Answer:
  =
     =          +
  +  
Step-by-step explanation:
To verify the identity:
sinx/1-cosx = cscx + cotx
we will follow the steps below;
We will take just the left-hand side and work it out to see if it is equal to the right-hand side
sinx/1-cosx
Multiply the numerator and denominator by 1 + cosx
That is;
 =
     =    
open the parenthesis on the right-hand side of the equation at the numerator and the denominator
sinx(1+cosx) = sinx + sinx cosx
(1-cosx)(1+cosx) = 1 - cos²x
Hence
  =
     =  
But 1- cos²x  = sin²x
Hence we will replace  1- cos²x  by  sin²x
     =
    =        =
     =   =
   =  
                              
                                   = +
   +   
                                    
                                    = +
   +   
               
                                    = +
  +  
  =
     =          +
  +  
Note that;
 =
  =  
                         
          
   =
   =       
                                      
 
        
             
        
        
        
The probability of picking a blue jelly bean is 10/12=0.833, since there are 10 blue and 12 jelly beans in total.
Each time the probability of picking blue is the same, since put back in the box whatever jelly bean we pick
P(blue, blue, blue) = P(blue) × P(blue) × P(blue) = 0.833×0.833×0.833=0.579
Answer: 0.579
        
             
        
        
        
Answer: The answer is  
  
Step-by-step explanation: We are given four different functions of the variable 'x' and a graph. We are told to select one of the four options that which function can be graphed as the graph given in the question.
To check, we start plotting the functions one by one on a graph paper. We see that the graph of first three functions do not match with the given graph, but the graph of the fourth function given by
 
matches exactly with the graph given in the question. The attached figure will show the graph for this function, which is exactly same as given.
Thus, the correct option is

 
        
                    
             
        
        
        
Answer:
0.1507 or 15.07%.
Step-by-step explanation:
We have been given that the manufacturing of a ball bearing is normally distributed with a mean diameter of 22 millimeters and a standard deviation of .016 millimeters. To be acceptable the diameter needs to be between 21.97 and 22.03 millimeters. 
First of all, we will find z-scores for data points using z-score formula.
 , where,
, where,
z = z-score,
x = Sample score,
 = Mean,
 = Mean,
 = Standard deviation.
 = Standard deviation.



Let us find z-score of data point 22.03.



Using probability formula  , we will get:
, we will get:

 
  
 
 
Therefore, the probability that a randomly selected ball bearing will be acceptable is 0.1507 or 15.07%.
 
        
             
        
        
        
Your answer would be translation (brainliest answer please)