.25 hours. And we want to find this probability:

P(T\geq 0.25h)

And we can use the result obtained from the definitions and we have this:

P(T\geq 0.25h)=e^{-(6)0.25}=0.22313

c. If you have already waited five minutes for the first bird to arrive, what is the probability that the bird will arrive within the next five minutes?

First we need to convert the 5 minutes to hours and we got 5(1/60)=0.0833h. And on this case we want a conditional probability. And for this case is good to remember the "Markovian property of the Exponential distribution", given by :

P(T \leq a +t |T>t)=P(T\leq a)

Since we have a waiting time for the first bird of 5 min = 0.0833h and we want that the next bird will arrive within 5 minutes=0.0833h, we can express on this way the probability of interest:

P(T\leq 0.0833+0.0833| T>0.0833)

P(T\leq 0.1667| T>0.0833)

And using the Markovian property we have this:

P(T\leq 0.0833)=1-e^{-(6)0.0833}=0.39347

3 0
3 years ago
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grandymaker [24]
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5 0
3 years ago
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ladessa [460]

Answer:

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Step-by-step explanation:

<u>Step 1:  Multiply inside the parenthesis </u>

2(5 * -3)

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<u>Step 2:  Multiply </u>

<u />2(-15)

2 * -15

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7 0
3 years ago
How do you solve 3y=6x-5?
jeka94

Answer:

Hope this helps

Step-by-step explanation:


5 0
3 years ago
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FromTheMoon [43]

B because there is only one negative and -63 divided by 7 equals -9. If it were -7 divided by 63 that would give you an answer in decimal form.

6 0
3 years ago
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