A baseball team consists of 14 American-born players and 11 foreign-born players. Nine players must be selected to start the game. Find the probability (to 4 decimal places) of selecting 5 American-born players and 4 foreign-born players

32.33%

Step-by-step explanation:

There is no marking that can differentiate the position or the player, so both of their order is not important. Since the order not important, we use combination instead of permutation.

There are 25 players and you can choose 9 of them. The number of ways to do this will be: 9C25= 25! / (9! * (25-9)! ) = 2042975 ways

You want to choose 5 American-born out of 14 American-born and 4 foreign-born out of 11 foreign-born. The ways to do that will be: 14C5 + 4C11=

14! / (5! * (14-5)! )  * 11! / (4! * (11-4)! ) =2002 * 330 = 660660 ways

The probability will be: 660660/2042975 = 0.3233= 32.33%

2

step-by-step explanation:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3