MATHEMATICS COLLEGE

During the period of time that a local university takes phone-in registrations, calls come inat the rate of one every two minutes.
a. What is the expected number of calls in one hour?
b. What is the probability of three calls in five minutes?
c. What is the probability of no calls in a five-minute period?

Answers

Answer 1
Answer:

Answer:

a) The expected number of calls in one hour is 30.

b) There is a 21.38% probability of three calls in five minutes.

c) There is an 8.2% probability of no calls in a five minute period.

Step-by-step explanation:

In problems that we only have the mean during a time period can be solved by the Poisson probability distribution.

Poisson probability distribution

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given interval.

a. What is the expected number of calls in one hour?

Calls come in at the rate of one each two minutes. There are 60 minutes in one hour. This means that the expected number of calls in one hour is 30.

b. What is the probability of three calls in five minutes?

Calls come in at the rate of one each two minutes. So in five minutes, 2.5 calls are expected, which means that \mu = 2.5. We want to find P(X = 3).

P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)

P(X = 3) = (e^(-2.5)*(2.5)^(3))/((3)!) = 0.2138

There is a 21.38% probability of three calls in five minutes.

c. What is the probability of no calls in a five-minute period?

This is P(X = 0) with \mu = 2.5.

P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)

P(X = 0) = (e^(-2.5)*(2.5)^(0))/((0)!) = 0.0820

There is an 8.2% probability of no calls in a five minute period.

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You have 14 gallons of lemonade to sell. You use cone-shaped cups that are 9 centimeters in diameter and 11 centimeters tall. Eachcustomer uses one paper cup. How many paper cups will you need if you sell all of the lemonade? (1 gal = 3785 cm)

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Answer:

You need to sell approximately 119 paper cups to sell all of the lemonade.

Step-by-step explanation:

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What is the value of X?

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Answer:x equals 4

Step-by-step explanation:

What the volume of the figure

Answers

Answer:

1,530

Step-by-step explanation:

box 1 (left one): 10*9*9=810

box 2 (right one): 18*4*10=720

720+810=1,530

Answer:

1530 cm^3

Step-by-step explanation:

They are two Rectangular Prism.

prism 1.

length l = 18 cm

width w = 10 cm

height h = 4 cm

diagonal d = 20.976177 cm

total surface area S_tot = 584 cm^2

lateral surface area S_lat = 224 cm^2

top surface area St_op = 180 cm2

bottom surface area S_bot = 180 cm^2

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height h = 9 cm

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bottom surface area Sbot = 90 cm^2

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Add 720 cm^3+810 cm^3 = 1530 cm^3

Agenda: l = length

w = width

h = height

d = diagonal

S_tot = total surface area

S_lat = lateral surface area

S_top = top surface area

S_bot = bottom surface area

V = volume

Formula: Volume of Rectangular Prism:  V = lwh

An animal shelter spends $2.00 per day to care for each bird and $6.00 per day to care for each cat. Maya noticed that the shelter spent $70.00 caring for birds and cats on Thursday. Maya found a record showing that there were a total of 27 birds and cats on Thursday. How many birds were at the shelter on Thursday ?

Answers

Answer:there were 23 birds and 4 cats

Step-by-step explanation:

Let x represent the number of birds at the shelter on Thursday.

Let y represent the number of cats at the shelter on Thursday.

Maya found a record showing that there were a total of 27 birds and cats on Thursday. This means that

x + y = 27

An animal shelter spends $2.00 per day to care for each bird and $6.00 per day to care for each cat. Maya noticed that the shelter spent $70.00 caring for birds and cats on Thursday. This means that

2x + 6y = 70 - - - - - - - - - - - - - - 1

Substituting x = 27 - y into equation 1, it becomes

2(27 - y) + 6y = 70

54 - 2y + 6y = 70

- 2y + 6y = 70 - 54

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y = 4

x = 27 - y = 27 - 4

x = 23

HELP ME PLZ THXxx u

Answers

Answer:

1. Line g

2. Line j (not sure)

3. Plane S

4. 3 ( QT, QR, TR )

Step-by-step explanation:

A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 45 dumpster loads of waste removed. In week 10, there were 30 dumpster loads removed. Assume that the reduction in the amount of waste each week is linear. Write an equation in function form to show the amount of trash removed each week.f(x) = −3x + 45
f(x) = 3x + 45
f(x) = −3x + 60
f(x) = 3x + 60

Answers

Answer:

f(x) = -3x+60

Step-by-step explanation:

For the slope of the function:

  • Comparing week 5 to week 10: we know that as time goes on, the number of dumpster loads decreases from 45 to 30. This means the slope has to be negative.

For the intercept of the function:

  • Since it's a negative-sloped linear function, we know that the y-intercept has to be bigger than the y-value at week 5. This means it has to be 60.

Therefore:

f(x) = -3x+60

Answer:

c

Step-by-step explanation:
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