An insurance company sells one-fourth as many preferred policies as standard policies and one-fourth as many ultra-preferred policies as preferred policies. All policies are classified as standard, preferred, or ultra-preferred. Calculate the probability that a randomly selected policy is ultra-preferred.

4.7619%

Step-by-step explanation:

Let's suppose the insurance company sells 16 standard policies.

For every 16 standard policies sold, the company sells 1/4 x 16, or 4, preferred policies.

For every 4 preferred policies sold, the company sells 1/4 x 4, or 1, ultra-preferred policy.

Therefore, for every ultra-preferred policy sold, the company sells:

16+4+1=21 total policies

So the probability of any 1 random policy selected being ultra-preferred is 1/21, or 4.7619%

- "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."