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Stels [109]
3 years ago
7

Determine the fraction of total interest owed using the rule of 78. After the six month of a 12 month loan, the numerator is: {(

n+11)+(n+10)+(n+9)+(n+8)+(n+7)+(n+6)} = The denominator is: {(n)+(n+1)+...+(n+11)} = Therefore, the fraction is numerator/denominator (to the nearest tenth) =
Mathematics
1 answer:
Dima020 [189]3 years ago
5 0

Answer:

The fraction of total interest owed is  \frac{57}{78}

The value of it to the nearest tenth is 73.1%

Step-by-step explanation:

Let us solve it using the rule of 78

∵ The loan = 12 month

∵ The numerator is after 6 month

- Substitute n by 1 in each bracket

∴ The numerator = {(1 + 11) + (1 + 10) + (1 + 9) + (1 + 8) + (1 + 7) + (1 + 6)}

∴ The numerator = {12 + 11 + 10 + 9 + 8 + 7}

∴ The numerator = {57}

∴ The numerator of the fraction is 57

∵ The denominator = {(n) + (n + 1) + (n + 2) + .......... + (n + 11)}

- substitute n by 1 in each bracket

∴ The denominator = {1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12}

∴ The denominator = {78}

∴ The denominator of the fraction is 78

The fraction of total interest owed is  \frac{57}{78}

Now find the value of the fraction

∵ The fraction = \frac{57}{78}

∴ Its value = 0.7307692308 × 100%

∴ Its value = 73.07692308%

- Round it to the nearest tenth

∴ Its value = 73.1%

The value of it to the nearest tenth is 73.1%

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olchik [2.2K]
The correct answer is:  [B]:  " 25 a²⁵ b²⁵ " .
_________________________________________________________
<span>Explanation:
_________________________________________________________
Given the expression: 
_________________________________________________________
       </span>→  " (−5a⁵b⁵)² (a³b³)⁵  " ;   Simplify.
_________________________________________________________
Let us being by examining:
______________________________________
       →    "(−5a⁵b⁵)² " . 

→  "(−5a⁵b⁵)²  = (-5)² * (a⁵)² * (b⁵)²  = (-5)(-5) * a⁽⁵ˣ²⁾ * b⁽⁵ˣ²⁾  = 25a⁽¹⁰⁾b⁽¹⁰⁾ ;

{Note the following properties of exponents:
    (xy)ⁿ = xⁿ * yⁿ ; 

    (xᵃ)ᵇ = x⁽ᵃ * ᵇ) ; 

    (xᵃ) * (xᵇ) = x⁽ᵃ ⁺ ᵇ⁾ .}.
______________________________________

Then, we examine:
______________________________________
      →    "(a³b³)⁵ " .

→  "(a³b³)⁵ = a⁽³ˣ⁵⁾b⁽³ˣ⁵⁾ = a⁽¹⁵⁾b⁽¹⁵⁾ .
______________________________________

So:   " (−5a⁵b⁵)² (a³b³)⁵ = (-5)a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾  " ; 
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Now, we simplify:

          →  " 25a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ " ; 

→  " 25a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ ;
 
               =  25a⁽¹⁰⁾ a⁽¹⁵⁾b⁽¹⁰⁾ b⁽¹⁵⁾  ;

               =  25a⁽¹⁰ ⁺¹⁵⁾ b⁽¹⁰⁺¹⁵⁾ ;

               =  25a⁽²⁵⁾ b⁽²⁵⁾ ; 
_______________________________________________
  →  which is:  Answer choice:  [B]:  " 25 a²⁵ b²⁵ " .
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