Me ! a spinner and two cards are shown below. which table correctly identifies the sample space of spinning the spinner and then selecting a card?

The answer is choice A

The sample space is basically the set of all possible outcomes. Each outcome is a pair of results from drawing a card coupled with spinning a spinner. 

Table A represents all of the possible outcomes properly. The card results are along the column on the left side. The spinner results along the row up at the top. Each cell is an intersection of the left and top result. For example, row1,column3 has "red,purple" to indicate you got "red" on the spinner and "purple" on the card. Each cell in table A is correctly labeled.

The other tables (B, C, D) are improperly labeled in at least one cell. 
* Table B has "blue, green" in the top row" middle cell when it should be "blue, purple"

* Table C has "green, green" in the upper left corner when it should be "green, purple"

* Table D has "blue, blue" in the bottom middle cell when it should be "blue, green". Saying "blue,blue" is impossible as there isn't a blue card.

The three items mentioned above help us eliminate choices B through D.

J= r + 9 because since jessica rode 9 more miles than roger, you add 9 miles to rogers mileage.