An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently.

What is the probability that all of the sprinklers will operate correctly in a fire?

Answers

Answer 1

Answer:

2.82% probability that all of the sprinklers will operate correctly in a fire

Step-by-step explanation:

For each sprinkler, there are only two possible outcomes. Either they will operate correctly, or they will not. The probability of a sprinkler operating correctly is independent of other sprinklers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The researchers estimate the probability of a sprinkler to activate correctly to be 0.7.

This means that [tex]p = 0.7[/tex]

10 sprinklers.

This means that [tex]n = 10[/tex]

What is the probability that all of the sprinklers will operate correctly in a fire?

This is P(X = 10).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282[/tex]

2.82% probability that all of the sprinklers will operate correctly in a fire

Answer 2

The probability that all sprinklers will operate correctly in a fire is 0.028

How to determine the probability

The given parameters are:

p = 0.7 ---- the probability that a sprinkler to activate correctly

n = 10 --- the number of sprinklers

The probability that all sprinklers activate correctly is calculated as:

[tex]P(10) = p^n[/tex]

So, we have:

[tex]P(10) = 0.7^{10[/tex]

Evaluate

[tex]P(10) = 0.028[/tex]

Hence, the probability that all sprinklers will operate correctly in a fire is 0.028

Read more about probability at:

https://brainly.com/question/25870256


Related Questions

Manuel was laying in the floor kitchen. The room measured 12 feet in length and 8 feet on width. What is the area of the kitchen floor.

Answers

Answer:

96 feet

Step-by-step explanation:

12 feet × 8 feet = 97 feet

Petra has 12 pound and ski has nothing. They both receive the same money for doing a delivery job.
Now Petra has three times as much as ski.
How much did they get for the job?

Answers

Answer:

6 pounds

Step-by-step explanation:

Originally

Petra : 12 pounds

Ski: 0 pounds

Delivery job

Petra & Ski: Same amount.

Represent amount with 'D'

Total Amount

Petra: 12 + D pounds

Ski: D pounds.

Petra has three times as much as Ski, meaning

12 + D = 3 (D)

12 + D = 3D

12 = 3D - D

12 = 2D

Divide both sides by 2

6 = D...

What is the volume of a cylinder, in cubic cm, with a height of 19cm and a base
diameter of 10cm? Round to the nearest tenths place.

Answers

Answer:

549.8 cm (cubed)

Step-by-step explanation:

D3lt4 m4th 4n$wer

Karen bought 4⁄5 pound of broccoli and 2⁄10 pound of cauliflower. How many more pounds of broccoli did she buy?

Answers

Answer:

6/10 or 3/5

Step-by-step explanation:

4/5 = 8/10

8/10 - 2/10 = 6/10 or 3/5

⅗ or 6/10

Step-by-step explanation:

4/5=8/10

8/10-2/10=6/10 or ⅗

Which of these statements describes scarcity? A. It is a situation in which people cannot pay for goods and services. B. It is an economic situation where the government has to import items. C. It is the difference between limited resources and wants and needs. Reset N

Answers

Answer:

C -- It is the difference between limited resources and wants and needs.

Step-by-step explanation:

I've done a lesson on scarcity before.

Plz click the Thanks button!

<Jayla>

It is the difference between limited resources and wants and needs. Reset N.

What is Government?

A government is the system or group of people governing an organized community, generally a state.

Scarcity "refers to the basic fact of life that there exists only a finite amount of human and nonhuman resources which the best technical knowledge is capable of using to produce only limited maximum amounts of each economic good.

In the given  statements.

A. It is a situation in which people cannot pay for goods and services.

B. It is an economic situation where the government has to import items. C. It is the difference between limited resources and wants and needs. Reset N

C describes scarcity.

Hence, It is the difference between limited resources and wants and needs. Reset N.

To learn more on Government click:

https://brainly.com/question/16940043

#SPJ2

Evaluate 5x3 - 2 + 7 when x= -2.

Answers

Answer:

-995

Step-by-step explanation:

5(-2)^3 - 2 + 7

first you would multiply the 5 by -2

(-10)^3 - 2 + 7

then the exponents

-1000 - 2 + 7

then you would subtract -1000 by 2

-1002 + 7

then add the 7

-995

omeone hacked into an employee's computer and erased all of their data. All data for the past three weeks was lost as that was when the employee last performed a backup. Which type of network is the company more than likely using?

Centralized
Client server
GUI
Peer-to-peer

Answers

Answer:

GUI

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Client Server

Which is the graph of F(x)= sqrt 4x

Answers

The graph of f(x) = sqrt(4x) looks like this

So choose the one that looks like the image attached

The graph has been plotted.

What is a Graph?

Graph is a mathematical representation of relation between two objects.

A graph is plotted between two variables that depicts the relation between them which is helpful in prediction of the pattern of the function that it is following.

A function is a relation between a dependent and an independent variable.

The domain and range of a function is always defined.

A domain is the value that can be an input to the function and a range is all the possible output value that can be obtained from the function.

The function is

F(x)=  √4x

A square root is the factor of a number when multiplied by itself gives the number itself.

A square root function is also called as a radical function represented by

y = √x

the domain of f(x)=√x is x≥0 and the range is y≥0

The graph of the function is plotted and attached with the answer.

To know more about Graph

brainly.com/question/14375099

#SPJ2

I need help with this question, I attached a file, so it’s easier to read.

Answers

Hello there!

The median is the middle of the data set. Since we only have 7 numbers, we can arrange it from greatest to least, however the program has already done that. So, to find the median for this data set, all we have to do is simply find the middle number. The median would be 9 for this data set.

Answer:

9

Step-by-step explanation:

The median is the middle number of the set when ordered from least to greatest. We don't have to worry about that because it's already ordered like that. In this case, since there are 7 numbers, the median must be the 4th one, which is 9.

z\10 = -12 solve for z

Answers

Answer:

z=-120

Step-by-step explanation:

z\10 = -12

z=-12 x 10

z=-120

Answer:

120

Step-by-step explanation:

z divided by 10 is -12

z is equal to -12 times 10

z equals -120

Which number represents the country of Egypt
A) 1
B) 2
C) 3
D) 4

Answers

Answer:

2

Step-by-step explanation:

the way I remember is that Egypt is always the top right country

2 is the number represents the country of Egypt. Hence, option B is correct.

What country does Egypt belong to?

In 1922, modern Egypt attained independence. Egypt and Syria formed the United Arab Republic from 1958 to 1961. The Arab Republic of Egypt, as it is officially known, has a surface area of 1 million km2, which is more than twice the size of the US State of California or roughly twice the size of France.

Egypt's history as a British colony lasted from 1882, when British troops invaded it during the Anglo-Egyptian War, to 1956, during the Suez Crisis, when the last British troops left Egypt in accordance with the 1954 Anglo-Egyptian Accord.

Modern Standard Arabic, which is used in most written documents and educational institutions, is Egypt's official language. Nevertheless, Modern Standard Arabic primarily describes Arabic's literary form, which is

Thus, option B is correct.

For more information about country does Egypt belong to, click here:

https://brainly.com/question/1043169

#SPJ6

Through how many radians does the minute hand of a clock turn in 24 minutes?

Answers

Answer:

  4/5π

Step-by-step explanation:

30 minutes corresponds to π radians, so 24 minutes is ...

  (24/30)π = 4/5π radians

Lili needs to buy colored pencils . She buys 1 red , 2 yellow and 2 blue pencils . In tatal , she will buy 25 colored pencils . How many yellow pencils will lili expect to buy ?

Answers

Answer:

1+2+2+20=25 yellow pencils

Which of the following could be the equation of the function below?

On a coordinate plane, a curve crosses the y-axis at y = negative 3. It has a maximum at y = 1 and a minimum at y = negative 3. It goes through 1 cycle at pi.
y = negative 2 cosine (4 (x + pi)) minus 1
y = 2 cosine (x + pi) + 1
y = negative 2 cosine (2 (x + pi)) minus 1
y = 2 cosine (4 (x + pi)) + 2

Answers

Answer:

  y = negative 2 cosine (2 (x + pi)) minus 1

Step-by-step explanation:

The amplitude of the trig function will be half the difference of the minimum and maximum, so is ...

  A = (1 -(-3))/2 = 2

The coefficient of x is 2π divided by the period, so is ...

  B = (2π)/π = 2

The vertical offset is the average of the maximum and minimum:

  C = (1 +(-3))/2 = -1

Since the extreme negative value is at x=0, this can be the opposite of the cosine function:

  y = -A·cos(Bx) +C

The answer choices have a horizontal offset of pi, which does nothing, since the period is pi.

  y = -2cos(2(x+π)) -1

Answer:

C on E2020.

Step-by-step explanation:

The equation of the line that goes through the point ( 3 , 4 ) and is parallel to the line 3 x + 4 y = 2 can be written in the form y = m x + b

Answers

Answer:

y = -3/4x + 7/4

Step-by-step explanation:

For it to be parallel it needs the same slope. We can find this by putting the equation 3x + 4y = 2 into y = mx + b form and using the m.

3x+4y=2 can be written as y= -3/4x + 1/2

so the m for our new equation is -3/4

now to find b we just plug in the given point

y = -3/4x + b

4 = -3/4(3) + b

b = 4 + (-9/4)

b = 7/4 or b = 1.75

A basketball player attempts eight free throws. Each attempt results in a score or a miss. Find the number of possible outcomes.

Answers

Answer:

9

Step-by-step explanation:

For one throw the probability of a miss is 1/2 since there are just two outcomes

Similarly for one throw the probability of a score is 1/2 since there are two outcomes.

Therefore for 8 trials we expect at least for different trials starting from 1

8 miss 0 score

7 miss 1 score

6 miss 2 score

5 miss 3 score

4 miss 4 score

3 miss 5 score

2 miss 6 score

1 miss 7 score

0 miss 8 score

So the number of possible outcomes is 9

And this define by what we call the binomial probability and is defined as

find the output, g, when the input, r, is 4.

g = 25 - 3r

g = __

Answers

Answer:13

Step-by-step explanation:

g=25-3(4)

25-12

g=13

Hope this helps

Answer: g = 13

Step-by-step explanation:

g = 25 - 3r

g = 25 - 3(4)

g = 25 - 12

g = 13

(N) Northeast

(M) Midwest

(T) South

(W) West










(N) (M) (T) (W) Total

2009 (A) 0.9 1.2 1.9 1.2 5.2

2010 (B) 0.8 1.1 1.9 1.2 5.0

2011 (C) 0.8 1.1 1.9 1.1 4.9

Total 2.5 3.4 5.7 3.5 15.1


Use symbols to describe the given set.


The set of sales of existing homes in 2010 in the West and Midwest

Which one?


W ∩ (B ∪ M)


B ∪ (W ∪ M)


B ∩ (W ∪ M)


B ∩ (W ∩ M)


W ∪ (B ∪ M)


Compute its cardinality.

? million

Answers

Answer:

B ∩ (W ∪ M)2.3 million

Step-by-step explanation:

Apparently, these sets represent sales of existing homes. Then (values of) the homes sold in 2010 are those listed in set B.

The English wording "West and Midwest" doesn't actually mean homes that are categorized as both West and Midwest. There aren't any such homes, because these sets are mutually exclusive. That wording logically means "West or Midwest", so would represent the union W ∪ M.

Then the homes in W∪M that were sold in 2010 will be ...

  B ∩ (W ∪ M) . . . . . matches the 3rd choice on the list

_____

The "cardinality" of a set is the number of elements in the set. Since the sets B and W and M are not shown, we cannot tell the cardinality.

Here, that word is apparently intended to mean the sum of the numbers designated as W and as M. For 2010, we have W=1.2, M=1.1, so ...

  for 2010, W +M = 1.2 +1.1 = 2.3 . . . million

plz help Marshmello i have 15 more

Answers

Answer:

53

Step-by-step explanation:

so you would subtract 30 from 401 to get 372 then divide it by the number of buses in this case it's 7 to get 53

Imagine that there are 100 different researchers each studying the sleeping habit of a college freshman. Each researcher takes a random sample size of 50 from the same population of freshman. Each researcher is trying to estimate the population mean hour of sleep freshman get at night, and each one construct a 95% confidence interval for the mean. Approximately how many of these 100 confidence will not capture the true mean

Answers

Answer:

Approximately 5 intervals will not capture the true mean hour of sleep freshman get at night.

Step-by-step explanation:

The (1 - α)% confidence interval for population mean implies that there is a (1 - α) probability that the true value of the mean is included in the interval.

Or, the (1 - α)% confidence interval for the mean implies that there is (1 - α)% confidence or certainty that the true mean value is contained in the interval.

And, if 100 such (1 - α)% confidence interval for the mean are computed then 95 of these 100 interval will consist of the true mean value.

In this case it is provided that 100 researchers estimate the population mean hour of sleep freshman get at night, and each one construct a 95% confidence interval for the mean.

Then approximately 95 of these 100 confidence intervals will capture the true mean hour of sleep freshman get at night. And approximately 5 intervals will not capture the true mean hour of sleep freshman get at night.

Suppose that you are in charge of evaluating teacher performance at a large elementary school. One tool you have for this evaluation is reports of the average student reading test score in each classroom. You also know that across the whole school, the average student reading score was 80 points and the standard deviation in scores was 10 points.
Determine:
(a) If each class has 25 students in it, what is the standard error of the classroom average score?
(b) In what range do you expect the average classroom test score to fall 95% of the time?
(c) What is the approximate probability that a classroom will have an average test score of 79 or higher?
(d) Do you think the probability that a classroom has an average test score of 79 or higher would be greater or smaller if there were only 15 students in a class? Explain your answer in 2-3 sentences.
(e) Do you think the probability that a classroom has an average test score of 79 or higher would be greater or smaller if the standard deviation of individual student reading scores was only 5 points (instead of 10)?

Answers

Answer:

a) Standard error = 2

b) Range = (76.08, 83.92)

c) P=0.69

d) Smaller

e) Greater

Step-by-step explanation:

a) When we have a sample taken out of the population, the standard error of the mean is calculated as:

[tex]\sigma_m=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{25}}=\dfrac{10}{5}=2[/tex]

where n is te sample size (n=25) and σ is the population standard deviation (σ=10).

Then, the standard error of the classroom average score is 2.

b) The calculations for this range are the same that for the confidence interval, with the difference that we know the population mean.

The population standard deviation is know and is σ=10.

The population mean is M=80.

The sample size is N=25.

The standard error of the mean is σM=2.

The z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_M=1.96 \cdot 2=3.92[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 80-3.92=76.08\\\\UL=M+t \cdot s_M = 80+3.92=83.92[/tex]

The range that we expect the average classroom test score to fall 95% of the time is (76.08, 83.92).

c) We can calculate this by calculating the z-score of X=79.

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{79-80}{2}=\dfrac{-1}{2}=-0.5[/tex]

Then, the probability of getting a average score of 79 or higher is:

[tex]P(X>79)=P(z>-0.5)=0.69146[/tex]

The approximate probability that a classroom will have an average test score of 79 or higher is 0.69.

d) If the sample is smaller, the standard error is bigger (as the square root of the sample size is in the denominator), so the spread of the probability distribution is more. This results then in a smaller probability for any range.

e) If the population standard deviation is smaller, the standard error for the sample (the classroom) become smaller too. This means that the values are more concentrated around the mean (less spread). This results in a higher probability for every range that include the mean.

8/9 Divided by 6/9 = ?
A. 17/54


B. 16/27


C. 4/3


D. 24/5


Answers

Answer:

4/3

Step-by-step explanation:

[tex] \frac{8}{9} \div \frac{6}{9} \\ \\ \implies \: \frac{8}{9} \times \frac{9}{6} \\ \\ \implies \: \frac{8}{1} \times \frac{1}{6} \\ \\ \implies \: {\boxed {\purple{\frac{4}{3} }}}[/tex]

Rob's boss gave him $100 to buy 7 lunches for a team meeting, After buying the lunches he had $14.25 leftover, How
much did each lunch cost?
A)
$11.75
B)
$12.25
C)
$12.50
D)
$12.75

Answers

Answer:

Each lunch cost $12.25

Step-by-step explanation:

Subtract 14.25 from 100 and then divide that by 7

PLEASE HELP ???
????

Answers

Answer:

Option (3)

Step-by-step explanation:

From the given figure,

Two triangles ΔABC and ΔDEF are similar.

ΔABC ~ ΔDEF

By the definition of similarity of two triangles, corresponding sides of the similar triangles are in the same ratio.

[tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}[/tex]

Now from this relation,

[tex]\frac{BC}{EF}=\frac{AC}{DF}[/tex]

[tex]\frac{DF}{EF}=\frac{AC}{BC}[/tex]

Therefore, Option (3) will be the correct proportionality statement.

I’m thinking of an integer. Half of this integer is 3 more than one third of the next integer. What is the integer?""

Answers

Answer:

I think its 6

Step-by-step explanation:

half of 6 is 3

PLEASE HELP ?

Find the length of BC

A: 72

B: 54

C: 40.5

D: 108

Answers

D: 108 is the answer.

Answer:

its 72

Step-by-step explanation:

i did itand it showed 72

Which is greater: 5 yards or 150 inches?

Answers

Answer:

5 yards.

Step-by-step explanation:

5 yards = 180 inches

In the year 2001 Youth Risk Behavior survey done by the U.S. Centers for Disease Control, 747 out of 1168 female 12th graders said they always use a seatbelt when driving. Please construct a 98% confidence interval for the proportion of 12th-grade females in the population who always use a seatbelt when driving. 1) Use R to find the score CI for the proportion of 12th-grade females in the population who always use a seatbelt when driving (please round to 4 decimals).

Answers

Answer:

98% of confidence interval of Population proportion is determined by

(0.60683 ,0.67217)

Step-by-step explanation:

Given the sample size n = 1168

Given 747 out of 1168 female 12th graders said they always use a seatbelt when driving

The sample proportion 'p' = [tex]\frac{x}{n} = \frac{747}{1168} = 0.6395[/tex]

98% of confidence interval of Population proportion is determined by

[tex]p^{-} -Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^-)}{n} }, p^- +Z_{\frac{\alpha }{2} } \sqrt{\frac{p^-(1-p^-)}{n} } }[/tex]

The tabulated value Z₀.₀₂ score  = 2.326

[tex](0.6395 -2.326 \sqrt{\frac{0.6395(1-0.6395)}{1168} }, 0.6395 +2.326 \sqrt{\frac{0.6395(1-0.6395)}{1168} } })[/tex]

on calculation , we get

(0.6395 -0.03267 , 0.6395 +0.03267)

(0.60683 ,0.67217)

the expression that represents the following statement: add 24 to the quotient of 16 and 8.

Answers

Answer:

26

Step-by-step explanation:

The quotient of 16 and 8 = 16/8 = 2

24 + 2 = 26

Answer:

  16/8 +24

Step-by-step explanation:

The quotient of 16 and 8 is written as ...

  16/8

If we start with this as the first element of the sum then the sum that represents 24 added to this is ...

  16/8 +24

What is the area of trapezoid ABCD in square centimeters?

Answers

Answer:

99

Step-by-step explanation:

Area of trapezium = 1/2 × (sum of parallel sides × height)

The parallel sides of the trapezium are the left and right edge.

( 9 + 13) = 22

The height is the vertical distance between the parallel sides and when you turn the shape 90degrees towards the left, we would have the parallel sides been the bottom and top edge and the vertical height between will be 9

Hence the area = 1/2 × 22 × 9

= 11 ×9 = 99

You would add the unit if measure.

Other Questions
What are the positions of the sun, moon, and Earth relative to each other when we have stronger tides? The two line plots below show the times that Marco and Antonio ran in ten trials of the 40-yard dash. antonio's:4.5,4.5,4.6,4.6,4.6,4.8,4.8,5.2,5.2,5.3,5.5Marcos's:4.8,4.8,4.9,4.9,4.9,4.9,5.0,5.0,5.0,5.1Which of the following can be inferred from the data?A. Antonio runs the race faster than Marco on average.B. Marco always runs a better time than Antonio.C. Marco is more likely than Antonio to improve after a poor race.D. Antonio's average time is about 5.1 seconds, Which of the following are alternate interior angles? Select all that apply. A.5 and 4B.6 and 5C.2 and 8D.8 and 1E.3 and 5 WILL GIVE BRAINLIEST ;)What could Hitler have learned from Napoleon Bonapartes invasion of Russia in 1812? A 124-kg balloon carrying a 22-kg basket is descending with a constant downward velocity of 10.8 m/s . A 1.0-kg stone is thrown from the basket with an initial velocity of 14.3 m/s perpendicular to the path of the descending balloon, as measured relative to a person at rest in the basket. That person sees the stone hit the ground 18.8 s after it was thrown. Assume that the balloon continues its downward descent with the same constant speed of 10.8 m/s.(a) How high was the balloon when the rock was thrown out? (b) How high is the balloon when the rock hits the ground?(c) At the instant the rock hits the ground, how far is it from the basket? Why did Gorbachev believe the Soviet system needed to be reformed? solve the system of equations y=4x+1, y=x2+2x-2 Is 313756 divisible by 9? The First Battle of the Marne occurred about a year after World War Istarted.TrueFalse Identify the zero(s) of [tex]f(x)=4x^{2} - 20x - 56[/tex]. -- Urgent 10 minutes! Many points! A circle has a radius of 6/7 units and is centered at (-2.3, 0). Write the equation of this circle. PLEASEEE HELPPP MEE WITH THIS QUESTION!!!!!!! I REALLY NEED HELP!!!!! PLS ANSWER IT CORRECTLY NO GUESSING PLSS HELP ASAP!!!!!!! True or False: After coming to a complete stop, motorists are not permitted to complete a right turn during a presentation of a CIRCULAR RED signal. A left turn into a left moving one way street is also permitted. insert three arithmetic means between 25 and 9 What landform runs from Texas to Georgia? Do the functions have the same concavity?f(x)=-3x^(2)+12x-32A. Yes, f and g are both concave down.B. Yes, f and g are both concave up.C. No, f is concave up and g is concave down.D. No, f is concave down and g is concave up. Asap help It's very important The oblique pyramid has a square base.What is the volume of the pyramid?2.5 cm35 cm36 cm7.5 cm3.75 cm2 cm 2. Explain why carbon dioxide in the atmosphere is increasing.3. Describe one explanation for why Earths climate is becoming warmer.4. Analyze the factors that have limited the effectiveness of the Kyoto Protocol. Organ systems work together to meet the needs of the human body. How is the skeletal system related to the nervous system?A.The skeleton protects the brain and spinal cord.B.The brain determines how the skeleton develops.C.The brain and spinal cord hold the skeleton together.D.The skeletal system works as a part of the nervous system.