In how many ways can the letters of the word POLICEMAN be arranged if the 'word' must begin with L and end with a vowel? & What is the probability the 'word will begin with L and end with a vowel?

20160 ways

Probability = 0.0556

Step-by-step explanation:

We have 9 different letters, so the total number of words we can make is:

If we want just the words that begin with L and end with a vowel, we would have the first letter "locked", so we have 8 letters remaining, and it must end with a vowel, so the last "slot" has just 4 possible values (A, E, I or O). Then we would have 4 possible values for the last letter and 7 remaining letters in the middle of the word:

The probability is calculated by the division of the number of words we want over the total number of words:

g(x) is the negative form of f(x)? because whenever its the negative form it reflects its self over the x axis. idk if this is right though.

step-by-step explanation:

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you