A small social network contains seven people who are network friends with six other people in the network, one person who is network friends with five other people in the network, and three people who are network friends with four other people in the network. The rest are network friends with three other people in the network. The network contains 52 pairs of network friends.(a) How many people are network friends with three other people in the network? (b) How many people are in the network?

a) 15

b) 26

Step-by-step explanation:

If we take a look at this question as a graph question; whereby we relate each people as a vertex and a pair of network friend as an edge.

Given that there are 52 edges; the degree sum = 52 × 2 =104

Now; it is said that 7 people connected with 6 other people in the network;

the degree of these vertex = 7 × 6 = 42

However; 1 person connected with 5 other people = 1 × 5 = 5

Also, 3 people connected with 4 other people = 3 × 4 = 12

We assume that , the number of the rest people who are friends with three other people in the network be y.

SO, the total degree of these people will be 3 × y = 3y

∴ 42 + 5 + 12 + 3y = 104

59 + 3y = 104

3y = 104 - 59

3y = 45

y =

y = 15

Thus, 15 people  are network friends with 3 other people in the network

Total number of people in the network = 7 +1 +3 + 15 = 26

answer: a. 13/44

step-by-step explanation: judging by the information given to us, we are looking for experimental probability. we can see that 13 males have chosen chocolate ice cream. there are 44 ice creams in total (remember that the total is always the denominator). so our answer is 13/44.

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.