Let the original number be ‘x’
Then half of that number= 1/2x or simply x/2
Similarly one fifth of that number = x/5
According to the question
x+x/2+x/5=51
Taking LCM
10x/10+2x/10+5x/10=51
Multiplying 10 throughout
10x+2x+5x=510
17x=510
x=510/17
Therefore x=30
        
             
        
        
        
Answer:
The probability of NOT hitting a boundary is (4/5).
Step-by-step explanation:
Let E: Be the event of hitting a boundary
now, Probability of any event E =  
Here, number of favorable outcomes = 6
So, P(E)  = 
⇒Probability of hitting a six is 1/5
Now, P(E)  + P(not E)  = 1
So, P(not hitting a boundary ) = 1  -  P(hitting a boundary)
= 1 - (1/5)  = 4/5
Hence, the probability of NOT hitting a boundary is (4/5).
 
        
             
        
        
        
Given function is 

now we need to find the value of k such that function f(x) continuous everywhere. 
We know that any function f(x) is continuous at point x=a if left hand limit and right hand limits at the point x=a are equal.
So we just need to find both left and right hand limits then set equal to each other to find the value of k
To find the left hand limit (LHD) we plug x=-4 into 3x+k
so LHD= 3(-4)+k
To find the Right hand limit (RHD) we plug x=-4 into 

so RHD= 
Now set both equal





k=-0.47
<u>Hence final answer is -0.47.</u>
 
        
             
        
        
        
X<-7 so the answer would be greater*