Final number of white sheep = 5 - 2 =3
Final number of black sheep = 7 - 2 = 5
ANSWER product = 3*5 = 15
Answer: Work done by the particle is 78 N.
Step-by-step explanation:
If C is the path the particle follows, then work done is
.
According to the question the force
and all four points are in the plane
.
therefore, if S is the at surface with boundary C, so that S is the portion of the plane
over the rectangle D=[0,2]\times [0,4].
Now,

By the Stoke's theorem:
![\int_{C}^{}F.dx=\iint_{s}^{}curlF.dS\\\\=\iint_{D}^{}[-8y(0)-2z\left ( \frac{1}{4} \right )+5y]dA\\\\=\iint_{D}^{}\left ( -\frac{1}{2}z+5y \right )dA](https://tex.z-dn.net/?f=%5Cint_%7BC%7D%5E%7B%7DF.dx%3D%5Ciint_%7Bs%7D%5E%7B%7DcurlF.dS%5C%5C%5C%5C%3D%5Ciint_%7BD%7D%5E%7B%7D%5B-8y%280%29-2z%5Cleft%20%28%20%5Cfrac%7B1%7D%7B4%7D%20%5Cright%20%29%2B5y%5DdA%5C%5C%5C%5C%3D%5Ciint_%7BD%7D%5E%7B%7D%5Cleft%20%28%20-%5Cfrac%7B1%7D%7B2%7Dz%2B5y%20%5Cright%20%29dA)

![\int_{0}^{2}\left [ \frac{39}{16}y^2 \right ]_{0}^{4}dx\\\\=\int_{0}^{2}39\, \, dx\\\\=39\times 2\\\\=78 \, N](https://tex.z-dn.net/?f=%5Cint_%7B0%7D%5E%7B2%7D%5Cleft%20%5B%20%5Cfrac%7B39%7D%7B16%7Dy%5E2%20%5Cright%20%5D_%7B0%7D%5E%7B4%7Ddx%5C%5C%5C%5C%3D%5Cint_%7B0%7D%5E%7B2%7D39%5C%2C%20%5C%2C%20%20dx%5C%5C%5C%5C%3D39%5Ctimes%202%5C%5C%5C%5C%3D78%20%5C%2C%20N)
Answer and Explanation:
Given : The random variable x has the following probability distribution.
To find :
a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.
b. Calculate the expected value of x.
c. Calculate the variance of x.
d. Calculate the standard deviation of x.
Solution :
First we create the table as per requirements,
x P(x) xP(x) x² x²P(x)
0 0.25 0 0 0
1 0.20 0.20 1 0.20
2 0.15 0.3 4 0.6
3 0.30 0.9 9 2.7
4 0.10 0.4 16 1.6
∑P(x)=1 ∑xP(x)=1.8 ∑x²P(x)=5.1
a) To determine that table shows a probability distribution we add up all five probabilities if the sum is 1 then it is a valid distribution.


Yes it is a probability distribution.
b) The expected value of x is defined as

c) The variance of x is defined as

d) The standard deviation of x is defined as



The diagonals of a rhombus are :
Perpendicular and bisect each other
Opposite angles of a rhombus have equal measure
hope this helps
Answer:
I believe it should be d
Step-by-step explanation: