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Home » These 12 Spanish Months Will Explain Why Every Season Feels LIKE a Festival! - Midis

These 12 Spanish Months Will Explain Why Every Season Feels LIKE a Festival! - Midis

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 A patent attorney negotiates royalties on a tech patent: the inventor receives $3 per unit sold for the first 100,000 units, then $4.50 per unit thereafter. If 145,000 units are sold, how much royalty does the inventor earn?

📌 First 100,000 units: 100,000 × $3 = $<<100000*3=300000>>300,000

📌 Next 45,000 units: 45,000 × $4.50 = $<<45000*4.5=202500>>202,500

📌 Total royalty: $300,000 + $202,500 = $<<300000+202500=502500>>502,500

📌 #### 502500

📌 An epidemiologist models a city’s vaccination rollout: 60% of the population must be immune to achieve herd immunity. The city has 2.4 million people. Vaccination efficiency is 90% per dose, meaning only 90% of administered doses confer immunity. How many doses must be administered to reach herd immunity?

📌 Immune needed: 60% of 2,400,000 = 0.6 × 2,400,000 = <<0.6*2400000=1440000>>1,440,000

📌 Each dose gives 90% immunity, so immune per dose = 0.9

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Final answer: $\boxed{2x^4 - 14x^2 + 23}$
Question: A comet follows a hyperbolic trajectory described by $ 4x^2...
Solution: Rewrite the equation by completing the square. Group $ x $ a...
4(x^2 - 8x) - 9(y^2 - 6y) = -115.
Complete the square for $ x $: $ x^2 - 8x = (x - 4)^2 - 16 $.
For $ y $: $ y^2 - 6y = (y - 3)^2 - 9 $.
4[(x - 4)^2 - 16] - 9[(y - 3)^2 - 9] = -115 \implies 4(x - 4)^2 - 64 -...
4(x - 4)^2 - 9(y - 3)^2 + 17 = -115 \implies 4(x - 4)^2 - 9(y - 3)^2 =...
Divide by $ -132 $ to standardize:
\frac{(y - 3)^2}{\frac{132}{9}} - \frac{(x - 4)^2}{\frac{132}{4}} = 1.

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