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The condition that the number of apps Jessica has, represented by 'x', is divisible by 5 can be expressed using modular arithmetic as the congruence relation $x \equiv 0 \pmod{5}$. This formula signifies that the remainder is 0 when x is divided by 5.

Mathematical Representation of Divisibility by 5 (Jessica's Apps Problem)

A software program uses a counter, represented by the variable 'c', to track the number of times a user performs an action. The program needs to trigger a specific function every time the action count is perfectly divisible by 5. Which of the following mathematical conditions correctly represents the logic for triggering the function?

Based on the scenario provided, will the administrator's configuration cause the script to run on the correct days? Justify your answer by explaining the mathematical meaning of the condition `d ≡ 5 (mod 5)` and state the most conventional way to write this condition.

Task Scheduler Logic Evaluation

An automated warehouse system groups items into batches of 5 for shipping. A system alert should be triggered only when the total number of items, represented by the variable 'n', can be perfectly grouped into these batches with no items leftover. Using the notation of modular arithmetic, write the specific congruence relation that the system should use to check for this condition.

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