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Home » Growth in 2023: 4800 × 1.15 = 5520. - Midis

Growth in 2023: 4800 × 1.15 = <<4800*1.15=5520>>5520. - Midis

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Thus, the number of valid combinations is $ \boxed{126} $.

📌 Question: In a wildlife reserve, 6 types of birds are monitored, each with a GPS device. Each device can transmit data in one of 4 frequency bands. If at least one bird must use each band, how many ways can the frequency bands be assigned to the 6 birds?

📌 Wait — that's similar to a previous problem. Let's adjust to a fresh version.

📌 Corrected question:

📌 A conservationist is deploying GPS trackers on 7 endangered birds, assigning each to one of 3 operational frequency bands. How many assignments ensure that each band is used by at least one bird?

📌 Solution: We want the number of onto functions from 7 birds to 3 bands. Using inclusion-exclusion:

📌 \sum_{k=0}^{3} (-1)^k \binom{3}{k} (3 - k)^7

📌 Compute terms:

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Solution: Note $ x^2 - 2x + 1 = (x - 1)^2 $. Use polynomial division o...
Solution: We are to count how many integers from 1 to 120 are relative...
First, factor 12:
$ 12 = 2^2 imes 3 $.
\phi(12) = 12 \left(1 - rac{1}{2}
ight)\left(1 - rac{1}{3}
ight) = 12 imes rac{1}{2} imes rac{2}{3} = 4.
So, among every 12 consecutive integers, exactly 4 are relatively prim...
Now, the total number of full cycles of 12 in 120 is:
$ rac{120}{12} = 10 $.

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