3. A googol is a very large number expressed as 10100. Ms. Rogers asked her students to
determine which number is larger, a googol
or 10010. Explain how her students might use
the idea of repeated factors in order to find
the solution.

10^100 is larger than 100^10.

Step-by-step explanation:

10^100 compared to 100^10, we have 10^100 greater. 100^50 would equal to 10^100, as 10^2=100. 10^100 would be much more than 100^10.

Hope the explanation helps!

b.-4 units

all you   do is count how many times you move

- "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."