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Home » Increasing each side by \(50\%\) gives a new side length: - Coaching Toolbox

Increasing each side by \(50\%\) gives a new side length: - Coaching Toolbox

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Total grains per cm³ = 500 × 4 = 2,000

📌 Since grains are distributed uniformly over 1 cm², total grains per cm² = 2,000

📌 A linguist trains a language model on a dataset where 70% of the text is from the 20th century and 30% from the 21st century. If the model processes 1.2 million words, how many more 20th-century words are there than 21st-century words?

📌 20th-century words = 0.7 × 1,200,000 = 840,000

📌 21st-century words = 0.3 × 1,200,000 = 360,000

📌 Difference = 840,000 – 360,000 = 480,000

📌 An epidemiologist estimates that 60% of a city’s population is susceptible to a new virus, and the infection rate is 0.3 per infected person per day. If there are 1,000 initially infected individuals, and each day each infected person transmits to 0.3 susceptible people on average, how many new infections occur in the first day?

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