A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has eight identical components, each with a probability of 0.1 of failing in less than 1,000 hours. The sub system will operate if any four of the eight components are operating. Assume that the components operate independently. Find the probability that
a. exactly two of the four components last longer than 1000 hours.
b. the subsystem operates longer than 1000 hours.

Answers

Answer 1

Answer:

a) 0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b) 0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either they last more than 1,000 hours, or they do not. Components operate independently, which means that the binomial probability distribution is used 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.

One subsystem has eight identical components, each with a probability of 0.1 of failing in less than 1,000 hours.

So 1 - 0.1 = 0.9 probability of working for more, which means that [tex]p = 0.9[/tex]

a. exactly two of the four components last longer than 1000 hours.

This is P(X = 2) when [tex]n = 4[/tex]. So

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

[tex]P(X = 2) = C_{4,2}.(0.9)^{2}.(0.1)^{2} = 0.0486[/tex]

0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b. the subsystem operates longer than 1000 hours.

The subsystem has 8 components, which means that [tex]n = 8[/tex]

It will operate if at least 4 components are working correctly, so we want:

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

So

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

[tex]P(X = 0) = C_{8,0}.(0.9)^{0}.(0.1)^{8} \approx 0[/tex]

[tex]P(X = 1) = C_{8,1}.(0.9)^{1}.(0.1)^{7} \approx 0tex]

[tex]P(X = 2) = C_{8,2}.(0.9)^{2}.(0.1)^{6} \approx 0[/tex]

[tex]P(X = 3) = C_{8,3}.(0.9)^{3}.(0.1)^{5} = 0.0004[/tex]

Then

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0 + 0 + 0.0004 = 0.0004[/tex]

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0004 = 0.9996[/tex]

0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.


Related Questions

Here is the third problem:)

Answers

Answer:

15.0

Step-by-step explanation:

we are finidng the adjacent angle, they have given us the opposite and the missing adjacent side so we use tan

tan25=7/x

since x is at the bottom then switch

x= 7/tan25

x= 15. 012

Answer:

x = 15.01

Step-by-step explanation:

Given degrees 25

Since x is between the right angle and 25, x is adjacent

7 being the other shortest side would be the opposite

Given adjacent and opposite, you can use tangent

Tangent = opposite/adjacent

Tan(25) = 7/x

0.4663076582 = 7/x

x = 7/0.4663076582 (use calculator)

Solution: x = 15.0115484421

PLZ HELP I WILL GIVE BRAINLIEST

Answers

Answer:

33 m^2

Step-by-step explanation:

Since the area of a kite can be found by h1*b1 + h2*b2, the area is

3 * 1 + 3 * 10 = 33 m^2

I nEd the answer pls

Answers

Answer:

C

Step-by-step explanation:

[tex]SA = 2(lw) + 2(lh) + 2(wh)[/tex]

Plz help me well mark brainliest if you are correct!!.....

Answers

Step-by-step explanation:

the base is 5unit and the height is 9unit

Answer:

The base is 5 units the height is 9 units

Step-by-step explanation:

Just count the blocks in the diagram

base  = 5

Height = 9

Start at the origin. Move 2 units right and 8 units up. What is the ordered pair for this point? pls help ASAP​

Answers

Answer: (2,8)

Step-by-step explanation:

The origin is the point (0,0), so when you move two units right you land on the x-value of 2. From there you then add 8 units, putting you at the y-value of 8. Therefore, you end with the point (2,8) after this translation.

WILL




GIVE BRAINLIST ANSWER

...
.

..
.

..
.
.
.
.

Answers

Answer:

-10, -|-8|, -(-2), |-11|, 5²

Step-by-step explanation:

Answer:

YOU POST THIS TWICE

IT'S -10, -|-8|, -(-2), |-11|, 5²

Step-by-step explanation:

Simplify (x2y)3.

x2y3
x5y3
x6y3

Answers

Answer:

3x2^y

Step-by-step explanation:

brainleist plss

sum difference place value of 2 in 4242​

Answers

Answer:

[tex]\huge\colorbox{violet}{✏﹏ \: ᴀɴsᴡᴇʀ \: }[/tex]

4242

2 = 200 ( 2 is in hundred's place )

4242

2 = 2 ( one's place )

Difference = ?

[tex] = 200 - 2 \\ = 198[/tex]

Sum = ?

[tex] = 200 + 2 \\ = 2[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

[tex] \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]

What are the zeros of the function y = 2x2 + 9x+4 ?

Help pls! ;-;

Answers

Answer:

x = {-4, -1/2}

Step-by-step explanation:

2x² + 9x + 4 = 0

Factor

(2x + 1)(x + 4) = 0

2x + 1 = 0

x = -1/2

x + 4 = 0

x = -4

x = {-4, -1/2}

Solve for x. Round your answer to the nearest tenth

Answers

Answer:

Step-by-step explanation:

sin^1(17/19)

x= 63.475 round it how u want

Hannah and Corrine are playing a game by rolling two cubes, each numbered 1 through 6. If the sum of the numbers on the cubes is 7, Hannah wins. If the sum is not 7, Corrine wins. Corrine says Hannah can win only if the following occurs:
1 on the first cube, 6 on the second cube
2 on the first cube, 5 on the second cube
3 on the first cube, 4 on the second cube

Which best explains if Corrine is correct?

Corrine is correct because there are only three ways to have a sum of 7 when the cubes are rolled.

Corrine is correct because there are no 7s on the cubes, so Hannah must roll a greater number on the second cube.

Corrine is not correct because Hannah can also roll doubles on the cubes, such as 3 on the first cube and 3 on the second cube or 4 on the first cube and 4 on the second cube.

Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.

Answers

D. Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.

Step-by-step explanation:

To get a sum of 7 by rolling two cubes, we need to get one of the combinations from the list below:

1 on the first cube, 6 on the second cube

or

6 on the first cube, 1 on the second cube

2 on the first cube, 5 on the second cube

or

5 on the first cube, 2 on the second cube

3 on the first cube, 4 on the second cube

or

4 on the first cube, 3 on the second cube

Therefore, the correct answer option is D. Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.

Almost there! I can smell the victory

Answers

Answer:

165

Step-by-step explanation:

18 x 6 = 108

19 x 3 = 57

108 + 57 = 165

:)

165! Baiiiiiiiii! :3

A rectangular yard has dimensions 10 meters by 8 meters. In the middle of the yard is a rectangular pond of 8 square meters, leaving a uniform walkway around the pond. Write a quadratic equation in standard form to find the width of the walkway.

Answers

hahahaha i had this same question in my grade

PLEASE ANSWER ASAP FOR BRAINESLT!!!!!!!!
Mrs. Lee randomly surveyed 25 of her 125 students about their pets. Her survey indicate that 14 students have a dog, 7 students have a cat, 2 students have another kind of pet, and 8 students have no pet. (Note that some students have more than one pet). What is Mrs. Lee's best estimate of the total number of her students who have a dog?


A. 70

B. 35

C. 10

D. 40

Answers

Answer: Hello! When I tried solving the problem and I got the answer of 70.

Step-by-step explanation:

So, 14 out of the 25 kids have a dog. If you were to have 125 kids which if 5 times the first 25 kids it would be 14 x 5 which is 70.

can anyone help me with this?

Answers

Answer:

x = 51

Step-by-step explanation:

The figure shown is a pentagon

The angles in a pentagon add up to equal 540

Which means that 77 + 107 + 156 + 149 + x = 540

                                    ^ ( note that we just created an equation that we can      

                                        use to solve for x )

We then solve for x using that equation

77 + 107 + 156 + 149 + x = 540  

step 1 combine like terms

77 + 107 + 156 + 149 = 489

we now have 489 + x = 540

step 2 subtract 489 from each side

489 - 489 cancels out

540 - 489 = 51

we're left with x = 51

Property of 10+5=5+10

Answers

Answer:

Commutative Property of Addition

Answer:

Commutative property

Step-by-step explanation:

The commutative property is when the order of the addends is changed, the sum stays the same.

Ex. 3+7 = 7+3

Both 3+7 and 7+3 = 10

If a fair coin is tossed 7 times, what is the probability, to the nearest thousandth, of getting exactly 5 heads?

Answers

Answer:

0.164

Step-by-step explanation:

delta math said so but

n=7 ; r=5; p=1/2

q= 1- 1/2 = 1/2

7c5(1/2)^5 (1/2)^2 = 0.16406 which is 0.164

1
1
1
4
2
4
2
2
3
9
343
4 16
4
1
B
D
y
ху
1 12
1 3
2
1
25
3 3/2
37
4
2
9
Which table shows y as DIRECTLY PROPORTIONAL tox?
0
A)
A
B)
B
D
D
D

Answers

Answer:

what are you trying to do or say

I would greatly appreciate if you could solve this 4 me. Thank you!

Answers

Answer:

B would be your Answer

Step-by-step explanation:

There are three 2s, one 2 1/4, three 2 1/2, two 2 3/4, and one 3 (which is all displayed on B).

Hope this helped :)

The area formula also works with numbers that aren’t whole. A standardpiece of paper has a height of 8.5 inches and width of 11 inches. What is the area?

Answers

Answer:

it is 93.5

Step-by-step explanation:

ok im on

What is the volume of the cylinder below?

Answers

Answer:

[tex]Volume=80\pi[/tex] [tex]units^{2}[/tex]

Step-by-step explanation:

Perpendicular height of the base of cylinder h = 5 units

Slant height I = 6 units

Radius of the cylinder r = 4 units

Volume of the lateral cylinder is

[tex]V = \pi r^{2} h[/tex]-----------(1)

Where r is radius of the cylinder

And h is perpendicular height of the base of cylinder.

Now, we substitute r and h value in equation 1.

[tex]V=\pi[/tex] × [tex]4^{2}[/tex] × [tex]5[/tex]

[tex]V=\pi[/tex] × [tex]16[/tex] x [tex]5[/tex]

[tex]V=\pi[/tex] × [tex]80[/tex]

[tex]V=80\pi[/tex] [tex]units^{2}[/tex]

Therefore, the volume of the given cylinder is [tex]80\pi[/tex] [tex]units^2[/tex].

A cone has a height of 20 centimeters and a radius of 18 centimeters. What is its volume?

Use ​ ≈ 3.14 and round your answer to the nearest hundredth.

Answers

Answer:

6785.84

Step-by-step explanation:

HELPPPPPPP PLEASE. IM SO CONFUSED IM WEIRD

Answers

I think that the answer is A.

Kevin rented a truck for one day. There was a base fee of $20.95, and there was an additional charge of 94 cents for each mile driven, Kevin had to pay
$214.59 when he returned the truck. For how many miles did he drive the truck?
miles
?
PLS HELP

Answers

Answer:

Owner-operators may take in over $260,000 in gross revenue, but once you deduct expenses, maintenance and all of the costs that go along with running a truck, many don’t earn much more than experienced company drivers. It costs about $180,000 per year to run a commercial truck. Operating costs in the trucking industry are about $1.38 per mile.

Step-by-step explanation:

determine the perimeter of quadrilateral CGHI

Answers

Answer:

if the sides are 2, 3, 4.2, 2.6 then the perimeter is 11.8

Step-by-step explanation:

just add them together

1. A guitar is on sale with a 55% discount.
If it regularly sells for $270, what is the
amount of discount?

Answers

Answer:

it should be 148.5

Step-by-step explanation:

Answer:

$121.50 is  the new amount! The discount is $148.50

Step-by-step explanation:

A 10 ft board is to be cut into three pieces, two equal- length ones and the third 9 in shorter than each of the other two. If the cutting does not result in any length being lost, how long are the pieces?

Answers

Answer:

Let  x  represent one of the equal length sides making the third side which is  3  inches shorter than each of the other two equal to:

Third piece  =  x − 3 . Knowing that the whole board is  10  feet, in inches it is:

10  feet  ×  12  inches / 1  foot  =  120  inches

To find the length of the pieces, add them and equate it to the legth of the board in inches as shown below:

x  +  x  +  x  −  3  =  120  + 3

3 x /3  =  123 /3

x  =  41  inches

Third piece  =  x  −  3  =  

41  −  3  

=  38  inches

Step-by-step explanation:

evaluate the expression when a = -15 and b = -5 b+14/a

Answers

I would say the answer is -0.6

Determine the equation of the quadratic function shown below.

Answers

(x-3)^2+2! Also please do not click the link in the other comment, it could be a scam.

A new car is purchased for 17300 dollars. The value of the car depreciates at 9.25% per year. What will the value of the car be, to the nearest cent, after 15 years?

Answers

Answer:

1137004: A new car is purchased for 17000 dollars. The value of the car depreciates at 13.5% per year. What will the value of the car be, to the nearest cent, after 12 years?

Step-by-step explanation:

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