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Volgvan
3 years ago
11

Simplying radical expressions 75

Mathematics
1 answer:
Rudiy273 years ago
6 0
Sqrt(75)
factors of 75 are 1,3,5,15,25,75
factor 75 into 25*3
so then the sqrt(25*3)
then we can take the square root of the perfect square 25 to get 5
so 5*sqrt(3)
so the expression of sqrt(75) simplifies to 5*sqrt(3)
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3 years ago
If you bet $1 that a sum of 5 will turn up, what should the house pay (plus returning your $1 bet) if a sum of 5 turns up in ord
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Here is the complete question.

1). What are the odds for rolling a sum of 5 in a single roll of two fair dice?

2). If you bet $1 that a sum of 5 will turn up, what should the house pay (plus returning your $1 bet) if a sum of 5 turns up in order for the game to be fair?

Answer:

1).  \frac{1}{8}

2).  $8.

Step-by-step explanation:

1).

The sample space (S) for rolling two fair dice is given as the following parameters illustrated below:

\left[\begin{array}{cccccc}(1,2)&(1,2)&(1,3)&(1,4)&(1,5)&(1,6)\\(2,1)&(2,2)&(2,3)&(2,4)&(2,5)&(2,6)\\(3,1)&(3,2)&(3,3)&(3,4)&(3,5)&(3,6)\end{array}\right] \left[\begin{array}{cccccc}(4,1)&(4,2)&(4,3)&(4,4)&(4,5)&(4,6)\\(5,1)&(5,2)&(5,3)&(5,4)&(5,5)&(5,6)\\(6,1)&(6,2)&(6,3)&(6,4)&(6,5)&(6,6)\end{array}\right]

Let F represent the event that the sum of both dice turns up is 5.

F = [(1,4),(2,3),(3,2),(4,1)}

∴ The probability for an event F  is illustrated below as:

\frac{P(F)}{P(F')}  =\frac{\frac{4}{36} }{1-\frac{4}{36} }

=\frac{\frac{4}{36} }{\frac{32}{36} }

={\frac{4}{36}}*\frac{36}{32}

= \frac{1}{8}

2). From above, we can see that the probability for rolling a sum of 5 are 1 to 8. Therefore, if you roll a sum of 5, in order for the game to be fair, the house is required to pay $8.

5 0
3 years ago
A plane has 240 gallons of fuel. The plane averages 5 miles per gallon. How far can the plane go? ​
artcher [175]

Answer:

G ÷ M = 48

Step-by-step explanation:

 5 ⟌ 2 4 0

  0    

   5 ⟌ 2 4 0

       0    

   5 ⟌ 2 4 0

      0    

       0    

   5 ⟌ 2 4 0

     - 0    

       2    

       0    

   5 ⟌ 2 4 0

     - 0    

       2 4  

       0 4  

   5 ⟌ 2 4 0

     - 0    

       2 4  

  0 4  

   5 ⟌ 2 4 0

     - 0    

       2 4  

       2 0  

       0 4  

   5 ⟌ 2 4 0

     - 0    

       2 4  

     - 2 0  

         4  

   0 4  

   5 ⟌ 2 4 0

     - 0    

       2 4  

     - 2 0  

         4 0

0 4 8

   5 ⟌ 2 4 0

     - 0    

       2 4  

     - 2 0  

         4 0

       0 4 8

   5 ⟌ 2 4 0

     - 0    

       2 4  

     - 2 0  

         4 0

         4 0

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

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3 years ago
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