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Home » The discount amount is \(200 \times 0.15 = 30\) dollars. - Crosslake

The discount amount is \(200 \times 0.15 = 30\) dollars. - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: The growth of a tech companyâs market share follows $ \sqrt{a + 5} = 7 $. Solve for $ a $.

📌 Solution: Square both sides: $ a + 5 = 49 $. Subtract 5: $ a = 44 $. Verify by substituting back: $ \sqrt{44 + 5} = \sqrt{49} = 7 $. Final answer: $ oxed{44} $.

📌 Question: A materials scientist observes that the healing time $ t $ of a material satisfies $ rac{t}{3} + rac{t}{6} = 2 $. Solve for $ t $.

📌 Solution: Combine terms: $ rac{2t + t}{6} = 2 $, so $ rac{3t}{6} = 2 $, simplifying to $ rac{t}{2} = 2 $. Multiply by 2: $ t = 4 $. Final answer: $ oxed{4} $.Question: What is the least common multiple of 16 and 24, representing the synchronization interval of two bioinformatics tools analyzing genetic sequences?

📌 Solution: The prime factorization of 16 is $2^4$ and of 24 is $2^3 imes 3$. The LCM is the product of the highest powers: $2^4 imes 3 = 16 imes 3 = 48$. Thus, the LCM is $oxed{48}$.

📌 Question: How many integers between 1 and 150 are congruent to 3 modulo 7 and also congruent to 5 modulo 9, reflecting the overlap in experimental conditions for a lab protocol?

📌 Solution: Solve $x \equiv 3 \pmod{7}$ and $x \equiv 5 \pmod{9}$. Let $x = 7k + 3$. Substitute into the second congruence: $7k + 3 \equiv 5 \pmod{9} \Rightarrow 7k \equiv 2 \pmod{9}$. The modular inverse of 7 modulo 9 is 4 (since $7 imes 4 = 28 \equiv 1 \pmod{9}$), so $k \equiv 2 imes 4 = 8 \pmod{9}$. Thus, $k = 9m + 8$, and $x = 7(9m + 8) + 3 = 63m + 59$. The solutions are $59, 122, 185, \dots$. Within 1â150, only 59 and 122 satisfy. The count is $oxed{2}$.

📌 Question: What is the greatest common divisor of 98 and 126, representing the maximum batch size for shared reagents in a biotech workflow?

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is odd â must include the only even prime, 2, or use odd primes only...
Try including 2: then we need sum of distinct odd primes â¡ 37 mod 2...
So check: 39 = 2 + 37? Yes, 2 and 37 are distinct primes.
Is 37 â¤ 39 and prime? Yes.
And 2 + 37 = 39, and distinct â valid.
Check if 39 is the maximum possible. Can we get 39? Yes.
Is 40 possible? No, upper bound is less than 40.
Is 39 the maximum? Yes, since 38, 37, etc., are smaller.
But confirm: could 38 be written as sum of distinct primes?
is even. Use multiple odd primes.

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