Answer:
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Answer:
P ( 2.5 < X < 7.5 ) = 0.7251
Explanation:
Given:
- The pmf for normal distribution for random variable x is given:
f(x)=0.178 exp(-0.100(x-4.51)^2)
Find:
the fraction of individuals demonstrating a response in the range of 2.5 to 7.5.
Solution:
- The random variable X follows a normal distribution with mean u = 4.51, and standard deviation s.d as follows:
s.d = sqrt ( 1 / 0.1*2)
s.d = sqrt(5) =2.236067
- Hence, the normal distribution is as follows:
X ~ N(4.51 , 2.236)
- Compute the Z-score values of the end points 2.5 and 7.5:
P ( (2.5 - 4.51) / 2.236 < Z < (7.5 - 4.51 ) / 2.236 )
P ( -0.898899327 < Z < 1.337168651 )
- Use the Z-Table for the probability required:
P ( 2.5 < X < 7.5 ) = P ( -0.898899327 < Z < 1.337168651 ) = 0.7251
Answer:
The fluid property responsible for the development of velocity boundary layer is majorly the fluid's viscosity.
For non-viscous fluids (in theory, because no fluid is entirely non-viscous), there will be no velocity boundary layer.
Explanation:
The velocity boundary layer is the thin layer of viscous fluid that is in direct contact with the pipe surface. The velocity of fluid in this layer is 0 as fluid doesn't move in this layer.
This phenomenon is due to the viscosity of the fluid. Viscosity of the fluid refers to the internal friction that exists between fluid layers, so, the layer of fluid in contact with non-moving, static surface of the pipe experiences friction that causes this layer to not move, causing the fluid velocity to vary from 0 at this surface to the maximum value at the centre of the pipe, before the velocity begins to drop again until it reaches 0 at the other end of the circular pipe.
Since viscosity is the primary cause of this, non-viscous or inviscid fluids are saved from this phenomenon as their flows do not have the velocity boundary layer.
Although, a completely non-viscous or inciscid fluid is an idealized concept because all fluids will experience some sort of viscosity (no matter how small) between their fluid layers. Hence, a velocity boundary layer, no matter how thin (or of minute thickness), will exist in the flow of real fluids.
But, an idealized non-viscous or inviscid fluid will not have a velocity boundary layer.
Hope this Helps!!!
Answer:
Smaller impurity atom will nullify some of the compressive strain of a dislocation in a crystal. Because, smaller impurity atoms located near a dislocation creates tensile strain on atoms around it thereby partially nullifying compressive strain at the dislocation.
Answer:
The required cross-sectional area of the copper wires used to connect the source to the mine lights is 0.029mm²
Explanation:
Given.
Copper Resistivity = 1.69 *10^-8Ωm
The mine lights use a total of 5 kW and operate at 120 V dc.
So,
Power = 5kW
Power Required = 5% of 5kW
Power Required = 0.05 of 5000W
Power Required = 250W
Calculating the Resistance
The power lost in the wires is given by 120² / R, where R is the resistance.
250 = 120²/R
R = 120²/250
R = 57.6 Ω
This is small amount over 100 m.
Calculating the Cross-sectional area.
The resistance of the wires is given by:
R = 1.69 * 10^(-8) *100 / A
R = 1.69 * 10^-6/A, where A is the cross-sectional area.
1.69 * 10^(-6)/A = 57.6
A = 1.69 * 10^-6/57.6
A = 2.9340277777777E−8m²
A = 0.029mm²