Let the number of persons= n

Number of handshakes by first person= n- 1

(As he cannot handshake with himself)

Number of handshakes by second person = n- 2

(As he has already handshaked with first person)

Number of handshakes by third person= n- 3

.

.

Number of handshakes by second last i.e. ( n- 1)th person= n- (n- 1)= 1

Number of handshakes by last i.e. nth person= n- n= 0

So,

Total number of handshakes=(n- 1)+ (n- 2)+ (n- 3)+ 1+ 0

= 0+ 1+ 2+ 3+ ...........(n- 1)

= Sum of first (n- 1) terms

= (n- 1)(n- 1+ 1)/2

= n(n- 1)/ 2

So, Total number of handshakes= n(n- 1)/2

According to question,

n(n- 1)/ 2= 66

=> n^2 - n= 132

=> n^2- n- 132= 0

=> n^2- 12n+ 11n- 132= 0

=> n(n- 12) + 11(n- 12)= 0

=> (n- 12)(n+ 11) = 0

n= 12 or n= - 11(which is not possible as no. Of persons cannot be negat 

GDP by sector Services: 53.39%; Agriculture: 15.33% Industry: 31.28% (FY 2015-16)

Total Difference = 32 - (-13) = 45

Average hourly increase = 45/9=5

American man=3/8 x 2/3 =1/4 of all member All American member=(1- 3/5)=2/5 so American  woman=(2/5-1/4)=3/20

If we add or subtract a constant to each term in a set the standard deviation will not change.. If we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.

A= { 2, 3, 5} and B= {1, 3, 5} . Any of the 3 numbers in A could be added to nay of the 3 numbers in B, so 9 sums could be formed. However, there could be some duplication. List the sums systematically; first add 1 to each number in A, then 3, and then 5: 3, 4, 6; 5, 6(x), 10; 7, 8, 10(x). there are 7 different sums

area of equilateral triangle=√3/4 a2 =√3/4 x(10)2 =25√3

here, 2x+3x+3x+5x+5x=180 18x=180 x=10 2x=20

a=4πr2 c=2 πr r=c/2 π now,a=4πr2 =π x ( c/2 π)2 = c2/4π 

10 patients last for 14 days 1 patients last for 10 x 14 days 35 patients last for 10 x 14/35=4 days  

The value after 25% increase is tk 125 from tk 100 At 20% decrease, If 100 is the original than the new value is tk 80 if  1     is the original than the  new value is 80/100 If 125 is the original than the new value is tk 80 x125/100 =100 tk

(7a) (7b) = 7c/7d  7a+b=7c-d a+b=c-d d=c-a-b

let, sum of 6 of them=x=100

The sum of 4 of them=y so,x+y/10=-10 y=100 so average=-200/4=-50

60 miles per hour means, in 60 minutes goes 60 miles In 1 minutes goes 60/60 miles in 20 minutes goes 60 x 20/60 = 20 miles