10 kids are randomly grouped into an a team with five kids and a b team with five kids. each grouping is equally likely.

(a) what is the size of the sample space?
(b) there are two kids in the group, alex and his best friend jose. what is the probability that alex and jose end up on the same team?

Our required probability is 0.44.

Step-by-step explanation:

Since we have given that

Number of kids in team A = 5

Number of kids in team B = 5

(a) What is the size of the sample space?

So, the size of sample space would be

(b) There are two kids in the group, Alex and his best friend Jose. What is the probability that Alex and Jose end up on the same team?

Number of ways that Alex and Jose does not end up on same team would be

Number of ways that Alex and Jose  end up on same team would be

252-140=112

So, the probability that Alex and Jose end up on the same team would be

Hence, our required probability is 0.44.

step-by-step explanation:

divide, then simplify your answer.

1. make -15.66 ÷   5.8 a fraction. then divide.

2. simplify.  

3. final answer.  

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is