The varsity soccer team has 20 players. Three of the players are trained to be goalies while the remaining 17 can play any position. Only 11 of the players can be on the field at once.

A.) combination

B.) 167,960 ways

C.) 58,344 ways

Step-by-step explanation:

A.)

Choosing 11 players out of 20 available is a cbinationtuon problem simply because the order of choice of the 11 players does not matter on this scenario.

B.)

Here, the coach wants to select her 11 from all available 20:

We apply the combination formula :

nCr ; where ; n = 20 ; selection, r = 11

nCr = n! / (n-r)!r!

20C11 = 20! / 9!11!

20C11 = 167,960

C.)

1 goalie 10 players

1 goalie is selected from the 3 available goalies AND 10 players from the 17 available players :

This gives :

3C1 * 17C10

3C1 = 3

17C10 = 19,448

3C1 * 17C10 = 3 * 19448

= 58,344 ways

y > 1/3x

y < = -x + 4

hope this : )

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: