you pick a card, roll a die, spin the spinner, and find the sum. how many different sums are possible?

Explanation:

Step1: List all combinations

• Card values: 3, 4; Die values: 1, 2, 3, 4, 5, 6; Spinner values: 5, 6.
• When card = 3:
  • With die = 1 and spinner = 5, sum = 3 + 1+ 5=9; with die = 1 and spinner = 6, sum = 3 + 1+ 6 = 10;
  • With die = 2 and spinner = 5, sum = 3 + 2+ 5 = 10 (duplicate); with die = 2 and spinner = 6, sum = 3 + 2+ 6 = 11;
  • And so on for all die - spinner combinations with card = 3.
• When card = 4:
  • Repeat the process for all die - spinner combinations.

Step2: Count non - duplicate sums

• List out all sums: 9, 10, 11, 12, 13, 14, 15.

Answer:

7