Mariah borrowed 15 books from the library last month. she's already read 2/5 of them. how many of the 15 books has she read?

She has read 6 of the books from the library.

The answer is:  "6 (six) books" .
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Explanation:
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The number of books is:  "(⅖)*15" .
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Method 1)
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    * 15 =  [(15 ÷ 5) * 2] = 3 * 2 = 6 .
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Method 2) 
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* 15 ;

= *  ;

=  =  = 6 .
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Method 3)
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* 15 ;

= *  ;

   → At this point, we can "cancel out" the "5" to a "1"; &
                            we can "cancel out" the "15" to a "3" ; 

                         → {Since:  "15 ÷ 5 = 3" ;  and since: "5 ÷ 5 = 1"}.

  → And rewrite as: = *  ;

                    → At this point, we can rewrite as:

                                 " 2 * 3 " ;   and:  "2 * 3 = 6 " . 

             →  {since: "any value, divided by "1", equals that same value};

As such:  " = 2 ";  AND:  = 3 .

→  So: *   = {2 * 3} = 6 .

→ Alternately, we can continue as follows:

*  ;

=   = = 6 .
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Method 4)
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* 15 ;

           = *  ;

           =  

               →  At this point, we can "cancel out" the "15" in the numerator to a "3"; & we can "cancel out" the "5" in the denominator to a "1" ;
                 {Since:  "15 ÷ 5 = 3" ; and since:  "5 ÷ 5 = 1" ;

               → and rewrite as follows:

               →   ;

           → At this point:  since:  "2 * 3 = 6" ;  &  since "1*1 = 1" ;
   
             We can rewrite as:    

→     =    ;  

→  We can ELIMINATE the "denominator" completely; 
Since the denominator, "(1*1)" is equal to "1" ; and since any value (e.g. the "numerator"); divided by "1" (e.g. the value of the denominator); equals the same value (e.g. that same value of the numerator);

As such, we can rewrite; and simplify; our expression (as follows):

   →     = { 2 * 3 }  = 6 .
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Method 5)
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* 15 = ?

→ Convert "" to a decimal value:

Note:     = ? / 10  ??? 

What value belongs in the "question mark" ??

→ Let us examine the denominators.

We have "5" and "10". 
→ 5 * (what value?) = 10?  ( "2" , by recognition);

→Nonetheless, to get that value:  "10 ÷ 5 = ? " ;  The answer is: "2" ; 

→ To confirm:  "5 * 2 =? 10?  Yes!

→ As such:   ;
           
                =   ;
                        
                = ; 

Convert this value to a decimal value; 
               
     →   4/10 =  4 ÷ 10 ;  
          → To divide by "10" ; Take the decimal value (The decimal value in "4" is considered the value "directly after the "4"); and move that value backward ONE decimal space; {since we are DIVIDING by "10" ; and "10" has ONE "zero"};  to get: ".4" ;   → Write as:  "0.4"  ;
 
        →   = =  0.4  .

Alternately, use a calculator to convert "" to a decimal value:

      →    =  2 ÷ 5 = 0.4 .

Now, we can rewrite:

     →   * 15  ;

as:  "(0.4)(15)" ; & calculate:
 
      → (0.4)(15) = 6 .
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 The answer is:  "6 (six) books" .
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Iwould think that the correct answer is 8.1

a. geometricb. g[h] = (3/4)·g[h-1]; g[1] = 384c. g[h] = 384·(3/4)^(h-1)d. g[12] ≈ 16.2183 gallonse. g[12] ≈ 64.8732 quarts

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt