It can be proved by induction.
Consider any vertex i. Let it be connected to k other vertices in the bulbs section.
If you switch vertex i, we switch on k bulbs.
Consider the subgraph H formed by the other n-k switches and n-k bulbs.
Since this subgraph also satisfies the condition that...
Since the distribution is not given,a fair assumption is to take exactly 6 bookings that day
Let us say he books 1,2,3 as his time slot(of 1,2,3,4,5,6,7,8)
We first compute the probability that all the 3 time-slots are filled with all the dentists
Pr(of the 6 appointments,3 appointments fall...
The answer is
P(\text{getting n})=\frac{r_1^n+r_2^n+r_3^n+r_4^n+r_5^n}{7} +\frac{2}{7}
where r_1,r_2,r_3,r_4,r_5 are the roots of the equation
6x^5+5x^4+4x^3+3x^2+2x+1=0
The roots are:
r_1 = 0.29419455636014125+0.66836709744330092i
r_2=0.29419455636014125000+-0.66836709744330092000i...
The net acceleration is the coriolis acceleration and the centrepetal acceleration.
So
So the radial part is -rw^2
angular part is 2wv0
So the net acceleration is
sqrt(r^2.w^4+4w^2.v0^2)=mu.g
which gives
r=v0.t=sqrt(mu^2g^2-4w^2v0^2)/w^2
So
t=sqrt(mu^2.g^2-4w^2v0^2)/(v0.w^2)
It is clear...
Any bonafide moment generating function always maps to a unique distribution.
The random variable for the moment generating functi`on that you have given takes values at 1,2,3...infinity with probability 1/2,1/4,1/8...
ie p(k)=1/2^k for k in natural numbers and zero otherwise.
I did not know that.I just looked up the net and somewhere it was written cards have 4 colors.
In any case for a 2 color suite,I guess the answer would be 3/4
you have 2 cards left.
Since you already know the colors of all other cards,you know the colors that the last 2 cards can take
each of the card can take one of the 4 possible colors and you know the color pair
C1 C1
C1 C2
.
.
.16 pairs
for C1,C1 C2C2 C3C3 C4C4 you will judge it...
@Leach
I think you misread the question.The problem is not to find the time of catch when the dog is always heading towards the frisbee.
The dog is chasing the frisbee such that the angle formed by the line joining frisbee and the dog with the east west line is a constant as the equation...
It will follow the equation
y=\frac{16+\sqrt{91}}{9} x
ie y=x*{16+sqrt(9)}/9 which is a straight line
Since the equation is a straight line,it is the optimal way of catching the Frisbee.So the time is minimum.
You are almost done.Note that n^2-1 is (n-1)(n+1)
So product(n^2-1) for n=2 to n is 1.2.3^2.4^2.....=product(n^2)/2
Product(n^2+1) for n=1 to n =2.Product(1+n^2) for n=2 to n
So from the above expression
pi*cosech(pi)=2*product(n^2-1)/2*product(n^2+1)=product(n^2-1/n^2+1)
for n=2 to infty
Let us find the fraction of the number line(from 0 to 1) that will be filled:
Now we will find E(1) which is nothing but the expected fraction of the line(x=0 to x=1) given that each filling width is a small h
(h=1/N)
E(1)=h+E(1-h)
E(1-h)=(1-h){h+E(1-2h)}
and so on
hence we get...
Now turn the plane such that the 2 electrons are symmetrically moving.
ie e1 starts from -infty with speed v_0 at angle a/2
and e2 start at +infty at angle a/2
The vertical component does not change as there is no force in that direction
Energy(total) at infinity=mv^2/2+mv^2/2=mv^2
AlsoAt...
There are 6 people and you need that only if 4 combines all the locks will be opened
ie if you take any 3 people there will be 1 lock which needs to be opened and the key to that is available only with any of the other 3 people
Hence for any 3 people you need to distribute one lock among the...
Pr(5% broken is declared ok/1/2 are checked)=Pr(you get either 0 broken or 1 broken in the pile of 50)
=Pr(you get 0 or 1 faulty in 50/5 are faulty in 100)=50C5+50.50C4/{2*50C5+2*50C4*50+2*50C3*50C2}=0.1810892429
For problem 2,the position vector is given by
p(t)=a \left(Cos(\frac{kt^2}{2a}) \vec{i}+Sin(\frac{kt^2}{2a}) \vec{j}\right)
if the center is the origin and the line joining the center and the starting point is the x-axis
Now
\frac{dp(t)}{dt}=kt \left(-Sin(\frac{kt^2}{2a})...
E(e^{t\sum X_i})=\prod_{i}E(e^{t X_i})=e^{(e^t-1)(\lambda_1+..\lambda_n)}
Hence the resultant distribution is poisson with poisson parameter
\alpha_r
which is given by
\alpha_r=\sum_{i=1}^{n}\alpha_i
Using 2 dimes and 3 nickels,all the amonts within 1 dollar thar can be paid are
0c,5c,10c,15c,20c,25c,30c,35c which is 8
So when combined with $ it is
8*3-1(exclude 0$)=23
If the charge is free to move through the sphere,the motion will be a simple harmonic one
with time period=T where T is given by
T=2 \pi \sqrt{\frac{4 \pi \epsilon_0 R^3 m}{Qq}}
Consider any instant at which the missile is making an angle A with the horizontal
Consider along the direction in which the plane is moving
We have the relative velocity=
V-Ucos(A)
this is the rel vel along the line joining
missile and plane
so we have I(V-Ucos(A))dt,t:0->T)=d..(I is...
The force exerted by the ground is 3mg and the downward gravity is mg
Hence the deceleration is 3g-g=2g
hence we have
v^2=2(2g)(h)
or
h=v^2/(4g)
and v^2=2g.1.5
So
h=2*1.5/4=3/4=0.75 metres or 75 centimetres