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

c. 65°

step-by-step explanation:

we are given a triangle with two known angles, 62° and 53°, while the third angle x is unknown and we are to find its value.

we know that the sum of angles in a triangle is equal to a total of 180 degrees. so we can write it as:

x + 62° + 53° = 180°

solving to find the value of x:

x = 180 - (62 + 53) = 65°

therefore, the value of x in this triangle is 65°.

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