1. multiply 1 and 3 to equal 3 then subtract 4 to equal -1
        
             
        
        
        
Answer:
sqrt 11
Step-by-step explanation:
Pythagorean theorem again. a^2+b^2=c^2. The hypotenuse is the c value. One of the legs is either a or b, doesn't matter which. So you can make the equation 5^2+b^2=6^2. 25+b^2=36. Subtract 25 from each side to isolate the b variable. You're left with b^2=11. Now you take the square root of each side to get b. This makes b= sqrt 11.
 
        
                    
             
        
        
        
Complete Question
Statistics professors believe the average number of headaches per semester for all students is more than 18. From a random sample of 15 students, the professors find the mean number of headaches is 19 and the standard deviation is 1.7. Assume the population distribution of number of headaches is normal.the correct conclusion at  is?
 is?
Answer:
 There is no sufficient evidence to support the professor believe 
Step-by-step explanation:
From the question we are told that 
      The population mean is  
      The sample size is  
       The sample mean is  
       The standard deviation is  
       The level of significance is  
The null hypothesis is  
The  alternative hypothesis is  
  The critical value of the level of significance from the normal distribution table is    
          
The test hypothesis is mathematically represented as 
            
substituting values  
          
          
Looking at the value of  t and   we can see that
 we can see that  so we fail to reject the null hypothesis.
 so we fail to reject the null hypothesis. 
This mean that there is no sufficient evidence to support the professor believe 
       
        
 
        
             
        
        
        
To write the given quadratic equation to its vertex form, we first form a perfect square.
 
                x² - 2x + 5 = 0
Transpose the constant to other side of the equation,
                x² - 2x = -5
Complete the square in the left side of the equation,
              x² - 2x + (-2/1(2))² = -5 + (-2/1(2))² 
Performed the operation,
                x² - 2x + 1 = -5 + 1
Factor the left side of the equation,
               (x - 1)² = -4
Thus, the vertex form of the equation is,
          <em>  (x-1)² + 4 = 0</em>
        
             
        
        
        
Answer: p >  
 
Step-by-step explanation:
-21p + 69 > -49p + 81 
          -69                -69 
-21p > -49p + 12 
 +49p     +49p
28p > 12   divide both sides by 28 
p > 12/28 
reduce it  p> 3/7