Consider a component that fails according to the Exponential distribution with rate 2. Failures can be of three severities 1, 2, and 3, and the failure of severity i occurs with probability Oli. The repair time for failure of severity i is exponentially distributed with rate ui. Failures of severity 1 are show stoppers, that is, the system fails completely when a failure of severity 1 occurs. On the other hand, failures of severities 2 and 3 do not completely knock out the system, and it continues to operate in a degraded mode.
a) Draw a state transition diagram that represents the failure and repair processes of the component.
b) Derive an expression for the system to be completely available.
c) Derive an expression for the system to be operating in a degraded mode.

Answer:

95% confidence interval for the population is; -0.9525 < [tex]p[/tex] < -0.9505

Step-by-step explanation:

Given the data in the question;

correlation coefficient y between output and time under a load of 588 N was −0.9515

so first we determine the quantity W.

we know that; W = [tex]\frac{1}{2}[/tex]ln([tex]\frac{1 + r}{1 - r}[/tex])

we substitute -0.9515 for r

W = [tex]\frac{1}{2}[/tex]ln([tex]\frac{1 + (-0.9515 )}{1 - (-0.9515 )}[/tex])

W = [tex]\frac{1}{2}[/tex]ln([tex]\frac{1 - 0.9515 )}{1 + 0.9515 )}[/tex])

W = [tex]\frac{1}{2}[/tex]ln([tex]\frac{ 0.0485}{1.9515 }[/tex])

W = [tex]\frac{1}{2}[/tex]ln( 0.02485 )

W = [tex]\frac{1}{2}[/tex]( -3.6948975 )

W = - 1.8474

So the quantity W is normally distributed with  standard deviation given by;

σ[tex]_w[/tex] = 1 / √(n - 3)

given that n is 33,000, we substitute

σ[tex]_w[/tex] = 1 / √(33,000 - 3)

σ[tex]_w[/tex] = 1 / √32997  

σ[tex]_w[/tex] = 0.0055

Now, at 95% confidence interval, μ[tex]_w[/tex] will be;

⇒ - 1.8474 - 1.96( 0.0055 ) < μ[tex]_w[/tex] < - 1.8474 + 1.96( 0.0055 )

⇒ - 1.8474 - 0.01078 < μ[tex]_w[/tex] < - 1.8474 + 0.01078

⇒ -1.8582 < μ[tex]_w[/tex] < -1.8366

So to obtain 95% confidence interval for p, we use the following equation;

we transform the inequality

p = [( [tex]e^{2u_w} - 1[/tex] ) / ( [tex]e^{2u_w} + 1[/tex] )]

we substitute

[tex]\frac{e^{2(-1.8582 )}-1}{e^{2(-1.8582 )} + 1}[/tex] < [tex]\frac{e^{2u_w} - 1}{e^{2u_{w}} + 1}[/tex] < [tex]\frac{e^{2(-1.8366)}-1}{e^{2(-1.8366)} + 1}[/tex]

[tex]\frac{e^{-3.7164}-1}{e^{-3.7164} + 1}[/tex] < [tex]\frac{e^{2u_w} - 1}{e^{2u_{w}} + 1}[/tex] < [tex]\frac{e^{-3.6732}-1}{e^{-3.6732} + 1}[/tex]

[tex]\frac{0.02432-1}{0.02432 + 1}[/tex] < [tex]\frac{e^{2u_w} - 1}{e^{2u_{w}} + 1}[/tex] < [tex]\frac{0.025395-1}{0.025395 + 1}[/tex]

[tex]\frac{-0.97568}{1.02432}[/tex] < [tex]\frac{e^{2u_w} - 1}{e^{2u_{w}} + 1}[/tex] < [tex]\frac{-0.974605}{1.025395}[/tex]

-0.9525 < [tex]p[/tex] < -0.9505

Therefore,  95% confidence interval for the population is; -0.9525 < [tex]p[/tex] < -0.9505

Answer: 1/8

Step-by-step explanation:

Concept

Reciprocal is any number that is reverse to the given value. This means the original number times the reciprocal will equal 1. For a more graphical explanation, please refer to the attachment below.

Solve

8×(x)=1

x=1/8

Hope this helps!! :)

Please let me know if you have any questions

Answer:

C

Step-by-step explanation:

30 x 60 x 70 = 126,000

90 x 60 x 30 = 288,000

288,000 + 126,000 = 288,000cm^3

Answer: 288,000 [tex]cm^{3}[/tex]

Step-by-step explanation:

first, break down the shape thingy into two different shapes. there's more than one way to do it, but i'll be cutting the shape horizontally at the corner of the L shape (where the 40 cm and 90 cm lines connect)

small prism dimensions: 60 x 30 x 40 = 72,000

large prism dimensions: (30+90) x (70-40) x 60 / 120 x 30 x 60 = 216,000

add them to get 288,000 [tex]cm^{3}[/tex]

The maximum value of the objective function occurs at (-3, 0). The correct option is (-3, 0).

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) and x ∈ X and y ∈ Y.

The objective function is given as f(x, y) = −2x + y − 1.

For the maximum value all the options are analysed one by one as follows,

(a) Substitute x = 3 and y = 0 in the given objective function to obtain,

-2 × 3 + 0 - 1 = -7

(b) Substitute x = -3 and y = 0 in the given objective function to obtain,

-2 × -3 + 0 - 1 = 5

(c) Substitute x = 0 and y = -3 in the given objective function to obtain,

-2 × 0 + -3 - 1 = -4

(d)  Substitute x = 0 and y = 0 in the given objective function to obtain,

-2 × 0 + 0 - 1 = -1

Hence, the maximum value of the given objective function occurs at (-3, 0).

To know more about function click on,

https://brainly.com/question/21145944

#SPJ2

Answer:

3 x 2 − 2 x -5

Step-by-step explanation:

Answer:

[tex](2 {x}^{3} - 5 {x}^{2} + 8)(x + 3) \\ = (2 {x}^{4} - 5 {x}^{3} + 8x + 6 {x}^{3} - 15 {x}^{2} + 24) \\ = 2 {x}^{4} + {x}^{3} - 15 {x}^{2} + 8x + 24[/tex]

Answer:

[tex]2x^{4} + x^{3} - 15x^{2} + 8x + 24[/tex]

Step-by-step explanation:

Mark as Brainllest

Answer: $60

Step-by-step explanation:

Here is why:

For 20 -word ad it will be $20 because of twice the amount of the 10 word amount. and another $40 for the photo!

And you get $60!

Any Questions

It will cost $54 for an 20 word ad and a photo.

We have Antique Auto News agency which charges $10 for a 10-word classified ad. Each additional word costs $0.40 and for an extra $40, a seller can include a photo in the ad.

We have to determine much would it cost for a 20-word ad with a photo.

Initial count = x

Count increasing per second = 5

Assume that the bacteria count after t seconds is y. Then -

y = x + 5t

for t = 30 ↔ y = 150 + x

According to the question, we have -

Cost of 10-word classified ad → $10

Additional word cost → $0.40

Additional Photo cost → $40

Therefore -

Assume that for a 20-word ad with a photo costs $x.

Therefore -

x = 10 + 0.40 x 10 + 40

x = 10 + 4 + 40

x = 54

Hence, it will cost $54 for an 20 word ad and a photo.

To solve more questions on Amount estimation , visit the link below-

https://brainly.com/question/8158280

#SPJ2

Answer:

b. The margin of error would decrease.

Step-by-step explanation:

Margin of error of a confidence interval:

The margin of error of a confidence interval has the following format:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which z is related to the confidence level, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

This means that the margin of error is inversely proportional to the size of the sample, which means that if the sample size increases, the margin of error decreases.

In this question, the sample size is increased, leading to a smaller margin of error. So the correct answer is given by option b.

Answer:

A- using prior knowledge

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

The distance between each dot is 25%

From 68 to 70 is 25% and 70 to 74is 25%

Above 68 is 25+25 or 50 %

Answer:

Hey!!

Step-by-step explanation:

h = d − 5 /10 + x

Hope this helps!

Have a nice day<3

The angles inside a trapezoid add up to equal 360 degrees

X = 360-90-90-75 = 105 degrees.

Answer:

87

Step-by-step explanation:

just subtract 16 from 103

Answer:

72×5.75=414

Step-by-step explanation:

is the cost of 72 books

Answer: Length: 14; Width: 4

Step-by-step explanation:

Answer: They should be 1.5 apart from each other

Answer:

2acd^3b^-1

Step-by-step explanation:

About the domain, I don't understand that but i tried to help you.

9514 1404 393

Answer:

  a≠0 and b≠0 and c≠0 and d≠0

Step-by-step explanation:

No denominator is allowed to be zero. 'c' and 'd' are in the denominator of the numerator and denominator terms. 'a' and 'b' are in the numerator of the denominator term, so will make that term zero if they are zero. In short, none of a, b, c, or d may be zero.

__

The fact that the expression simplifies to ...

  2acd^3/b

does not mean that the only restriction is b≠0.

Solution :

a). The level curves of the function :

[tex]$C(x,y) = e^{-(x^2+2y^2)/10^4}$[/tex]

are actually the curves

[tex]$e^{-(x^2+2y^2)/10^4}=k$[/tex]

where k is a positive constant.

The equation is equivalent to

[tex]$x^2+2y^2=K$[/tex]

[tex]$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$[/tex]

which is a family of ellipses.

We sketch the level curves for K =1,2,3 and 4.

If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

[tex]$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$[/tex]

[tex]$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$[/tex] and

[tex]$\triangledown C$[/tex] points in the direction of most rapid increase in concentration, which means [tex]$\triangledown C$[/tex] is tangent to the most rapid increase curve.

[tex]$r(t)=x(t)i+y(t)j$[/tex]  is a parametrization of the most [tex]$\text{rapid increase curve}$[/tex] , then

[tex]$\frac{dx}{dt}=\frac{dx}{dt}i+\frac{dy}{dt}j$[/tex] is a tangent to the curve.

So then we have that [tex]$\frac{dr}{dt}=\lambda \triangledown C$[/tex]

[tex]$\Rightarrow \frac{dx}{dt}=-\frac{2\lambda x}{10^4}e^{-(x^2+2y^2)/10^4}, \frac{dy}{dt}=-\frac{4\lambda y}{10^4}e^{-(x^2+2y^2)/10^4} $[/tex]

∴ [tex]$\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{2y}{x}$[/tex]

Using separation of variables,

[tex]$\frac{dy}{y}=2\frac{dx}{x}$[/tex]

[tex]$\int\frac{dy}{y}=2\int \frac{dx}{x}$[/tex]

[tex]$\ln y=2 \ln x$[/tex]

⇒ y = kx^2 for some constant k

but we know that [tex]$y(x_0)=y_0$[/tex]

[tex]$\Rightarrow kx_0^2=y_0$[/tex]

[tex]$\Rightarrow k =\frac{y_0}{x_0^2}$[/tex]

∴ The path of the shark will follow is along the parabola

[tex]$y=\frac{y_0}{x_0^2}x^2$[/tex]

[tex]$y=y_0\left(\frac{x}{x_0}\right)^2$[/tex]

Answer:

13.5 answer is 13.5 and one cost 4.5

Answer:

92.727

Step-by-step explanation:

The formula for compound interest is [tex]P((1+i)^{t} -1)[/tex], where P is the principal amount, i is the interest rate and t is the time. Sub your values into this formula to find your answer.

1000((1+0.03)³-1)

1000(1.03³-1)

1000(1.092727-1)

92.727

1000(0.092727)

Answer: Fish tank = 9 other fishtank= 9,000 Jewlery box=9 other jewelry box=320

CANT SEE OTHER SORRY

Step-by-step explanation: Ok first IK UR NOT IN COLLEGE second dont

cheat imma give ya answer to be noice

Answer:

8192

Step-by-step explanation:

The answer is 8192 but in your multiple-choice problem it's [tex]2^{13}[/tex]

Answer:

Its the third answer choice

Step-by-step explanation:

Hope this helped!!!

Answer:

280.56 in

Step-by-step explanation:

A square has 4 sides

67/4  = 16.75

All 4 sides are 16.75

Now, area of a square

16.75 x 16.75 = 280.5625

Round to Hundreths, 280.56.

280.6

i took the test................................

The y intercept of the equation is the 70.8.

The answer would be

B. The winning men's high jump helght of the first Olympics was about 70.8 inches.

Answer:

the answer is c

Step-by-step explanation:

because x is the number of years since the first olympics in 1896 you would multiply x=225 for 2021 by 0.23in and get 51.75in which is how much the winning jump went up over the years. so it is predicted to rise by 0.23in every competition.