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irakobra [83]
3 years ago
13

Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter ???

?=0.5. What is
(a) the probability that a repair takes less than 4 hours?
(b) the conditional probability that a repair takes at least 12 hours, given that it takes more than 7 hours?
Engineering
1 answer:
Andrej [43]3 years ago
3 0

We need to define the variables,

So,

F_x (x) = 1-e^{-\lambda x}\\F_x (x) = 1-e^{-0.5x}

Therefore, the probability that the repair time is more than 4 horus can be calculate as,

P(x>4)=1-P(x4)= 1-F_x(4)\\P(x>4) = 1-e^{-0.5*4}\\P(x>4) = 1-0.98\\P(x>4) = 0.018

The probability that the repair time is more than 4 hours is 0.136

b) The probability that repair time is at least 12 hours given that the repair time is more than 7 hoirs is calculated as,

P(x\geq 12|x>7)=P(X\geq7+5|x>7)\\P(x\geq12|x>7)=P(X\geq5)\\P(x\geq12|x>7)=1-P(x\leq 5)\\P(x\geq12|x>7)=1-e^{-0.5(2)}

P(x\geq 12|x>7)=0.6321

The probability that repair time is at least 12 hours given that the repair time is more than 7 hours is 0.63

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Dennis_Churaev [7]

Answer:

composition of alpha phase is 27% B

Explanation:

given data

mass fractions  = 0.5 for both

composition = 57 wt% B-43 wt% A

composition = 87 wt% B-13 wt% A

solution

as by total composition Co = 57 and by beta phase composition  Cβ = 87  

we use here lever rule that is

Wα = Wβ   ...............1

Wα = Wβ = 0.5

now we take here left side of equation

we will get

\frac{C_\beta - Co}{C_\beta - Ca}   = 0.5

\frac{87 - 57}{87 - Ca} = 0.5  

solve it we get

Ca = 27

so composition of alpha phase is 27% B

8 0
3 years ago
Identify factors that can cause a process to become out of control. Give several examples of such factors.
Oliga [24]

Answer:

Explained

Explanation:

This situation can occur because of various factors such as:

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4 0
3 years ago
What is the resultant force on one side of a 25cm diameter circular plate standing at the bottom of 3m of pool water?
Tom [10]

Answer:

F=1.47 KN

Explanation:

Given that

Diameter of plate = 25 cm

Height of pool h = 3 m

We know that force can be given as

F= P x A

P=ρ x g x h

Now by putting the values

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P= 30 KPa

A=\dfrac{\pi}{4}\times 0.25^2\ m^2

A=0.049\ m^2

F= 30 x 0.049 KN

F=1.47 KN

So the force on the plate will be 1.47 KN.

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Marat540 [252]
What are the options?
7 0
3 years ago
Read 2 more answers
1. Fatigue equations are based solely on theoretical assumptions. Experimental data is only used to verify the theory. a. True.b
Rainbow [258]

Answer:

1.  b. False

2. b. False

3.  b. False

4.  b. False

5. a. True

6. a. True

7.  b. False

8.  b. False

9. a. True

Explanation:

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3. Although there is a cyclic stress, there are also stresses complex circumstances involving tensile to compresive and constant stress, where the solution is given into the mean stress and the stress amplitude or stress range, which is double the stress amplitude.

4. Low‐cycle fatigue is defined as few thousand cycles and high cycle fatigue is around more than 10,000 cycles.

5. The number of cycles for failure on brittle materials are less and determined compared with the ductile materials.

6.  The bending fatigue could be handled with specific load requirements  for uniform bending or axial fatigue of the same section size where the material near the surface is subjected to the  maximum stress, as in torsional fatigue, which can be performed on  axial-type specially designed machines also, using the proper fixtures if  the maximum twist required is small, in which linear motion is changed to rotational motion.

7.  A SN-Curve for a given material, is a plot displayed on logarithmic scales of the magnitude of an alternating stress in relation to the number of cycles to failure

8. The strain life method measures the strain resistance of local stresses and strains around stress concentration that controls the fatigue life of the material. It is more accurate than determining fatigue performance as the stress-life method is for long life millions of cycles in elastic stresses, but an it gets an effective stress concentration in fatigue loading.

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