The weight of
10,000
identical samples of a substance is
1
pound.
what is the weight of
10
samples?

The correct answer is:

1/1000 of a pound.

Explanation:

We will set up a proportion to solve this.

The first ratio of the proportion comes from our given information.  10,000 samples weigh 1 pound; this gives us the ratio 10,000/1.

The second ratio will be set up in the same fashion; in this case, the number of samples over the number of pounds.  We know we have 10 samples, but an unknown number of pounds; this means we use a variable to represent the number of pounds:

10/x

This makes our proportion

10,000/1 = 10/x

Cross multiplying, we have

10000(x) = 10(1)

10000x = 10

Divide both sides by 10000:

10000x/10000 = 10/10000

x = 10/10000 = 1/1000

- "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."