<span>the thing that everyone say after the bumpy airplane landing was : it's not the airplane's fault and it's not the pilot's fault so it's probably the asphalt
To be fair, there is no way for the passangers to know what may have caused the bump in landing. Everyone only created their own assumptions based om their personal perspective</span>
Answer:
a) 122,523,030
b) 72,930,375
c) 223,149,655
d) 100,626,625
Step-by-step explanation:
Consider that there are 5 vowels and 21 consonants in the English alphabet
a) exactly one vowel?
There a 6 possible positions for that vowel (6)
There are 5 ways to choose 1 vowel. (5)
There are 5 other positions to place one of the 21 consonants. (21^5)
b) exactly two vowels?
There are C(6,2) possible positions for both vowels (C(6,2))
There are 2 positions to choose a vowel out of 5 vowels. (5^2)
There are 4 other positions to place one of the 21 consonants. (21^4)
![N(_{v=2})=C(6,2)*5^2*21^4 = \frac{6!}{(6-2)!2!}*5^2*21^4\\N(_{v=2})= 72,930,375](https://tex.z-dn.net/?f=N%28_%7Bv%3D2%7D%29%3DC%286%2C2%29%2A5%5E2%2A21%5E4%20%3D%20%5Cfrac%7B6%21%7D%7B%286-2%29%212%21%7D%2A5%5E2%2A21%5E4%5C%5CN%28_%7Bv%3D2%7D%29%3D%2072%2C930%2C375)
c) at least one vowel?
The number of possibilities that the string contains at least one vowel is the number of total possible outcomes minus the number of outcomes with only consonants:
![N(_{v>0})=(21+5)^6-21^6 \\N(_{v>0})= 223,149,655](https://tex.z-dn.net/?f=N%28_%7Bv%3E0%7D%29%3D%2821%2B5%29%5E6-21%5E6%20%5C%5CN%28_%7Bv%3E0%7D%29%3D%20223%2C149%2C655)
d) at least two vowels?
The number of possibilities that the string contains at least two vowels is the number of possibilities that the string contains at least one vowel minus the number of possibilities that the string contains exactly one vowel:
![N(_{v>1})= 223,149,655 - 122,523,030\\N(_{v>1}) = 100,626,625](https://tex.z-dn.net/?f=N%28_%7Bv%3E1%7D%29%3D%20223%2C149%2C655%20-%20122%2C523%2C030%5C%5CN%28_%7Bv%3E1%7D%29%20%3D%20100%2C626%2C625)
To get the volume of the cylinder you'll need your formula, which is:
Volume = radius^2 • π • height
So we are trying to find the volume of the water in the cylinder, not the whole cylinder itself.
Let's find the radius. Our radius is half of the diameter, which in this case is 1, because 2 / 2 = 1
Now we need to find the height. So we need to find what 3/4 of 4 is.
If 1/4 of 4 is 1, then 3/4 of 4 equates to 3.
So our equation is:
Volume = 1^2 • π • 3
Volume = 9.42 (if you are rounding to the nearest hundredth.)
Answer:
It decreased by $14,840 and the current value is $197,160