A bag contains 31 checkers—13 red and 18 black. Determine whether the events "a red checker is selected, not replaced and then a black checker is selected" are independent or dependent, and find the probability.

dependent, 39/155

Step-by-step explanation:

Since the checkers are not replaced, the events are dependent since the number of checkers in the bag  when you pick the second time depends on the first pick.

31 checkers—13 red and 18 black.

P(red) = red/ total

          = 13/31

Keep the checker

Then 30 checkers—12 red and 18 black.

P(black) = black/ total

          = 18/30 = 3/5

P ( red, keep,black) = 13/31 *3/5

                                   39/155

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation:

- "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."