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) We want to find the number of possible groups of 11 players the coach can choose. Is this a
permutation or a combination?
(b) If the coach wanted to choose her 11 starters at random by drawing names from a hat, how many possible groups of 11 starters could she choose?
(c) The coach wants to make sure there is exactly one goalie on the field. How many ways can the
coach choose a lineup of 11 players if exactly 1 player must be a goalie?

What is the range of the relation in the table below? x y –2 0 –1 2 0 4 1 2 2 0

When y’all answer can y’all explain too !

For this option, you will work individually. the pythagorean theorem can be used in many real-world scenarios. part 1 write your own real-world scenario where the pythagorean theorem can be applied to find a missing piece. you may choose to write a problem that is two- or three-dimensional in nature. be sure that you will be able to draw a diagram of your scenario. write out your problem and submit it for part 1. be sure to end your scenario with a question. part 2 draw a diagram of the scenario you created in part 1. you may draw by hand and scan and upload your drawing or create a computer-generated drawing for submission. be sure to label all parts and dimensions of the drawing. part 3 solve the question that you posed in part 1. show all of your steps in answering the question. for this option, you will need to submit all three parts for full credit—your real-world problem and question, the diagram that you created, and your work solving the problem, showing all steps. * note that your instructor is looking for your own original idea. while it is acceptable to use the internet for research and inspiration, academic integrity policies apply.