Trick or treaters arrive to your house according to a Poisson process with a constant rate parameter of 20 per hour. Suppose you begin sitting on your front porch, observing these arrivals, at some point in time. Suppose a trick or treater arrived 30 minutes ago, but there have been none since. What is the expected value of interarrival time (in minutes) from the previous trick or treater to the next one

Answers

Answer 1
Answer:

Answer:

The expected value of interarrival time (in minutes) from the previous trick or treater to the next one is 3 minutes.

Step-by-step explanation:

We have a Poisson process with a constant rate parameter of 20 arrival per hour.

This type of processes are memory-less, meaning that no matter how much time has passed form the last event, the probabilities of an arrival stay the same.

The mean interarrival time can be calculated as the inverse of the mean arrival for the Poisson process.

If the Poisson process has a rate of 20 arrivals per hour, the mean interarrival time is:

\bar t=1/\lambda=1/20=0.05\,h/arrival=3 \,min/arrival


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PLZ HELP FAST looks easy​

I need help! Please include an explanation.

Answers

Answer:

J. 144

Step-by-step explanation:

Perimeter of equilateral triangle is P = 16 + 16 + 16 = 48

Perimeter of square is P = x + x + x + x = 4x

since 4x = 48 => x = 48/4 = 12

Area of square = 12 x 12 = 144

I need help with these questions

Answers

Answer:

1)10 months 2) 40 cm 3)8in

Step-by-step explanation:

1)1year =12 months

5/6year=?months

cross multiply

5x2=10

------

6x2=12

answer 12months

2)100cm in a meter

100divided by 5=20

1/5=20cm

2/5=40cm

answer:40 cm

3)12in in a foot

12divided by 3=4

1/3=4in

2/3=8 in

answer=8 in

thats all the time I have for now bye

Using the expression you found in part a, how many minutes will it take to make and pack an order for 15 parts?

Answers

Answer:

It will take 40 minutes to make and pack an order for 15 parts.

Step-by-step explanation:

That's the answer.

Answer:

It will take 40 minutes to make and pack an order for 15 parts.

Step-by-step explanation:

Josie bought 750 bags of peanuts for $375 he intends to sell each bag for $.15 more than you paid how much should he charge for each bag

Answers

Step-by-step explanation:

Jose bought 750 bags for $375.00

Each bag cost $375/750= $0.50

He  intends to sells them for $0.15 more

He should charge : $0.5 +$0.15=$0.65

(1 point) For the given position vectors r(t)r(t), compute the (tangent) velocity vector r′(t)r′(t) for the given value of tt . A) Let r(t)=(cos4t,sin4t)Let r(t)=(cos⁡4t,sin⁡4t). Then r′(π4)r′(π4)= ( , )? B) Let r(t)=(t2,t3)Let r(t)=(t2,t3). Then r′(5)r′(5)= ( , )? C) Let r(t)=e4ti+e−5tj+tkLet r(t)=e4ti+e−5tj+tk. Then r′(−5)r′(−5)= i+i+ j+j+ kk ?

Answers

Answer:

(a)

r'(\frac \pi 4) =(0.-4)

(b)

r'(5)= (10,75)

(c)

r'(-5) =4 e^(-20)\hat i-5e^(25)\hat j+\hat k

Step-by-step explanation:

(a)

Give that,the position vector is

r(t) = (cos 4t, sin 4t)

Differentiating with respect to t

r'(t) = (-4sin 4t, 4 cos 4t)    [(d)/(dt) cos mt = -m \ sin \ mt  and   (d)/(dt) sin mt = m \ cos \ mt]

To find the r'(\frac\pi 4), we put t=\frac \pi4

r'(\frac\pi 4) = (-4sin (4.\frac \pi 4), 4 cos  (4.\frac \pi 4))

        =(0, -4)

(b)

Give that,the position vector is

r(t) = (t²,t³)

Differentiating with respect to t

r'(t) = (2t, 3t²)

To find r'(5) ,  we put t=5

r'(5) = (2.5,3.5²)

      = (10,75)

(c)

Given position vector is

r(t) = e^(4t)\hat i+e^(-5t)\hat j+t\hat k

Differentiating with respect to t

r'(t) =4 e^(4t)\hat i+(-5)e^(-5t)\hat j+\hat k

\Rightarrow r'(t) =4 e^(4t)\hat i-5e^(-5t)\hat j+\hat k

To find r'(-5) ,  we put t= - 5 in the above equation

r'(-5) =4 e^(4.(-5))\hat i-5e^(-5.(-5))\hat j+\hat k

\Rightarrow  r'(-5) =4 e^(-20)\hat i-5e^(25)\hat j+\hat k

For the given position vectors r(t)r(t), compute the (tangent) velocity vector r′(t)r′(t) for the given value of tt  are:

A) r' (\pi /4) = (0, -4) \nB) r'(5) = (10, 75)\nC) r'(-5) = (4e^(-20), -5e^(25), 1)

To compute the velocity vector, we need to find the derivative of the position vector with respect to time (t). This will give us the tangent velocity vector.

A) Let r(t) = (cos⁡4t, sin⁡4t).

To find r'(t), we take the derivative of each component with respect to t:

r'(t) = (d/dt (cos⁡4t), d/dt (sin⁡4t))

r'(t) = (-4sin⁡4t, 4cos⁡4t)

To find r'(π/4), we substitute t = π/4 into r'(t):

r'(π/4) = (-4sin⁡(4(π/4)), 4cos⁡(4(π/4)))

r'(π/4) = (-4sin⁡π, 4cos⁡π)

r'(π/4) = (0, -4)

B) Let \ r(t) = (t^2, t^3).

To find r'(t), we take the derivative of each component with respect to t:

r'(t) = (d/dt (t^2), d/dt (t^3))\nr'(t) = (2t, 3t^2)

To find r'(5), we substitute t = 5 into r'(t):

r'(5) = (2(5), 3(5)^2)\nr'(5) = (10, 75)

C) Letr(t) = e^(4t)i + e^(-5t)j + tk.

To find r'(t), we take the derivative of each component with respect to t:

r'(t) = (d/dt (e^(4t)), d/dt (e^(-5t)), d/dt (t))]\n\nr'(t) = (4e^(4t)), -5e^(-5t), 1)

To find r'(-5), we substitute t = -5 into r'(t):

r'(-5) = (4e^(4{-5}), -5e^(-5(-5)), 1) \n\nr'(-5) = (4e^(-20), -5e^(25), 1)

So, the answers are:

A) r' (\pi /4) = (0, -4) \nB) r'(5) = (10, 75)\nC) r'(-5) = (4e^(-20), -5e^(25), 1)

To know more about vectors:

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A fruit company includes 1.655 ounces of pineapple juice in a 6.75 ounce bottle of a mixed fruit juice. How much of the bottle of mixed fruit juice is NOT pineapple juice?

Answers

5.095 ounces or, if you're looking for a percentage, then 75.48% (I don't know where you need it rounded to). To get the ounces, subtract the ounces of pineapple juice from the total ounces of fruit juice. To get the percentage, divide 5.095 by 6.75, then multiply by 100.