In a youth camp, each participant must take part in at least one of the following activities: chess, backgammon or dominoes.
Of the total of 55 in the camp, 25 participants participated in chess,
24 in backgammon, and 30 in dominoes, 15 in both chess and
backgammon, 10 in both backgammon and dominoes, 5 in both
chess and dominoes, and 2 in all three events.

Find the number of participants who:
a) take part in one activity only
b) take part in exactly two activities
c) do not take part in at least two activities
d) take part in chess, given that they take part in dominoes
e) take part in backgammon, given that they do not take
part in dominoes.

51-50

step-by-step explanation:

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

46

step-by-step explanation:

given

height = 168 cm

formula

height =2.47*f+54.13

solution

168 = 2.47f + 54.13             subtract 54.13 from both sides

168 - 54.13   = 2.47f             combine

113.87 = 2.47f                     divide by 2.47

113.87 / 2.47 = f                   combine

46.1 = f  

answer: 46 cm