After using the basic formula, the answer is down
It is a 1 in 9 chances
hope this helps
Answer:
If two distinct planes intersect, then their intersection is a line. If two distinct lines intersect, then they intersect in exactly one point. If there is a line and a point not in the line, then there is exactly one plane that contains them. If two distinct lines intersect, then they lie exactly in one plane.
Step-by-step explanation:
At first, let us solve The equation
We will subtract 4 from both sides
Then let us square both sides
Subtract 2 from both sides to get the value of x
You have two choices with 14
Which one will you choose?
To answer this you must know does this value including the domain or not
Let us try this value for x in the equation if the left-hand side equals the right-hand-side then the value is not extraneous
Since the right-hand side has the same value, so 14 is not extraneous.
So the correct answer is the third choice.
We have the equations:
<span>C(n,k) / C(n,k+1) = 1/2
</span>C(n,k+1) / C(n, k+2) = 2/3<span>
</span>[n! / (n-k)!k! ]/[ <span>n! / (n- (k+1))! (k+1)! ]= 1/2
You can cancel out similar terms. The definition of factorials is this
n! = n(n -1)(n -2)(n -3)...1
So,
</span> (n- (k+1))! (k+1)! / (n-k)!k! = 1/2
(n- k - 1)(n - k - 1 -1)! (k+1)(k + 1 - 1)! / (n-k)!k! = 1/2
(n- k - 1)(n - k - 2)! (k+1)(k)! / (n-k)!k! = 1/2
Cancel out terms.
(n- k - 1)(n - k - 2)! (k+1)/ (n-k)!= 1/2 [eqn 1]
[n! / (n-k+1)!(k+1)! ]/[ n! / (n- (k+2))! (k+2)! ]= 2/3
(n- (k+2))! (k+2)! / (n-(k+1))!(k+1)! = 2/3
(n- k-2)! (k+2)! / (n-k-1)!(k+1)! = 2/3
(n- k-2)(n - k -3)! (k+2)( k+1)k! / (n-k-1)(n-k-2)(n-k-3)!(k+1)k! = 2/3
Cancel out terms
(k+2)/ (n-k-1) = 2/3
You can solve for n in terms of k and substitute this to the fist equation which will allow you to solve for k.