The number of permutations of the 26 letters of the English alphabet that do not contain any of the strings fish, rat, or bird is 402619359782336797900800000
Let
Then
Note that since
,
But since
,
and
,
Since
where
and
What we are looking for is the number of permutations of the 26 letters of the alphabet that do not contain the strings fish, rat or bird, or
This link contains another solved problem on permutations:
Answer:
f(x):
g(x)
Step-by-step explanation:
When a function is of the form:
The equation of the axis of symmetry is
The given function is
We can see that h=-4
Hence the equation of axis of symmetry is
From the graph, the axis of symmetry of h(x) is the vertical line that divides the parabola into two congruent halves.
This line is
Answer:
The graph below shows the answer to
2x - 3y < 12
Also shown as
-3y < -2x + 12
Step-by-step explanation:
You can rearrange the inequality by subtracting 2x from both sides to isolate the y.
You now have -3y < 12 -2x
which can be put into the standard linear equation form of
-3y < -2x + 12
Then you divide both sides by -3 to get singular value of y, which is something like
-3/-3y < -2/-3x + 12/-3
which is
y > 2/3x -4
Note: I switched direction of the inequality because you are dividing both sides by a negative value.
