Answer:
1
Step-by-step explanation:
First, convert all the secants and cosecants to cosine and sine, respectively. Recall that  and
 and  .
. 
Thus: 


Let's do the first part first: (Recall how to divide fractions) 

For the second term: 

So, all together: (same denominator; combine terms)

Note the numerator; it can be derived from the Pythagorean Identity: 

Thus, we can substitute the numerator: 

Everything simplifies to 1. 
 
        
             
        
        
        
Answer:
Step-by-step explanation:
 
        
             
        
        
        
Answer:
15
Step-by-step explanation:
since c is the centroid, therefore PX=XQ=1/2 x PQ
∴ PX=15
 
        
             
        
        
        
Answer:
Mason recieved 15 points for answering the question correctly so that means that he had -15 points before. The points would be at -15 and 0.
 
        
                    
             
        
        
        
Answer:
Step-by-step explanation:
Hello!
Given the probabilities:
P(A₁)= 0.35
P(A₂)= 0.50
P(A₁∩A₂)= 0
P(BIA₁)= 0.20
P(BIA₂)= 0.05
a) 
Two events are mutually exclusive when the occurrence of one of them prevents the occurrence of the other in one repetition of the trial, this means that both events cannot occur at the same time and therefore they'll intersection is void (and its probability zero)
Considering that P(A₁∩A₂)= 0, we can assume that both events are mutually exclusive.
b)
Considering that  you can clear the intersection from the formula
 you can clear the intersection from the formula  and apply it for the given events:
 and apply it for the given events:


c)
The probability of "B" is marginal, to calculate it you have to add all intersections where it occurs:
P(B)= (A₁∩B) + P(A₂∩B)=  0.07 + 0.025= 0.095
d)
The Bayes' theorem states that:

Then:


I hope it helps!