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Nuetrik [128]
3 years ago
11

the perimeter of a rectangle is 74 feet. the length of the rectangle is 3 feet less than 4 times the width. what is the width of

the rectangle in feet?
Mathematics
1 answer:
Dima020 [189]3 years ago
6 0
74= 2l+2w
l=4w-3

Substitute the l value
74= 2(4w-3)+2w
74= 8w-6+2w
74=10w-6
80=10w
8=w

Final answer: 8 ft

To check, find length and plug values in
l= 4w-3
l=4(8)-3
l=32-3
l=29

74=2(29)+2(8)
True
29= 4(8)-3
True
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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
Un automovilista conduce hacia el norte durante 35.0 minutos a 23.61 m/s y ¿Cuál es su desplazamiento?
Nina [5.8K]
I don’t I thought this is math
3 0
3 years ago
Question 2: use the image and your knowledge of the isosceles triangle to find the value of x
pav-90 [236]

Answer:

x is 66 degrees

Step-by-step explanation:

since its a isosceles, two of the angles should be the same.

5 0
3 years ago
What is the gcd of 2563 and 4147
sdas [7]

Answer:

GCD=11

Step-by-step explanation:

Factors of 2563 are: 1 , 11 , 233 , 2563.

Factors of 4147 are: 1 , 11 , 13 , 29 , 143 , 319 , 377 , 4147.




7 0
3 years ago
Each week, a cook purchases 12 pounds of butter. During the last year, the cook has paid as little as $23.04 and at much as $29.
Tatiana [17]

Each week, a cook purchased 12 LBS. of Butter:

During the Last year:  (12 Months):

Cook Paid:

Little:   $23.04

Much:  $29.40, For Butter he or she purchased in a week:

Question: is: what is the Difference between, the Greatest price per pound, and the least price per pound of butter the cook paid within the last year?


EQUATION:

Least Paid / 12  =====>  23.04 /12

Most Paid / 12  ======>    29.40 / 12



Divide:

23.04 / 12    =     1.92 / LB

29.40 / 12     =     2.45 / LB

Now Subtract:

2.45   -     1.92

Answer   ======>    0.53 is the difference, between the greatest price per round, and least price per round of butter the cook would have paid within the last year.






Hope that helps!!!                                : )

4 0
3 years ago
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