Consider a series system consisting of n independent components. Assuming that the lifetime of the ith component is Weibull distributed with parameter X, and a, show that the system lifetime also has a Weibull distribution. As a concrete example, consider a liquid cooling cartridge system that is used in enterprise-class servers made by Sun Microsystems [KOSL 2001]. The series system consists of a blower, a water pump and a compressor. The following table gives the Weibull data for the three components. Component L10 (h) Shape parameter (a) Blower 70,000 3.0 Water pump 100,000 3.0 Compressor 100,000 3.0 L10 is the rating life of the component, which is the time at which 10 % of the components are expected to have failed or R(L10) = 0.9. Derive the system reliability expression.

Answers

Answer 1

The reliability expression for the system can be derived as follows :R(t) = e-(t/L10)9Therefore, the system reliability expression is e-(t/L10)9.

Let us take the following details of the given data, Blower: L10 (h) = 70,000 and Shape parameter (a) = 3.0Water pump: L10 (h) = 100,000 and Shape parameter (a) = 3.0Compressor: L10 (h) = 100,000 and Shape parameter (a) = 3.0Assuming that the lifetime of the ith component is Weibull distributed with parameter X and a, the system lifetime also has a Weibull distribution .Let R be the reliability of the system. Now, using the formula of Weibull reliability function ,R(t) = e{-(t/θ)^α}Where,α is the shape parameterθ is the scale parameter . We can say that the reliability of the system is given by the product of the reliability of individual components, which can be represented as: R(t) = R1(t)R2(t)R3(t) .Let, T1, T2, and T3 be the lifetimes of Blower, Water pump, and Compressor, respectively. Then, their cumulative distribution functions (CDF) will be given as follows :F(T1) = 1 - e(- (T1/θ1)^α1 )F(T2) = 1 - e(- (T2/θ2)^α2 )F(T3) = 1 - e(- (T3/θ3)^α3 )Now, the system will fail if any one of the components fail, thus: R(t) = P(T > t) = P(T1 > t, T2 > t, T3 > t) = P(T1 > t)P(T2 > t)P(T3 > t) = e(-(t/L10)3) e(-(t/L10)3) e(-(t/L10)3)  = e-(t/L10)9.

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Related Questions

You and your friend travel to Cuyahoga Valley National Park Your friend agrees to pay half the total cost of gas for the trip . The gas charges for the trip are $31 $16 and $ 41 How much money , in dollars , does your friend owe you ?

Answers

It is given that the friend agrees to pay half of the total cost of gas for the trip.

It is required to find the amount of money the friend is owing.

To do this, calculate the total cost of gas and evaluate half of it.

The total cost of gas is the sum of the gas charges given:

\(31+16+41=\$88\)

Calculate half of the total cost:

\(\frac{1}{2}\cdot88=\$44\)

It follows that the friend is owing $44.

The answer is $44.

write an equation that represents the proportional relationship between oil and vinegar explain the meaning of the point

write an equation that represents the proportional relationship between oil and vinegar explain the meaning

Answers

To write and equation we call y=oil and x=vinager, so:

\(\begin{gathered} y=k\cdot x \\ \text{Where k is some constant of proportionality} \end{gathered}\)

To find the constant k we can use the point in the picture (vinager, oil) = (x, y) = (1, 1.5), so:

\(\begin{gathered} x=1,y=1.5 \\ 1.5=k\cdot1\Rightarrow k=1.5 \end{gathered}\)

So, the equation is:

\(y=1.5x\)

Now, the meaning of the point (1, 1.5) is for 1 amount of vinager you need 1.5 amount of oil.

If a swimming pool is being filled at a rate of 5,000mL per minute how fast is the pull fillingnin Liters per hour?

Answers

Answer:

300 liters per hour

Step-by-step explanation:

5,000mL * 60(mins) = 300,000 mL per hour

we divide 300,000 mL by 1000 to get 300 liters per hour.

What is the correct answer?

What is the correct answer?

Answers

Answer:

2.38 yds^3

Step-by-step explanation:

Volume of a box = width x length x height

Now we multiply!!

? = 1 x 1.7 x 1.4

1 x 1.7 x 1.4 = 2.38

Have an amazing day!!

Please rate and mark brainliest!!

\( \huge\fbox\orange{ANSWER} \)

\( \mathsf \purple{v = l \times w \times h}\)

\( \mathsf \pink{v = 1.7 \times 1 \times 1.4}\)

\( \mathsf \purple{v = 2.38 {yd}^{3} }\)

2.38 cubic yards

Solve the equation from Part C so that y is by itself on one side of the equation. How are this equation and the equation of the line related? What does this relationship mean about any triangle created using this line?

Solve the equation from Part C so that y is by itself on one side of the equation. How are this equation

Answers

Answer:

Earlier we found that:

y/x = 2/1

If we put y on one side by itself the equation is:

y = 2x

This is same as the equation of the red line.

Any right triangle using this line will be similar to each other.

It's easier

We know the slope formula for origin crossing line

m=y/x

Here

m is 2

So

y/x=2y=2x

1000000000000000000000000000

1000000000000000000000000000

Answers

Answer:

1. List (in order) the five phases a single 2 solar mass will go through in its life.

2. List (in order) the five phases a single 25 solar mass will go through in its life.

3. List (in order) the five phases a single 60 solar mass will go through in its life.

Phase options (can be used more than once, some may not be used at all):

Type II Supernova

Protostar

White Dwarf

Giant Phase

Main sequence

Neutron Star

Brown Dwarf

Black Hole

Type 1a Supernova

Planetary Nebula

Step-by-step explanation:

A square sandbox has an area of 75 square feet. Estimate the length of one of the sides of the
sandbox. Round to the nearest tenths place.

Answers

Answer:

8.7

Step-by-step explanation:

Since a square has equal side lengths, the formula for area is s^2, where s stands for side. Since we are given the area, s^2=75 square feet. Take the square root of both sides to get s is equivalent to the square root of 75 square feet. When this becomes a decimal, it is 8.66 feet. Since we are supposed to round to the nearest tenths, it rounds up to 8.7 feet per side length

Answers the question please

Answers the question please

Answers

Answer:

I would say (B) 14,55

Step-by-step explanation:

What is the volume of the shape?

What is the volume of the shape?

Answers

Answer:

volume: 1/3 a²h

= 1/3 ×2²x6

= 8 feet³

is it resonable to use the assumption ofn equal standard deviations when we analyze these data give a reason

Answers

The reasonableness of assuming equal standard deviations depends on factors such as sample size, data distribution, and prior knowledge. It is important to assess these factors and make an informed decision based on the specific context and characteristics of the data being analyzed.

To determine whether it is reasonable to assume equal standard deviations when analyzing the data, we need to consider the nature of the data and the underlying assumptions of the statistical analysis method being used.

Assuming equal standard deviations means that we are assuming that the variability of the data is the same across all groups or populations being compared. This assumption is often made in statistical analyses such as analysis of variance (ANOVA) or t-tests when comparing means between groups.

Whether it is reasonable to assume equal standard deviations depends on the specific context and characteristics of the data. Here are a few factors to consider:

Sample size: If the sample sizes for each group or population being compared are similar, it may be more reasonable to assume equal standard deviations. Larger sample sizes provide more reliable estimates of the standard deviation and can help ensure that the assumption is met.

Similarity of data distribution: If the data in each group or population exhibit similar distributions and variability, assuming equal standard deviations may be reasonable. However, if the data distributions are visibly different or have varying levels of variability, assuming equal standard deviations may not be appropriate.

Prior knowledge or research: If there is prior knowledge or research suggesting that the standard deviations are likely to be equal across groups, it may be reasonable to make this assumption. However, if there is prior information indicating unequal standard deviations, it would be more appropriate to consider unequal standard deviations in the analysis.

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Find the equation of the line that has a slope of -3 and a y-intercept at 5. y = -3x + 5 y = 5x - 3 y = -5x + 3 y = 3x - 5
will give brainliest and points if correct

Answers

Answer:

y = -3x + 5

Step-by-step explanation:

m = -3 (slope)

y- intercept = 5

Answer:

y = -3x + 5

Step-by-step explanation:

Amelia went to an amusement park with $45 to spend. She bought lunch for $10.25 and paid $5.00 for each ride. What is the greatest number of rides Amelia could ride?

Answers

Answer:

Your answer is $34.75

Step-by-step explanation:

plz mark me brainliest

Answer:

6

Step-by-step explanation:

Question 1 Consider the equation 8x + 4y = 64. If we graph the equation, what is the slope of the graph? ​

Answers

Answer:

The slope is 2

Step-by-step explanation:

what+is+the+present+value+of+$5,000+received+in+two+years+if+the+interest+rate+is+7%?

Answers

The present value of $5,000 received in two years with an interest rate of 7% is approximately $4,366.93.

To calculate the present value of $5,000 received in two years with an interest rate of 7%, we need to discount the future value to its present value using the formula:

Present Value = Future Value / (1 + Interest Rate)^n

Where:

Future Value = $5,000 (the amount to be received in two years)

Interest Rate = 7% (expressed as a decimal, 0.07)

n = 2 (number of years)

Substituting the given values into the formula, we have:

Present Value = $5,000 / (1 + 0.07)^2

Calculating the expression inside the parentheses:

(1 + 0.07)^2 = 1.07^2 = 1.1449

Dividing $5,000 by 1.1449:

Present Value ≈ $4,366.93

Therefore, the present value of $5,000 received in two years with an interest rate of 7% is approximately $4,366.93.

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how many nonzero terms of the maclaurin series for ln(1 x) do you need to use to estimate ln(1.4) to within 0.00001?

Answers

To accurately estimate ln 1.4 to within 0.0001., we need at least 7 terms.

What does Maclaurin series mean?

Given the values of the function's successive derivatives at zero, a Maclaurin series is a power series that enables one to construct an approximation of a function with input values close to zero.

The Maclaurin series is what?

A Taylor series centered on zero is referred to as a Maclaurin series.

Presented function is:

f(x)=ln(1+x)

We are aware of the following expansion of ln(1+x) near zero (up to 7 terms):

\(ln(1+x)=x-\frac{x^{2} }{2} +\frac{x^{2} }{3}-\frac{x^{2} }{4}+\frac{x^{2} }{5}-........\)
Where \(-1\leq x\leq 1\)
Put x=0.4 in the preceding series for ln 1.4.

\(ln(1+0.4)=x-\frac{0.4^{2} }{2} +\frac{0.4^{2} }{3}-\frac{0.4^{2} }{4}+\frac{0.4^{2} }{5}-........\)
\(ln(1.4)=0.3365333\)

Therefore, to estimate ln 1.4 to within 0.0001, we require at least 7 terms.

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Complete the point-slope equation of the line through (-1, 6) and (1,5).
Use exact numbers.
y - 6=

Answers

Answer:

-1/2 (x + 1)

Step-by-step explanation:

y2 - y1 / x2 - x1

5 - 6 / 1 - (-1)

-1/2

y - 6 = -1/2 (x + 1)

The table below shows the number of animals at a local petting zoo.
Animal
Goats
Number
3
Ponies
3
Rabbits
8
Sheep
6
0/1
Write the ratio of ponies and goats to rabbits and
sheep.
You may write the ratio in ANY of the three forms. Remember to REDUCE the ratio, if
possible.

The table below shows the number of animals at a local petting zoo.AnimalGoatsNumber3Ponies3Rabbits8Sheep60/1Write

Answers

Answer:

3/7

Step-by-step explanation:

3 ponies + 3 goats = 6 total

8 rabbit + 6 sheep = 14 total

6/14 simplified is 3/7.


In order to save for a new computer and printer, Joseph has a summer job working at the marina where he earns $8.50 per hour. His weekly earnings are listed in the table below
The computer he wants costs $1575, and the printer costs $225. Joseph has to earn at least how much more money, m, in order to be able to afford the computer and printer?

In order to save for a new computer and printer, Joseph has a summer job working at the marina where

Answers

The correct answer is B

Explanation:

He has already made $1088 which means he needs at least (greater than or equal to) $712 more.

Mrs. Conley asks her class what kind of party they want to have to celebrate their excellent behavior. Out of all the students in the class, 555 want an ice cream party, 777 want a movie party, 101010 want a costume party, and the rest are undecided.
If 20%20%20, percent want an ice cream party, how many students are in the class?

Answers

Answer:

let 'x' represent the total number of students in the class

5 = 20% of x

0.20x = 5 divide both sides by 0.20

x = 25 students

there are 25 students in the class.

Step-by-step explanation:

1. Using the right triangle above, fill in the correct ratios for each trigonometric function. (do not simplify) numbers on the triangle: 77, 85, 36 (there is a right angle)

1. Using the right triangle above, fill in the correct ratios for each trigonometric function. (do not

Answers

Answer:

Below in bold.

Step-by-step explanation:

sin S = opposite side / hypotenuse = 77/85

cos S = adjacent side / hypotenuse = 36/85

tan S = opposite side / adjacent side = 77/36.

Answer:

see explanation

Step-by-step explanation:

sin S = \(\frac{opposite}{hypotenuse}\) = \(\frac{TU}{TS}\) = \(\frac{77}{85}\)

cos S = \(\frac{adjacent}{hypotenuse}\) = \(\frac{SU}{TS}\) = \(\frac{36}{85}\)

tan S = \(\frac{opposite}{adjacent}\) = \(\frac{TU}{SU}\) = \(\frac{77}{36}\)

The average weight of the top 5 fish at a fishing tournament was 13.3 pounds. Some of the
weights of the fish are shown in the table.

The average weight of the top 5 fish at a fishing tournament was 13.3 pounds. Some of theweights of the

Answers

Answer:

15.4 lbs

Step-by-step explanation:

Since the average of the top five is 13.3 this says that:

total weight of all the fish / 5 = 13.3 lbs

Therefore, the total weight of all five fish is equal to:

13.3 * 5 = 66.5

With this number, I subtracted all the other weights and found that the missing weight was:

15.4lbs.

Therefore, Wayne S. had the biggest fish weighing 15.4lbs

Answer:

15.4

Step-by-step explanation:

(14.2 + 13.4 + 12.1 + 11.4 + X) / 5 = 13.3

(51.1 + X) / 5 = 13.3

Cross:

51.1 + X = 66.5

then X = 66.5 - 51.1

= 15.4

7th grade, 25 points plus brainliest to the correct answer, no point theives please, the question is in the picture.

7th grade, 25 points plus brainliest to the correct answer, no point theives please, the question is

Answers

Answer:

I don't see any attachement or a picture or anything

Step-by-step explanation:

The answer is D

Sherry earns $16 per hour tutoring student-athletes at Montgomery College. If she tutored for 14.5 hours last month, how much money did she earn?

Answers

Answer:$232

Step-by-step explanation:14.5x16=232

Answer:

$232

(If you want to round, the answer would be $200)

Step-by-step explanation:

This is just a one-step equation:

16 x 14.5 = $232

find the value of k , the effective spring constant. use 16.0 and 12.0 atomic mass units for the masses of oxygen and carbon, respectively

Answers

To find the value of the effective spring constant (k), we are given the masses of oxygen (16.0 atomic mass units) and carbon (12.0 atomic mass units). We will use this information to determine the value of k.

The effective spring constant (k) is a measure of the stiffness of the spring and is usually given in units of force per unit length or mass per unit time squared. In this case, we need to determine k based on the masses of oxygen and carbon.

To find k, we can use the formula for the effective spring constant in a molecular vibration system, which is given by:

K = (ω^2)(μ)

Where ω is the angular frequency of the vibration and μ is the reduced mass of the system.

Since we are given the masses of oxygen and carbon, we can calculate the reduced mass (μ) as follows:

Μ = (m1 * m2) / (m1 + m2)

Where m1 and m2 are the masses of oxygen and carbon, respectively.

Using the given masses:
M1 = 16.0 atomic mass units (oxygen)
M2 = 12.0 atomic mass units (carbon)

We can substitute these values into the equation for μ:

Μ = (16.0 * 12.0) / (16.0 + 12.0)
= 192.0 / 28.0
≈ 6.857 atomic mass units

Now, to find the value of k, we need the angular frequency (ω) of the vibration. Unfortunately, the angular frequency is not provided in the given information. Without the angular frequency, we cannot determine the exact value of k.

Therefore, we can calculate the reduced mass (μ) using the given masses of oxygen and carbon, but we cannot find the value of k without the angular frequency.

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How much do you pay to have 3 meals per day every 7 days ?

Answers

Answer:

$53.48

Step-by-step explanation:

you pay $7.64 per day so,you times it buy 7 and you get $53.48

Natalie has 8 socks in a drawer.
5 of the socks are black.
3 of the socks are white.
Natalie takes out a sock at random, writes down its colour and puts it back into
the drawer.
Then Natalie takes out a second sock, at random, and writes down its colour.

Answers

Answer:

Probability that the two socks picked by Natalie are of the same colours = (17/32) = 0.53125

Step-by-step explanation:

Complete Question

Natalie has 8 socks in a drawer.

5 of the socks are black.

3 of the socks are white.

Natalie takes out a sock at random, writes down its colour and puts it back into

the drawer. Then Natalie takes out a second sock, at random, and writes down its colour.

Work out the probability that the two socks are of the same colour.​

Solution

This is a probability that involves replacement.

Probability of an event is given as the number of elements in the event divided by the total number of elements in the sample space.

If the event that a black socks is picked = P(B)

Then, the event that a white socks is picked = P(W)

P(B) = n(B) ÷ n(S)

n(B) = 5

n(S) = 8

P(B) = (5/8)

P(W) = n(W) ÷ n(S) = (3/8)

Probability that the two socks picked by Natalie are of the same colours = (Probability that the two socks picked are black) + (Probability that the two socks picked by Natalie are white)

Probability that the two socks picked are black = (5/8) × (5/8) (since the socks are picked and replaced, the probability stays the same)

= (25/64)

Probability that the two socks picked by Natalie are white = (3/8) × (3/8) = (9/64)

Probability that the two socks picked by Natalie are of the same colours

= (25/64) + (9/64)

= (34/64)

= (17/32) = 0.53125

Hope this Helps!!!

which is greater than 4? a. 5 b. -5 c. -15

Answers

Answer: A
Other two is less then 0

Select all of the following that are quadratic equations.
5x - 1 = 3 x+8
5 X-3 = 0
02-2x= 4 x+1
2 x2+ 12 x = 0
ox3.6 x2 + 8 = 0
9X+6 x-3=0

Answers

Answer:

2 x2+ 12 x = 0

Step-by-step explanation:

I think this is right but I am not sure :(

Answer:

2x^2+ 12 x = 0

3.6x^2 + 8 = 0

Step-by-step explanation:

Quadratic equations are those with the variable to the power of 2

2x^2+ 12 x = 0

3.6x^2 + 8 = 0

None of the other equations have the variable raised to the power of 2

Which statement is true? 1. Parallelism are frameworks 2. A square is always a rhombus 3.A rhombus is always a square 4. A rectangle is a trapezoid

Answers

Answer:

2

Step-by-step explanation:

A square is a quadrilateral with four equal sides.

Characteristics of a square includes:

• The diagonals bisect each other at 90°.

• Opposite sides parallel and of equal length

• The four angles of a square are equal.

A rhombus is a four sides quadrilateral with the four sides equal in length

The area of a rhombus =  

where p and q are the two diagonals  

Volume of a pyramid = 1/3 x ( length base x height)

Please help me ….. it’s urgent !

Please help me .. its urgent !

Answers

Answer:

1. 3.2 x 10^4

2. 6 x 10^4

3. 1.04 x 10^5

4. 1.82 x 10^7

5. 9.23 x 10^6

6. 4.05 x 10^5

7. 2.019 x 10^3

8. 3.02 x 10^4

Step-by-step explanation:

Next time don't randomly comment on other people's questions to get points without putting in the effort. Spread credibility, not liability. Do the rest by yourself; there are multiple resources online that you can learn from!

Answer:

1. 3.2 x 10^4

2. 6 x 10^4

3. 1.04 x 10^5

4. 1.82 x 10^7

5. 9.23 x 10^6

6. 4.05 x 10^5

7. 2.019 x 10^3

8. 3.02 x 10^4

Step-by-step explanation:

I really hoped this helped

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