the real solutions for the equation  are -
 are -

Step-by-step explanation:
     =
 = 
     = 0
  = 0 
    We can write 64 as   
 
    +
 +  = 0
 = 0
   using the identity  (  )
 ) 
 we get,
   = 
   =  ....................(1)
    ....................(1)
  solving the quadratic equation  ,
     =0
 =0
solutions of this quadratic equation can be obtained by 
    
 let use y for factors




<u /> ..................(2)
    ..................(2)
from the equation 1 we have,

which gives solution  
 
 and from equation 2 we got  
so the real solutions for the equation  are -
 are - 

 
        
             
        
        
        
Answer:
the probability that the woman is taller than the man is  0.1423
Step-by-step explanation:
Given that :
 the men's heights are normally distributed with mean  68
  68 
standard deviation  = 3.1
   = 3.1 
And
the women's heights are normally distributed with mean  65
  65
standard deviation  = 2.8
   = 2.8
We are to find the probability that the woman is taller than the man.
For woman now:
mean   = 65
 = 65
standard deviation  = 2.8
 = 2.8

![\\ 1 -p  \ P[(x - \mu ) / \sigma < (68-25)/ 2.8]](https://tex.z-dn.net/?f=%5C%5C%201%20-p%20%20%5C%20P%5B%28x%20-%20%5Cmu%20%29%20%2F%20%5Csigma%20%3C%20%2868-25%29%2F%202.8%5D)
= 1-P (z , 1.07)
Using z table,
= 1 - 0.8577
= 0.1423
Thus, the probability that the woman is taller than the man is  0.1423
 
        
             
        
        
        
Answer:
13
1.57
Step-by-step explanation:
So we have two equations regarding the number of quarters <em>q</em> and the number of pennies <em>p:</em>
<em /> <em />
<em />
Which represents the total amount of coins and
 
 
Which represents the total amount of money in dollars. 
So we are asked to evaluation each expression for the situation in which we have 6 quarters and 7 pennies. Thus, plug 6 in for <em>q</em> and 7 in for <em>p:</em>
<em /> <em />
<em />
This tells us that we have 16 coins in total. 

This tells us that we have a total amount of $1.57. 
 
        
                    
             
        
        
        
Answer:Production rate  = 4.56 x 10³ bulbs/week
Production time = 9.36 x 10² weeks
Number of bulbs produced is
Answer: 4.27 x 10⁶ bulbs
Step-by-step explanation: