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

Explanation:

Step1: List all combinations

List all sums of card - number and spinner - number. For card number 3: $3 + 5=8$, $3 + 6 = 9$, $3+7 = 10$, $3 + 8=11$. For card number 4: $4 + 5 = 9$, $4+6 = 10$, $4 + 7=11$, $4 + 8 = 12$. For card number 5: $5 + 5 = 10$, $5+6 = 11$, $5 + 7=12$, $5 + 8 = 13$. For card number 6: $6 + 5 = 11$, $6+6 = 12$, $6 + 7=13$, $6 + 8 = 14$. For card number 7: $7 + 5 = 12$, $7+6 = 13$, $7 + 7=14$, $7 + 8 = 15$.

Step2: Remove duplicates

The set of sums is ${8,9,10,11,12,13,14,15}$.

Answer:

8