There are 130 people in a sport centre. 65 people use the gym. 51 people use the swimming pool. 44 people use the track. 15 people use the gym and the pool. 14 people use the pool and the track. 10 people use the gym and the track. 1 person uses all three facilities. Given that a randomly selected person uses the gym and the track, what is the probability they do not use the swimming pool?

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

nlgqer

step-by-step

the answer is 8/21

hope this