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

Explanation:

Step1: List all possible outcomes

Spinner 1 has 2 outcomes (2, 3), Spinner 2 has 2 outcomes (1, 2), die has 6 outcomes (1 - 6).

Step2: Find the minimum sum

Minimum values: 2 from Spinner 1, 1 from Spinner 2, 1 from die. Sum is $2 + 1+1=4$.

Step3: Find the maximum sum

Maximum values: 3 from Spinner 1, 2 from Spinner 2, 6 from die. Sum is $3 + 2+6 = 11$.

Step4: Check for all possible sums

List out all combinations and check for unique sums. The possible sums range from 4 to 11.

Answer:

8