Exercise 3. A company gives each of its employees the title of either 'programmer' or 'project manager'. In any given year, 70% of programmers remain in that position, 20% are promoted to project manager, and 10% are fired. On the other hand, 95% project managers remain in that position and only 5% are fired. How long on average does a programmer work before they are fired?

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A: The given integral is sec2(4x).

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Q: But what is the value of y? Need the solution for y as a actual number.

A: An equation,

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Q: these ans

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A: Solve the given problem.

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A: By using surface area formula, we calculate the required surface area.

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Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.