There are 32 teams participating in a single-elimination soccer tournament, in which only the winning teams from each round progress to the next round of the tournament the graph shows the number of teams, fx) that are still in the tournament after x rounds have been completed f(x)

D = {0 , 1 , 2 , 3 , 4 , 5} and R = {1 , 2 , 4 , 8 , 16 , 32} ⇒ answer D

Step-by-step explanation:

* Lets talk about the domain and the range of a function

- The domain is the input values

- The range is the output values

- f(x) = y,  x is the input then x is the domain of the function and y is the

  output then y is the range of the function

- Example:

# If x = {2 , 3 , 5) and f(x) = 2x

- The input is x to find f(x) substitute the values of x in f(x)

- f(2) = 2(2) = 4 , f(3) = 2(3) = 6 , f(5) = 2(5) = 10

- The output is f(x) = {4 , 6 , 10}

- From all steps above the domain of f(x) is {2 , 3 , 5) and the range

 is {4 , 6 , 10}

* Lets solve the problem

- There are 32 teams participating  in a single-elimination soccer

 tournament

- x is the number of rounds

- f(x) is the number of teams

- only the winning teams from each round progress to the next

 round of the tournament

* Lets look to the graph and find the domain and the range

- The domain the the values of x and the range is the values of f(x)

∵ At x = 0 then f(0) = 32 ⇒ 32 teams inter the 1st round

∵ At x = 1 then f(1) = 16 ⇒ 16 teams inter the 2nd round

∵ At x = 2 then f(2) = 8 ⇒ 8 teams inter the 3rd round

∵ At x = 3 then f(3) = 4 ⇒ 4 teams inter the 4th round

∵ At x = 4 then f(4) = 2 ⇒ 2 teams inter the 5th round

∵ At x = 5 then f(5) = 1 ⇒ 1 team in win

- From all above:

∴ The domain is {0 , 1 , 2 , 3 , 4 , 5} and the range is {1 , 2 , 4 , 8 , 16 , 32}

* D = {0 , 1 , 2 , 3 , 4 , 5} and R = {1 , 2 , 4 , 8 , 16 , 32}

408,844,800.

Step-by-step explanation:

(a) There are 26 letters in the alphabet and 10P7 ways of ordering  7 digits.

10P7 = 10!/3! = 604800

The answer is 26* 604800  * 26

= 26^2 * 604800

= 408844800.