Answer:
a) 
b) 
Step-by-step explanation:
Let's define the following events first:
F: The event that a course has a final exam.
R: The event that a course requires a research paper
From the info provided we have that:
 P(F and R) =0.32
 P(F and R) =0.32
So then we can create a Venn diagram as we can see on the figure attached.
a. Find the probability that a course has a final exam or a research project. 
For this case we can find the probability like this:

b. Find the probability that a course has NEITHER of these two requirements.
For this case we can use the complement rule and we can find the probability like this:

And that's the same value obtained with the diagram.
 
        
             
        
        
        
Answer:
31
Step-by-step explanation:
(24/3)+(7x2)-(15/5)+(6*2)
8+(7x2)-(15/5)+(6*2)
8+14-(15/5)+(6*2)
8+14-3+(6*2)
8+14-3+12
22-3+12
19+12
31
Sorry if I did my math wrong :)
 
        
             
        
        
        
   27
- 3.204
  10.8
----------
12.996 ?
        
                    
             
        
        
        
Answer:
correct option is C)  2.8
Step-by-step explanation:
given data 
string vibrates form =  8 loops
in water loop formed =  10 loops
solution
we consider  mass of stone = m
string length = l 
frequency of tuning = f 
volume = v 
density of stone =  
 
case (1)  
when 8 loop form with 2 adjacent node is  
 
so here 
 ..............1
      ..............1

and we know velocity is express as
velocity = frequency × wavelength   .....................2
 =   f ×
   =   f ×  
 
here tension = mg 
so 
 =   f ×
   =   f ×  ..........................3
     ..........................3
and 
case (2)  
when 8 loop form with 2 adjacent node is  
 
 ..............4
      ..............4

when block is immersed 
equilibrium  eq will be 
Tenion + force of buoyancy = mg 
T + v ×  × g = mg
 × g = mg 
and 
T = v ×  - v ×
 - v ×  × g
 × g     
from equation 2 
f ×  = f  ×
 = f  ×  
  
 .......................5
     .......................5 
now we divide eq 5 by the eq 3 

solve irt we get 

so 
relative density 
relative density = 2.78 ≈ 2.8 
so correct option is C)  2.8