What is the inverse of the statement? a number that has exactly two distinct factors is prime. if a number has exactly two distinct factors, then the number is prime. if a number does not have exactly two distinct factors, then the number is not prime. if a number is not prime, then the number does not have exactly two distinct factors. if a number is prime, then the number has exactly two distinct factors.

The correct answer is:

 If a number does not have exactly two distinct factors, then the number is not prime.

We are given a statement as:

          A number that has exactly two distinct factors is prime.

We know that for any conditional statement of the type:

           if p then q i.e. the statement p implies q

the inverse statement is given by:

  If not p then not q i.e. not p implies not q.

Here p is: A number has exactly two distinct factors.

q is:  It is a  prime number.

Hence, the inverse statement is:

If a number does not have exactly two distinct factors, then the number is not prime.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."