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

Answer

Explanation:

Step1: List all possible values

Spinner values: 5, 6, 7, 8. Die values: 1, 2, 3, 4, 5, 6.

Step2: Find the minimum sum

The minimum spinner - value is 5 and the minimum die - value is 1. So the minimum sum is $5 + 1=6$.

Step3: Find the maximum sum

The maximum spinner - value is 8 and the maximum die - value is 6. So the maximum sum is $8 + 6 = 14$.

Step4: List out all sums and count distinct ones

When spinner is 5: sums are $5+1 = 6$, $5 + 2=7$, $5+3 = 8$, $5+4 = 9$, $5+5 = 10$, $5+6 = 11$. When spinner is 6: sums are $6+1 = 7$, $6 + 2=8$, $6+3 = 9$, $6+4 = 10$, $6+5 = 11$, $6+6 = 12$. When spinner is 7: sums are $7+1 = 8$, $7 + 2=9$, $7+3 = 10$, $7+4 = 11$, $7+5 = 12$, $7+6 = 13$. When spinner is 8: sums are $8+1 = 9$, $8 + 2=10$, $8+3 = 11$, $8+4 = 12$, $8+5 = 13$, $8+6 = 14$. The distinct sums are 6, 7, 8, 9, 10, 11, 12, 13, 14.