An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in firecontrol 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.

Required:
a. What is the probability that all of the sprinklers will operate correctly in a fire?
b. What is the probability that at least 7 of the sprinklers will operate correctly in a fire?
c. What is the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.98?

Answers

Answer 1

Answer:

0.028 ; 0.649 ; 4

Step-by-step explanation:

P(correctly activation), p = 0.7

Number of sprinklers, n = 10

q = 1 - p = 1 - 0.7 = 0.3

Using the binomial probability relation :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

Probability that all sprinklers activate correctly;

P(x = 10) = 10C10 * 0.7^10 * 0.3^0

P(x = 10) = 1 * 0.0282475249 * 1

P(x = 10) = 0.028

Probability that atleast 7 will operate correctly :

P(x ≥ 7) = p(x = 7) + p(x = 8) + p(x = 9) + p(x = 10)

P(x ≥ 7) = 0.267 + 0.233 + 0.121 + 0.028

P(x ≥ 7) = 0.649

3.)

Probability of atleast 1 operates :

P(x ≥ 1) = 0.98

1 - probability of 0 operates

1 - p(x =0)

P(x = 0) = nC0 * 0.7^0 * 0.3^n = 0.02

Recall :

nC0 = 1 ;

1 - p(x = 0)

P(x = 0) = 1 * 1 * 0.3^n = 0.02

0.3^n = 0.02 - - - (1)

0.3^3.24 = 0.02 - - - (2)

Comparing (1) and (2)

n = 3.24

Since, n cannot be a fraction ;

Then n is rounded to the next whole number = 4


Related Questions

IT DIVISION ITS NOT ADDING.

Answers

If you mean 13 divided by 3 then it’s 4.3/4remander 3


Rafael plans to watch 2 movies each month. Write an equation to represent the total number of movies n that he will watch in m months.

Answers

Answer:What is m?

Step-by-step explanation:

What is 1/2 divided by 1/8?

Answers

Answer:

8/2

Step-by-step explanation:

Answer:

8/2 will be your first answer but then you simplify to get the answer of 4

Use the distributive property to write an equivalent expression for 28+14y (find the greatest common factor)

Answers

14(2+y) hope this helps

Find an equation of the plane. The plane through the points (0, 9, 9), (9, 0, 9), and (9, 9, 0) Incorrect: Your answer is incorrect.

Answers

Answer:

The equation of the plane is represented by [tex]\frac{1}{18}\cdot x + \frac{1}{18}\cdot y + \frac{1}{18}\cdot z = 1[/tex].

Step-by-step explanation:

Algebraically speaking, a plane can be represented by following vectorial product:

[tex](a,b, c)\,\bullet\,(x,y,z) = 1[/tex] (1)

Where:

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Plane coeffcients.

[tex]x[/tex], [tex]y[/tex], [tex]z[/tex] - Coordinates.

We need three distinct points to determine all coefficients. If we know that [tex](x_{1},y_{1},z_{1}) = (0,9,9)[/tex], [tex](x_{2},y_{2}, z_{2}) = (9,0,9)[/tex] and [tex](x_{3},y_{3},z_{3}) = (9,9,0)[/tex], the system of equations to be solved is:

[tex]9\cdot b + 9\cdot c = 1[/tex] (1)

[tex]9\cdot a + 9\cdot c = 1[/tex] (2)

[tex]9\cdot a + 9\cdot b = 1[/tex] (3)

The solution of this system is [tex]a = \frac{1}{18}[/tex], [tex]b = \frac{1}{18}[/tex], [tex]c = \frac{1}{18}[/tex].

Hence, the equation of the plane is represented by [tex]\frac{1}{18}\cdot x + \frac{1}{18}\cdot y + \frac{1}{18}\cdot z = 1[/tex].

Please help with this question ASAP

Answers

scan it with photo math it helps

Answer:

B.  28/15

Step-by-step explanation:

7/3 x 4/5 = 28/15

(3x^2 + 8x - 4 ) -(-x^2 +5x +2) simplify​

Answers

Answer:

4x^2+3x-6

Step-by-step explanation:

Answer:

4x^2+3x-2

Step-by-step explanation:

I hope this helps

What is the perimeter of ABCD?

Answers

Answer:

360°

Step-by-step explanation:

Based on what I know that the total of degrees has to be 360°. So, two sides of the rhombus have to have two acute angles and two obtuse angles. So, the  Image shows that the 63° is an acute angle. So, multiply 63 by 2 which is 126. Then subtract 126 from 360 which is 234. Then, divide 234 by 2 which is 117. Lastly, add 63 with 63 and 117 with 117 which is 360.

Hopefully, you understand.

At the beginning of spring, Andrew planted a small sunflower in his backyard. The sunflower's height in inches, h, after weeks, is given by the equation h = 2.5w + 19 What could the number 19 represent in the equation ?

Answers

Answer:

The sunflower's height when it was planted.

Step-by-step explanation:

The sunflower's height in inches, h, after weeks, is given by the equation :

h=2.5w + 19

We need to tell that what the number 19 represent in the equation.

If we put w=0, we get,

h=2.5(0) + 19

h = 19 inches

It means when the number of weeks is equal to 0, its height is equal to 19 inches i.e. 19 represents the initial height of the sunflower. So, the correct option is (c) "The sunflower's height when it was planted."

anie spent 2.5 hours doing homework she spent 1/3 of the time on the history project she spent all remaining time writing an essay how much time did Annie spent writing the essay answer fast!!!!!!!!!!

Answers

1 hour and 40 minutes, or 100 minutes.

Divide the following. Put your answer in
scientific notation.

(77) divided by (4.9 X10^6)

Answers

Answer:

1.225 × 10 to the power 5 + 3.655 × 10³ = 1.26155 x 10 to the power 5

Step-by-step explanation:

Standard Notation:

122500 + 3655 = 1.26155 x 10 to the power 5

Scientific Notation:

1.225 × 10 to the power 5 + 3.655 × 10³ = 1.26155 x 10 to the power 5

E Notation:

1.225e5 + 3.655e3 = 1.26155e5

Shape p is translated to shape Q using vector (a b).
Please find A.
Photo attached.

Answers

Answer:

-7

Step-by-step explanation:

you basically just move across and because its moving to the left its a negative

Shape P is translated to shape Q using b[tex]\left[\begin{array}{ccc}7\\4\end{array}\right][/tex]..

What is translation of a graph?

In mathematics, a translation is the up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are congruent with one another.

Given:

The shape P is mentioned on the graph is translated to shape Q.

So, the shape shifted 7 units to left.

and, the shape needs to shift downwards 4 places.

Hence, the required vector is [tex]\left[\begin{array}{ccc}7\\4\end{array}\right][/tex].

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The temperature fell by 15 degrees Fahrenheit today.
Write a signed number to represent this temperature change.

Answers

Answer is   -15

We read this out as "negative 15" or you could write "negative fifteen".

The negative indicates the temperature went down. It doesn't necessarily mean that the final temperature is -15 degrees.

For example, if it starts being 50 degrees F, and drops by 15 degrees, then 50+(-15) = 50-15 = 35 degrees is the temperature after that drop. It might help to use a vertical number line.

There are 10 years in 1 decade. Deron is 2 decades, 4 years, and 8 months old. His brother John is half as old. How old is John?

Answers

Answer:

John is 1 decade, 2 years, and 4 months old

Step-by-step explanation:

Since we knot that John is half as old we just have to divide Derons age by two, and we will do that by dividing the number of decades, a number of years, and a number of months by two, and so we get that John is...

(2/2) decades, (4/2) years, and (8/2) months old =

= 1 decades, 2 years, and 4 months old

John is 1 decades, 2 years, and 4 months years old.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

There are 10 years in 1 decade.

And, Deron is 2 decades, 4 years, and 8 months old.

Since, His brother John is half as old.

Hence, Age of John is,

⇒ (2 decades, 4 years, and 8 months) / 2

⇒ 1 decades, 2 years, and 4 months

Thus, John is 1 decades, 2 years, and 4 months years old.

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Taylor completed 2/3 of her homework. Riian completed 7/8 of her homework. Taylor and Riian have the same amount of homework. Who completed a greater amount of homework?

Answers

Answer:

Riian completed a greater amount of homework.

Step-by-step explanation:

The fraction 7/8 is greater than the fraction 2/3.

y - 4= -8 (x - 1)
linear or nonlinear?

Answers

The answer would be it ~linear~

Hope this helps

Have a great day/night!
It’s linear because it going at a constant rate

If /Il m, what is the value of x?

Answers

Answer:

x= 137 hope it helps have a nice day

Answer:

137

Step-by-step explanation:

180-43 (these two angles plug into all the angles)

What value of m gives the system infinitely many solutions?
-X + 4y = 32
y = mx + 8

Answers

4y=32+x

y=32+x/4

32+x/4=mx+8

32+x=4mx+32

32-32+x=4mx

x=4mx

x/:=4m

1=4m

m=1/4

At 8p.m., the temperature was -9 degrees Fahrenheit. Over the next five hours, the temperature dropped by 18 degrees. What is the temperature after five hours?

Answers

Answer:

-27 if im reading the question right.

Step-by-step explanation


AB = AD
Show that ABCD is a kite.
Give a reason for each stage of your working.

Answers

It’s a kite because angle B is equal to angle D (both 105) and it all adds up to 360 making it a quadrilateral.
I hope this helps

Please help!!!!! 20pts

Answers

Answer:

vertically Angle is correct answer

The first one is none of these.

The second is Vertical, like the person above said.

I think that’s it. Sorry if i’m wrong.

If Tn =n^+2n. Find third term of the sequence

Answers

Answer:

The third term of the sequence Tₙ = n² + 2n is:

T₃ = 15

Step-by-step explanation:

Given

As the sequence is given by

Tₙ = n² + 2n

To determine

The third term of the sequence

The third term of the sequence can be determined by substituting n = 3 in the sequence

Tₙ = n² + 2n

T₃ = (3)² + 2(3)

T₃ = 9 + 6

T₃ = 15

Therefore, the third term of the sequence Tₙ = n² + 2n is:

T₃ = 15

1 poin
Sylvia is going to buy a new jacket. The regular price is $68.00 and the
jacket is on sale for 25% off. There is a 15% sales tax on the jacket. How
much will Sylvia pay for the jacket? *
86.18
$85.00
$58.65
$61.20

Answers

Sylvia will pay $58.65

Answer:

58.65 because I just know what the answer is



Identify the percent of change as an increase or decrease. Then find the percent of
change. Round to the nearest tenth of a percent, if necessary.
$18.75 to $18.60
Answers:
Increase; 15%
Decrease; 0.15%
Decrease: 0.008%
Decrease; 0.8%

Answers

Answer:

Decreasing; 0.8%

Explain 5 different ways you use Math in your everyday life.
This is a telpas thing btw

Answers

Answer:

School, Looking at what episode of anime I am on, Looking at the time, Looking at my calendar, and another is when I am doing brain teasers!

Step-by-step explanation:

Does this count?

Answer:

Time deltas

Step-by-step explanation:

A salesman earns 6% commission on all the merchandise that he sells. Last month he sold $9000 worth of merchandise. How much
commission (in dollars) did he earn last month?

Answers

$540

6% = .06
“of” = multiply
so 6% of 9000 can be written as .06 x 9000 , which is 540

The commission (in dollars) did he earn last month is 540$.

We have given

A salesman earns 6% commission on all the merchandise that he sells.

Last month he sold $9000 worth of merchandise.

Salesman earns 6% =6/100=0 .06

What is the meaning of commission?

Earning a commission means that a portion of your salary is based on the amount of sales revenue you generate or another similar performance-based goal.

So we have to determine 6% of 9000

We can be written as

=0.06 x 9000,

= 540$

The commission (in dollars) did he earn last month is 540$.

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If y= cx" and dy/dx =
4/root x

what are the values of c and n?

Answers

Answer:

c = 8

n = 1/2

Step-by-step explanation:

Since dy/dx is the derivative form, we can integrate the answer to get the value of y.

The values of c and n are obtained by forming the equations as 1/2 and 8 respectively.

What is differentiation?

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = (f(x + h) - f(x)) /(x + h - x).

It can be stated in terms of geometry as the slope of tangent of the function at a given point.

It is given as y = cxⁿ and dy/dx = 4/√x.

Take the derivative of y = cxⁿ with respect to x as,

dy/dx = cd(xⁿ)/dx

⇒ nc × xⁿ⁻¹

Compare the obtained derivative with 4/√x to obtain,

nc = 4   and  n - 1 = -1/2

⇒ n = 1/2 and c = 8

Hence, the values of c and n are 1/2 and 8 respectively.

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3
8
8
1
.
2. I need help!!!!!

Answers

Answer:

3 7/8

Step-by-step explanation:

8 3/8 - 4 1/2 =

8 3/8 - 4 4/8=

7 11/8 - 4 4/8 =

3 7/8

Answer:

The person above is correct

Step-by-step explanation:

When subtracting fraction you should make sure the deniminators (bottom number of fraction) of both fractions are the same number so you can subtract evenly. Also note whatever you do to the deniminator, you do to the numerator (top number). In this example you turn 1/2 to 4/8 in order to subtract.

A fair dice has six sides, numbered 1 to 6
After it is rolled, five of the numbers can be seen.
a) Write down the probability that one of these five numbers is 3
b) Work out the least possible sum of the five numbers​

Answers

(a). The probability that one of these five numbers is 3 is [tex]\frac{5}{6}[/tex].

(b). The least possible sum of the five numbers​ is 15

Probability:

Probability is the ratio of number of favourable outcomes to the total number of outcomes.

When a fair dice has six sides, numbered 1 to 6 ,After it is rolled, five of the numbers can be seen.

The probability that one of these five numbers is 3 is computed as,

                        [tex]P(E)=\frac{5}{6}[/tex]

The least possible sum of the five numbers, when the number 6 is hidden.

Least sum = 1 + 2 + 3 + 4 + 5 = 15

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Can someone please solve this, thankyou <3

Answers

Step-by-step explanation:

[(4³)² × 5⁶] ÷ 6⁶

(4⁶ × 5⁶) ÷ 6⁶

(4 × 5)⁶/6⁶

20⁶/6⁶

=

[tex]( \frac{20}{6} )^{6} [/tex]

=

[tex] (\frac{10}{3} ) ^{6} [/tex]

Correct answer below :
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