Question

a spinner (circle) divided into 8 equal parts, labeled with numbers: 9, 4, 10, 13, ?, 17, 11, 8. the label at the top is c.

Explanation:

Step1: Identify opposite pairs

The circle is divided into 8 parts, so we can pair numbers opposite each other. Let's list the pairs:

• 4 and 17 (opposite)
• 9 and 13 (opposite)
• 8 and 10 (opposite)
• 11 and? (opposite)

Step2: Find the sum of each pair

Check the sum of the first three pairs:

• \(4 + 17 = 21\)
• \(9 + 13 = 22\)? Wait, no, maybe I made a mistake. Wait, 4 + 17 = 21, 9 + 13 = 22? No, wait, 8 + 10 = 18. Wait, maybe another pattern. Wait, 4 and 17: 17 - 4 = 13; 9 and 13: 13 - 9 = 4; 8 and 10: 10 - 8 = 2. No, that's not consistent. Wait, maybe sum is constant. Wait 4 + 17 = 21, 9 + 13 = 22? No, 8 + 10 = 18. Wait, maybe I paired wrong. Let's count the number of segments. The circle is divided into 8 equal parts, so the opposite of 4: let's see the positions. Let's index the numbers: starting from 4, then 10, 13,?, 17, 11, 8, 9, back to 4. So the pairs are (4,?), (10,17), (13,8), (?,11)? Wait, no, maybe each pair adds up to 21? Wait 10 + 11 = 21? No, 10 + 11 = 21? 10 + 11 = 21, 13 + 8 = 21, 9 + 12 = 21? No, 9 + 12 is not. Wait 10 + 11 = 21, 13 + 8 = 21, 17 + 4 = 21, 9 + 12 = 21? No, the missing number. Wait 17 + 4 = 21, 13 + 8 = 21, 10 + 11 = 21, so 9 +? = 21? Then? = 21 - 9 = 12? Wait, no, let's check again. Wait the numbers are 4, 10, 13,?, 17, 11, 8, 9. Let's pair 4 and 17: 4 + 17 = 21; 10 and 11: 10 + 11 = 21; 13 and 8: 13 + 8 = 21; so the remaining pair is 9 and?, so 9 +? = 21, so? = 21 - 9 = 12. Wait, but let's confirm. 4 + 17 = 21, 10 + 11 = 21, 13 + 8 = 21, 9 + 12 = 21. Yes, that works. So the missing number is 12.

Answer:

12