Paul can clean a classroom floor in 3 hours. when his assistant him, the job takes 2 hours. how long would it take the assistant to do it alone?

6 hours

Step-by-step explanation:

If Paul takes 3 hours to clean the floor, then he cleans 13 of the floor per hour. His assistant takes some time t hours to do the same job, so he cleans 1t of the floor each hour. Working together, they clean the floor in 2 hours. This can be written as:

--> 1/3 + 1/t = 1/2

Multiply each side by the least common denominator, 6t.

6t(1/3+1/t)=6t(1/2)

Simplify and solve.

2t+6=3t

2t+6−2t=3t-2t

6=t

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.  

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: