Apair of fair dice is rolled. what is the probability of rolling a sum of 10? what are the odds against rolling a sum of 10?

Explanation:

1) Sample space:

         4+ 6, 5 + 5, and, 6 + 4

2)  Probability of rolling a sum of 10 = number of combinations that sum 10 / number of total possible combinations

3) The odds against rolling a sum of 10 is the complement, this is 1 - 1/12 = 11/12 = 0.917

it's

- "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."