Answer:
Step-by-step explanation:
Let <em>A</em> be the event of getting an odd number.
<em>P(A)</em> be the probability of getting an odd number.
Total odd numbers here are 6 i.e. 
Here, total numbers in the game are 12 i.e 
.
Formula for probability of an <em>event E</em> can be observed as:
Let <em>B</em> be the event of getting 11.
<em>P(B)</em> be the probability of getting 11.
Total number of possible cases is 1.
is the probability that we get 11 and an odd number.
Possible number of cases = 1
<em>P(B/A)</em> is the probability that we get an 11 given that it is an odd number.
Hence, P(B/A) =
Find an equation of the plane that contains the points p(5,−1,1),q(9,1,5),and r(8,−6,0)p(5,−1,1),q(9,1,5),and r(8,−6,0).
topjm [15]
Given plane passes through:
p(5,-1,1), q(9,1,5), r(8,-6,0)
We need to find a plane that is parallel to the plane through all three points, we form the vectors of any two sides of the triangle pqr:
pq=p-q=<5-9,-1-1,1-5>=<-4,-2,-4>
pr=p-r=<5-8,-1-6,1-0>=<-3,5,1>
The vector product pq x pr gives a vector perpendicular to both pq and pr. This vector is the normal vector of a plane passing through all three points
pq x pr
=
i j k
-4 -2 -4
-3 5 1
=<-2+20,12+4,-20-6>
=<18,16,-26>
Since the length of the normal vector does not change the direction, we simplify the normal vector as
N = <9,8,-13>
The required plane must pass through all three points.
We know that the normal vector is perpendicular to the plane through the three points, so we just need to make sure the plane passes through one of the three points, say q(9,1,5).
The equation of the required plane is therefore
Π : 9(x-9)+8(y-1)-13(z-5)=0
expand and simplify, we get the equation
Π : 9x+8y-13z=24
Check to see that the plane passes through all three points:
at p: 9(5)+8(-1)-13(1)=45-8-13=24
at q: 9(9)+8(1)-13(5)=81+9-65=24
at r: 9(8)+8(-6)-13(0)=72-48-0=24
So plane passes through all three points, as required.
Answer:
value of x is for values that are excludedor or left out
If you are travelling at 65 mph, you have to think of it as if you are moving at a constant speed. By dividing 65 by 60, you are calculating how many miles you are moving each minute. In doing so, you can calculate that you are moving at 1.083333 miles each minute. That's approximately 5720 feet per minute. (This is calculated by multiplying 1.083333 by 5280 (the number of feet in a mile)). 5720 x 22 minutes, you will have traveled 125,840 feet.
Hope this helps!
