Step-by-step explanation:
midpoint is = (x1 + x2)/2, (Y1+Y2)/2
=(-1+-7)/2, (-2+11)/2
=(-8/2,9/2)
=(-4,4.5)
(2x-1)^7
=(2x)^7+7(2x)^6(-1)+21(2x)^5(-1)^2+35(2x)^4(-1)^3+35(2x)^3(-1)^4+21(2x)(-1)^5+7(2x)(-1)^6+(-1)^7
=128x^7+7(64x^6)(-1)+21(32x^5)+35(16x^4)(-1)+35(8x^3)+21(4x^2)(-1)+14x-1
=128x^7-7(64x^6)+672x^5-35(16x^4)+280x^3-21(4x^2)+14x-1
=128x^7-448x^6+672x^5-560x^4+280x^3-84x^2+14x-1
The coefficient of x^2 is -84
Answer:
The probability is ![P(X > x) = 0.0013499](https://tex.z-dn.net/?f=P%28X%20%3E%20x%29%20%3D%200.0013499)
Step-by-step explanation:
From the question we are told that
The mean is ![\mu = 25](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%2025)
The standard deviation is ![\sigma = 5 \ minutes](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%205%20%5C%20minutes)
The random number ![x = 40](https://tex.z-dn.net/?f=x%20%3D%2040)
Given that the time taken is normally distributed the probability is mathematically represented as
![P(X > x) = P[\frac{X -\mu}{\sigma } > \frac{x -\mu}{\sigma } ]](https://tex.z-dn.net/?f=P%28X%20%3E%20x%29%20%3D%20%20P%5B%5Cfrac%7BX%20-%5Cmu%7D%7B%5Csigma%20%7D%20%3E%20%5Cfrac%7Bx%20-%5Cmu%7D%7B%5Csigma%20%7D%20%5D)
Generally the z-score for the normally distributed data set is mathematically represented as
![z = \frac{X - \mu}{\sigma }](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX%20%20-%20%5Cmu%7D%7B%5Csigma%20%7D)
So
![P(X > x) = P[Z > \frac{40 -25}{5 } ]](https://tex.z-dn.net/?f=P%28X%20%3E%20x%29%20%3D%20%20P%5BZ%20%3E%20%5Cfrac%7B40%20-25%7D%7B5%20%7D%20%5D)
![P(X > x) = 0.0013499](https://tex.z-dn.net/?f=P%28X%20%3E%20x%29%20%3D%200.0013499)
This value is obtained from the z-table
Assuming a Poisson Distribution then probability it receives "k" calls is:
![P(x=k) = \frac{\lambda^k e^{-\lambda}}{k!}](https://tex.z-dn.net/?f=P%28x%3Dk%29%20%3D%20%5Cfrac%7B%5Clambda%5Ek%20e%5E%7B-%5Clambda%7D%7D%7Bk%21%7D)
where
Answer:
Length=8 m,Breadth=6 m,Height=3 m
We know,
LSA=2(l+b)×h
LSA=2×14×3=84 m
2
Therefore, cost of painting = 84×60=Rs.5040.