1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Marrrta [24]
2 years ago
14

There are three workstations available having steady-state probabilities of 0.99, 0.95, 0.85 of being available on demand. What

is the probability that at least two of the three will be available at any given time?
Mathematics
1 answer:
faust18 [17]2 years ago
3 0

Answer:

99.065% probability that at least two of the three will be available at any given time.

Step-by-step explanation:

We have these following probabilities:

99% probability of the first workstation being available

95% probability of the second workstation being available

85% probability of the third workstation being avaiable

Two being available:

We can have three outcomes

First and second available, third not. So

0.99*0.95*0.15 = 0.141075

First and third available, second not. So

0.99*0.05*0.85 = 0.042075

Second and third available, first not. So

0.01*0.95*0.85 = 0.008075

Adding them all

P(2) = 0.141075 + 0.042075 + 0.008075 = 0.191225

Three being available:

P(3) = 0.99*0.95*0.85 = 0.799425

What is the probability that at least two of the three will be available at any given time?

P = P(2) + P(3) = 0.191225 + 0.799425 = 0.99065

99.065% probability that at least two of the three will be available at any given time.

You might be interested in
During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time
Lana71 [14]

Answer:

The population is of 500 after 10.22 hours.

Step-by-step explanation:

The rate of change of the population of a certain organism is proportional to the population at time t, in hours.

This means that the population can be modeled by the following differential equation:

\frac{dP}{dt} = Pr

In which r is the growth rate.

Solving by separation of variables, then integrating both sides, we have that:

\frac{dP}{P} = r dt

\int \frac{dP}{P} = \int r dt

\ln{P} = rt + K

Applying the exponential to both sides:

P(t) = Ke^{rt}

In which K is the initial population.

At time t = 0 hours, the population is 300.

This means that K = 300. So

P(t) = 300e^{rt}

At time t = 24 hours, the population is 1000.

This means that P(24) = 1000. We use this to find the growth rate. So

P(t) = 300e^{rt}

1000 = 300e^{24r}

e^{24r} = \frac{1000}{300}

e^{24r} = \frac{10}{3}

\ln{e^{24r}} = \ln{\frac{10}{3}}

24r = \ln{\frac{10}{3}}

r = \frac{\ln{\frac{10}{3}}}{24}

r = 0.05

So

P(t) = 300e^{0.05t}

At what time t is the population 500?

This is t for which P(t) = 500. So

P(t) = 300e^{0.05t}

500 = 300e^{0.05t}

e^{0.05t} = \frac{500}{300}

e^{0.05t} = \frac{5}{3}

\ln{e^{0.05t}} = \ln{\frac{5}{3}}

0.05t = \ln{\frac{5}{3}}

t = \frac{\ln{\frac{5}{3}}}{0.05}

t = 10.22

The population is of 500 after 10.22 hours.

7 0
2 years ago
Please help thank you and show all work.
Daniel [21]
Question 1:

Look at the first attached image.

We want to solve for the height of the smaller building. Let's start by making a right triangle with angle of 15 degrees and adjacent side of 51 m.

Let's solve for the other leg. Multiply the tangent with 51 m to get the length of the other leg.

51*tan(15)
\approx 14

Now, subtract that from 207 to get the height of the smaller building.

207-14=193

That's your answer.

Question 2:

The angle of elevation is congruent to the angle of depression because they are alternate interior angles.

Thus, you can choose the 1st and 4th choices as your answer.

Question 3:

Look at the second attached image.

Angle E is congruent to angle D for the same reasons mentioned in the last question.
We can create an equation.

3x+1=2(x+8)

Distributive property

3x+1=2x+16

Subtract both sides by 1 and 2x

x=15

Since E and D are congruent, just plug this value into one of the equations for E or D. You get 46.

The third choice is your answer. Hope this helps! :)

6 0
3 years ago
Solve the equation.<br> -7= z/3
Mariana [72]

Step-by-step explanation:

- 7 =  \frac{z}{3}  \\ by \: cross \: multiplication \\  z =  - 7 \times 3 \\ z =  - 21

7 0
2 years ago
Read 2 more answers
Find the complete quotient when P(x) is divided by the binomial following it.
Nutka1998 [239]

Answer:

Q(x) = x -11

Explanation:

<em>Please refer to the attached image for the Solution</em>

4 0
2 years ago
Plz helpp FASTT
Burka [1]
Are you sure about your solves??

I think correct answer is 6,

I don't know but the standard way is in the photo:

5 0
3 years ago
Read 2 more answers
Other questions:
  • List Things you could measure in milliliters and liters.<br><br><br> Help , thanks
    11·1 answer
  • In which direction does the parabola open?
    11·1 answer
  • What percent of people in the survey took echinacea?(I will give brainliest to best answer)
    7·1 answer
  • What is x in the equation 3x=9
    11·2 answers
  • Tue or False? The first distribution shown below had a smaller mean than does the second distribution
    11·1 answer
  • Sanford the elf has been asked to choose toys for a child who wants a baby doll, a jigsaw puzzle, and a stuffed dog. He looks on
    12·1 answer
  • Estimate: 5.56 x 32.958
    10·2 answers
  • Cyclone cleared leaves from the same number of yards each day for 5 days. Then on day 6, he cleared the leaves from 8 more yards
    15·1 answer
  • Help me pls thank you so much
    9·1 answer
  • Can i get the answer with work?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!