Real-World Applications of Modulo

To find out which step a player lands on after moving 29 spaces in a cycle of 7 steps, you need to calculate the remainder of 29 divided by 7. This can be done by performing the operation 29 mod 7, which equals 1. Therefore, the player lands on step 1.

To find the time after 19 hours from 9:00, add 19 to the current hour. 9 + 19 = 28. Since there are 24 hours in a day, subtract 24 from 28, which gives 4. Therefore, the clock will show 4:00.

The clock chimes every 20 minutes. After the first chime at 12:00, the subsequent chimes occur at 12:20, 12:40, 1:00, 1:20, 1:40, 2:00, 2:20, 2:40, 3:00, and finally at 3:20 for the 10th chime. Therefore, the 10th chime occurs at 3:00.

To determine which play is shown on the 23rd day, we need to calculate the position in the rotation of 8 plays. The plays cycle every 8 days. Therefore, we can find the equivalent day by calculating 23 modulo 8. This gives us 23 % 8 = 7. Since the 1st play is on Monday, the 7th play corresponds to Play 7, which is the answer.

To find which horse number you are on after counting 95 horses, you can use the modulo operation. Since there are 18 horses, you calculate 95 modulo 18. This gives you 95 % 18 = 5, which means you are on horse number 5.

The password resets every 30 days. Since it last reset on day 8, adding 30 days gives us day 38. Therefore, the password will reset again on day 38.

To determine which song you end on after listening to 37 songs, you can use the modulo operation with the total number of songs in the playlist. The calculation is 37 mod 12, which gives a remainder of 1. This means after completing the full cycles of the 12 songs, you will end up at the first song in the playlist.

To find the day of the 7th sale, start with the first sale on day 3 and add 15 days for each subsequent sale. The formula for the nth sale is: day = 3 + (n - 1) * 15. For the 7th sale, n = 7: day = 3 + (7 - 1) * 15 = 3 + 90 = 93.

To determine the day of the week after 50 days, we can divide 50 by 7 (the number of days in a week). The remainder will tell us how many days beyond the last complete week we go. 50 divided by 7 equals 7 weeks with a remainder of 1. Since today is Wednesday, after 7 complete weeks (49 days), it will still be Wednesday, and adding 1 more day brings us to Thursday.

To determine which seat loads the 35th person, we can use modular arithmetic. Since there are 16 seats, we can find the position by calculating 35 modulo 16. This gives us 35 % 16 = 3. Therefore, the 35th person will sit in seat 3.