Answer:
i) P(X<33) = 0.9232
ii) P(X>26) = 0.001
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that the mean of the Population = 30
Given that the standard deviation of the Population = 4
Let 'X' be the Normal distribution
<u>Step(ii):-</u>
i)
Given that the random variable X = 33
![Z = \frac{x-mean}{S.D}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7Bx-mean%7D%7BS.D%7D)
>0
P(X<33) = P( Z<1.5)
= 1- P(Z>1.5)
= 1 - ( 0.5 - A(1.5))
= 0.5 + 0.4232
P(X<33) = 0.9232
<u>Step(iii) :-</u>
Given that the random variable X = 26
![Z = \frac{x-mean}{S.D}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7Bx-mean%7D%7BS.D%7D)
>0
P(X>26) = P( Z>3.5)
= 0.5 - A(3.5)
= 0.5 - 0.4990
= 0.001
P(X>26) = 0.001
The motion of the mass as it moves on the bottom of the spring is a
repetitive motion.
Reasons:
The general form of the equation of the simple harmonic motion of the
mass is <em>d</em> = a·sin(ω·t)
Where;
d = The distance of the mass from the rest position
a = The maximum displacement of the mass from the equilibrium position = 6 cm
ω = The frequency of rotation
t = The time of motion
ω = The frequency of rotation
![\displaystyle \omega = \mathbf{\frac{2 \cdot \pi}{T}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Comega%20%3D%20%5Cmathbf%7B%5Cfrac%7B2%20%5Ccdot%20%5Cpi%7D%7BT%7D%7D)
Where;
T = The time to complete one cycle (the period of oscillation) = 4 seconds
![\displaystyle \omega = \frac{2 \cdot \pi}{4} = \frac{\pi}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Comega%20%3D%20%5Cfrac%7B2%20%5Ccdot%20%5Cpi%7D%7B4%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B2%7D)
Combining the above values gives the modelling equation as follows;
![\displaystyle d = 6 \cdot sin\left(\frac{\pi}{2} \cdot t \right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%206%20%5Ccdot%20sin%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B2%7D%20%5Ccdot%20t%20%5Cright%29)
Learn more here:
brainly.com/question/12904891
To find the constant of proportionality here let's look at the equation of a line for a straight graph that passes through the origin. y is your vertical y-value for any given point on the line, x is your horizontal x-value for any given point on the line, and m is the slope.
((2d)/3)^3=(2d)/3*(2d)/3*(2d)/3=(8d^3)/27
Sorry if this is confusing