G. how many different 6-letter arrangements can be formed using the letters in the word absent, if each letter is used only once? a. 6 b. 36 c. 720 d. 46,656

720

Step-by-step explanation:

Given : The word  ABSENT

To Find: How many different 6-letter arrangements can be formed using the letters in the word ABSENT, if each letter is used only once?

Solution:

Number of letters in ABSENT = 6

So, No. of arrangements can be formed using the letters in the word ABSENT, if each letter is used only once = 6!

                                                   =

                                                   =

So, Option C is true

Hence there are 720 different 6-letter arrangements can be formed using the letters in the word ABSENT.

1. To solve this exercise you must apply the "Trapezoid midsegment theorem", which says that the length of the midsegment is equal to half the sum of the lengths of the bases of the trapezoid. Therefore, you have:
 
 x=(a+b)/2
 
 "x" is the midsegment (x=19).
 "a" and "b" are the bases (a=27).
 
 2. When you clear the second base "b" from the formula  x=(a+b)/2 and you substitute the values, you obtain: 
 
 x=(a+b)/2
 2x=a+b
 b=2x-a
 b=2(19)-27
 b=38-27
 b=11
 
 What is the length of the 2nd base of a trapezoid?
 
 The answer is: 11