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Home » Gesamtzeit**: \(2.5 \, \texth + 1.5 \, \texth = 4 \, \texth\) - 500apps

Gesamtzeit**: \(2.5 \, \texth + 1.5 \, \texth = 4 \, \texth\) - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 \[ f(a + b) = f(a) + f(b), \]

📌 assuming linearity, the function satisfies this by the very definition of linearity (additivity and homogeneity). Thus, the only functions meeting the criteria are those of the form \( f(x) = kx \). Since \( k \) can be any real number, there are infinitely many such linear functions, one for each real number \( k \). Therefore, the number of such functions is:

📌 \boxed{\infty}

📌 Question: The perimeter of a rectangle is 50. What is the largest possible area of the rectangle?

📌 Solution: Let the length and width of the rectangle be \( l \) and \( w \), respectively. The perimeter is given by:

📌 \[ 2l + 2w = 50 \quad \Rightarrow \quad l + w = 25. \]

📌 \[ A = lw. \]

📌 Express \( w \) in terms of \( l \): \( w = 25 - l \). Sub

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Case analysis on the two prime rolls:
Case 1**: Both primes are even → only possible if both are 2 → 1 outco...
Odd primes: 0
Odd non-primes: 0
Even non-primes: 0
Then odd count = odd number of non-prime odds = 0 (even) → acceptable
Contribution: even + even + even + even = even → valid
Prime selections: only (2,2) → 1 way
Non-prime: (4,4), (4,6), (6,4), (6,6) → 4 ways
Number of assignments: $ 1 \times 4 = 4 $

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