Marleny is creating a game of chance for her family. she has 5 different colored marbles in a bag: blue, red, yellow, white, and black. she decided that blue is the winning color. if a player choose any other color, he or she loses 2 points. how many points should the blue marble be worth for the game to be fair?
4
6
8
10

Third option is correct.

Step-by-step explanation:

Let the worth of blue marble for the game to be fair be 'x'.

Number of points he or she loses on choosing any other color = 2 points

There are five colors :

Blue, red, yellow, white and black.

Probability of getting blue is

Probability of getting any other color is

So, According to question, the game is to be fair :

Hence, the worth of blue marble should be 8 for the game to be fair.

Therefore, Third option is correct.

- "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."