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

Explanation:

Step1: List all combinations

The spinner has 2 values (6, 7) and the cards have 8 values (1 - 8). We find all sums. When the spinner shows 6, the sums are 6 + 1=7, 6+2 = 8, 6 + 3=9, 6+4 = 10, 6+5 = 11, 6+6 = 12, 6+7 = 13, 6+8 = 14. When the spinner shows 7, the sums are 7 + 1=8, 7+2 = 9, 7 + 3=10, 7+4 = 11, 7+5 = 12, 7+6 = 13, 7+7 = 14, 7+8 = 15.

Step2: Remove duplicates

The set of sums is {7, 8, 9, 10, 11, 12, 13, 14, 15}. Counting the non - duplicate values.

Answer:

9