Manny rolls a number cube labeled 1 through 6 and spins a spinner with
four equal sections labeled 1, 2, 3, and 4. If both numbers are odd, he wins.
Otherwise, Gabriel wins. Usa a list to find the sample space. Then find the
probability that Gabriel wins.

The winning probability of Gabriel would be = 3/4.

Step-by-step explanation:

Given,

The sides of number cube = 6 {1, 2, 3, 4, 5, 6}

The sides of a spinner = 4  {1, 2, 3, 4}  

If both the gadgets are played together, the sample space (S) size would be:

6 x 4 = 24

Hence,

S = { (1, 1), (1, 2), (1, 3), (1, 4)  

       (2, 1), (2, 2), (2, 3), (2, 4)

       (3, 1), (3, 2), (3, 3), (3, 4)

       (4, 1), (4, 2), (4, 3), (4, 4)

       (5, 1), (5, 2), (5, 3), (5, 4)

       (6, 1), (6, 2), (6, 3), (6, 4) }

Manny wins if both the number are odd.

So, the winning chances of many are (1, 1), (1, 3), (3, 1), (3, 3) (5, 1) (5, 3) = 6

Therefore, the winning chances of Gabriel would be = 24 - 6 = 18

Therefore, the winning probability of Gabriel would be = 18/24 = 3/4.

- "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."