What does this map show about the Viking civilization?

A fatigue test is performed on 69 rotating specimens made of 5160H steel. The measured number of cycles to failure (L in kcycles

tensa zangetsu [6.8K]

Answer:

(a) Mean = 122.9, σ = 30.071

(b) No. of failed specimens at less than 115k cycles are 27.

(c) μ = 39.07

Explanation:

We are given:

L 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210

f 2 1 3 5 8 12 6 10 8 5 2 3 2 1 0 1

(a) First we need to calculate the mean and standard deviation. The formula for calculating mean is:

Mean = ∑fx/∑f

And for standard deviation we have:

S.D. = √Var

Var = ∑fx²/∑f - (Mean)²

∑fx = (2*60) + (1*70) + (3*80) + (5*90) + (8*100) + (12*110) + (6*120) + (10*130) + (8*140) + (5*150) + (2*160) + (3*170) + (2*180) + (1*190) + (0*200) + (1*210)

= 120 + 70 + 240 + 450 + 800 + 1320 + 720 + 1300 + 1120 + 750 + 320 + 510 + 360 + 190 + 0 + 210

∑fx = 8480

Mean = ∑fx/∑f

= 8480/69

Mean = 122.9

∑fx² = (2*60²) + (1*70²) + (3*80²) + (5*90²) + (8*100²) + (12*110²) + (6*120²) + (10*130²) + (8*140²) + (5*150²) + (2*160²) + (3*170²) + (2*180²) + (1*190²) + (0*200²) + (1*210²)

=7200+4900+19200+40500+80000+145200+86400+169000+156800+112500+51200+86700+64800+36100+0+44100

∑fx² = 1104600

Var = ∑fx²/∑f - (Mean)²

= 1104600/69 - (122.9)²

= 16008.69565 - 15104.41

Var = 904.2856

S.D = √Var

σ = √904.2856

σ = 30.071

(b) Let X be the number of failed specimen.

We will use the z-score to calculate the probability. The formula for z-score is:

z = (X-μ)/σ

P(X<115) = P(z<(115-122.9)/30.071)

= P(z<-0.26)

Using the normal distribution probability table, we can compute the value of P(z<-0.26).

P(X<115) = 0.3974

So, no. of failed specimens at less than 115k cycles are: 0.3974*69 = 27 specimens

(c) σ = 30.071

P(x<115) = 0.99

P(z<(115-μ)/30.071) = 0.99

From the normal distribution table we find that 0.99 lies between the z values 2.52 and 2.33. Hence, we get 2.525 as the z-value at which the probability is 0.99.

z = (x-μ)/σ

2.525 = (115 - μ)/30.071

75.93 = 115 - μ

μ = 115 - 75.93

μ = 39.07

4 0

3 years ago

The air contained in a room loses heat to the surroundings at a rate of 60 kJ/min while work is supplied to the room by computer

charle [14.2K]

Answer:

The net amount of energy change of the air in the room during a 10-min period is 120 KJ.

Explanation:

Given that

Heat loss from room (Q)= 60 KJ/min

Work supplied to the room(W) = 1.2 KW = 1.2 KJ/s

We know that 1 W = 1 J/s

Sign convention for heat and work:

1. If heat is added to the system then it is taken as positive and if heat is rejected from the system then it is taken as negative.

2. If work is done by the system then it is taken as positive and if work is done on the system then it is taken as negative.

So

Q = -60 KJ/min

In 10 min Q = -600 KJ

W = -1.2 KJ/s

We know that

1 min = 60 s

10 min = 600 s

So W = -1.2 x 600 KJ

W = -720 KJ

WE know that ,first law of thermodynamics

Q = W + ΔU

-600 = - 720 + ΔU

ΔU = 120 KJ

The net amount of energy change of the air in the room during a 10-min period is 120 KJ.

4 0

3 years ago

Read 2 more answers

A(n)_____ is a device that provides the power and motion to manipulate the moving parts of a valve or damper used to control flu

Lesechka [4]

Answer:

Out of the four options provided

option A. actuator

is correct

Explanation:

An actuator is the only device out of the four mentioned devices that provides power and ensures the motion in it in order to manipulate the movement of the moving parts of the damper or a valve used whereas others like ratio regulator are used to regulate air or gas ratio and none mof the 3 remaining options serves the purpose

5 0

2 years ago

A particle moving on a straight line has acceleration a = 5-3t, and its velocity is 7 at time t = 2. If s(t) is the distance fro

Vikki [24]

Given acceleration a = 5-3t, and its velocity is 7 at time t = 2, the value of s2 - s1 = 7

<h3>How to solve for the value of s2 - s1</h3>

We have

= $\frac{dv}{dt} =v't = 5-3t\\\\\int\limits^a_b {v'(t)} \, dt$

$= \int\limits^a_b {(5-3t)} \, dt$

$5t - \frac{3t^2}{2} +c$

v2 = 5x2 - 3x2 + c

= 10-6+c

= 4+c

$s(t) = \frac{5t^2}{2} -\frac{t^3}{2} +3t + c$

S2 - S1

$=(5*\frac{4}{2} -\frac{8}{2} +3*2*c)-(\frac{5}{2} *1^2-\frac{1^2}{2} +3*1*c)$

= 6 + 6+c - 2+3+c

12+c-5+c = 0

7 = c

Read more on acceleration here: brainly.com/question/605631

5 0

2 years ago

What different tests did the team perform to come up with a workable design?

I am Lyosha [343]

They ran different shapes and materials through a wind tunnel to see which shape and material would decrease energy output so that it takes in equal COthan it puts out.

5 0

3 years ago