There were 60 runners to start a race. in the first half of the race, 2/3 of them dropped out. in the second half of the race, 4/5 of the remaining runners dropped out. how many runners finished the race?

4 runners finished the race

Step-by-step explanation:

There were 60 runners to start a race.

In the first half of the race, 2/3 of them dropped out. This means that the number of runners that dropped out would be

2/3 × 60 = 40 runners

The number of runners that is left out would be

60 - 40 = 20

In the second half of the race, 4/5 of the remaining runners dropped out. This means that the number of runners that dropped out would be

4/5 × 20 = 16 runners

Therefore the number of runners left and also finished the race would be

20 - 16 = 4

4 runners finished the race

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: