Answer:
The distributive property of multiplication
Step-by-step explanation:
<u>explanation</u>:-
The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first can be distributed to both of those numbers and multiplied by each of them separately,then adding the two products together for the same result as multiplying the first number by sum.
a(b+c) = a.b + a.c
so -2 ( -3+7) = -2(-3) + (-2)(7)
    -8  =  6 -14
    -8 = - 8
give data we will use distributive property of multiplication
 
        
                    
             
        
        
        
Answer:
mok
Step-by-step explanation:
mok
 
        
             
        
        
        
Answer:
$4.25
Step-by-step explanation:
4 quarters is 1 dollar
1 nickel is 5 cent
14 divided by 4 = 3.5 
3.5 + 5 times 5 =  $4.25
 
        
                    
             
        
        
        
Answer:
 
g(1) = 0
There is a remainder of 10 so you can automatically cross out 3 and 4. 
 
        
                    
             
        
        
        
Answer:
a) 0.96
b) 0.016
c) 0.018
d) 0.982
e) x = 2
Step-by-step explanation:
We are given with the Probability density function f(x)= 2/x^3 where x > 1.
<em>Firstly we will calculate the general probability that of P(a < X < b) </em>
         P(a < X < b) =   =
 =  
 
                             = ![2[ \frac{x^{-3+1} }{-3+1}]^{b}_a   dx](https://tex.z-dn.net/?f=2%5B%20%5Cfrac%7Bx%5E%7B-3%2B1%7D%20%7D%7B-3%2B1%7D%5D%5E%7Bb%7D_a%20%20%20dx) { Because
    { Because ![\int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a](https://tex.z-dn.net/?f=%5Cint_%7Ba%7D%5E%7Bb%7D%20x%5E%7Bn%7D%20dx%20%3D%20%5B%20%5Cfrac%7Bx%5E%7Bn%2B1%7D%20%7D%7Bn%2B1%7D%5D%5E%7Bb%7D_a) }
 }
                             = ![2[ \frac{x^{-2} }{-2}]^{b}_a](https://tex.z-dn.net/?f=2%5B%20%5Cfrac%7Bx%5E%7B-2%7D%20%7D%7B-2%7D%5D%5E%7Bb%7D_a) =
 = ![\frac{2}{-2} [ x^{-2} ]^{b}_a](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B-2%7D%20%5B%20x%5E%7B-2%7D%20%5D%5E%7Bb%7D_a) 
 
                             = ![-1 [ b^{-2} - a^{-2}  ]](https://tex.z-dn.net/?f=-1%20%5B%20b%5E%7B-2%7D%20-%20a%5E%7B-2%7D%20%20%5D) =
 =  
 
a) Now P(X < 5) = P(1 < X < 5)  {because x > 1 }
      Comparing with general probability we get,
      P(1 < X < 5) =  =
 =  = 0.96 .
 = 0.96 .
b) P(X > 8) = P(8 < X < ∞) = 1/ - 1/∞ = 1/64 - 0 = 0.016
 - 1/∞ = 1/64 - 0 = 0.016 
c) P(6 < X < 10) =  =
 =  = 0.018 .
 = 0.018 .
d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞) 
                                 =  + (1/
 + (1/ - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982
 - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982
e) We have to find x such that P(X < x) = 0.75 ;
                ⇒  P(1 < X < x) = 0.75 
                ⇒   = 0.75
 = 0.75 
                ⇒   = 1 - 0.75 = 0.25
 = 1 - 0.75 = 0.25 
                ⇒   =
 =  ⇒
   ⇒  = 4 ⇒ x =
 = 4 ⇒ x =  
  
Therefore, value of x such that P(X < x) = 0.75 is 2.