Answer:
The 8th term of the sequence is 896/2187. 
Step-by-step explanation:
We want to find the 8th term of a geometric sequence whose common ratio is 2/3 and whose first term is 7. 
We can write a direct formula. Recall that the direct formula of a geometric sequence is given by: 

Where <em>a</em> is the initial term and <em>r</em> is the common ratio. 
Substitute: 

To find the 8th term, let <em>n</em> = 8. Substitute and evaluate: 

In conclusion, the 8th term of the sequence is 896/2187. 
 
        
             
        
        
        
Answer:
11
Step-by-step explanation:
ez
 
        
                    
             
        
        
        
Step-by-step explanation:
I am not sure what your problem here is. 
you understand the inequality signs ?
anyway, to get
6×f(-2) + 3×g(1)
we can calculate every part of the expression separately, and then combine all the results into one final result. 
f(-2)
we look at the definition.
into what category is -2 falling ? the one with x<-2, or the one with x>=-2 ?
is -2 < -2 ? no.
is -2 >= -2 ? yes, because -2 = -2. therefore, it is also >= -2.
so, we have to use
1/3 x³
for x = -2 that is
1/3 × (-2)³ = 1/3 × -8 = -8/3
g(1)
again, we look at the definition. 
into what category is 1 falling ? the one with x > 2 ? or the one with x <= 1 ?
is 1 > 2 ? no. 
is 1 <= 1 ? yes, because 1=1. therefore it is also <= 1.
so we have to use
2×|x - 1| + 3
for x = 1 we get
2×0 + 3 = 3
6×f(-2) = 6 × -8/3 = 2× -8 = -16
3×g(1) = 3× 3 = 9
 and so in total we get
6×f(-2) + 3×g(1) = -16 + 9 = -7
 
        
             
        
        
        
Answer:

Step-by-step explanation:
Given
Let
 Undergraduates
 Undergraduates
 Graduates
 Graduates
So, we have:
 -- Total students
 -- Total students
 --- students to select
 --- students to select
Required

From the question, we understand that 2 undergraduates are to be selected; This means that 2 graduates are to be selected.
First, we calculate the total possible selection (using combination)

So, we have:





Using a calculator, we have:

The number of ways of selecting 2 from 3 undergraduates is:




The number of ways of selecting 2 from 5 graduates is:




So, the probability is:




 
        
             
        
        
        
Answer:
hope it helps...any queries comment me!!!