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Home » Log In MyGlHyth Now: Unlock Your Free Personalized Health Dashboard – Act Fast! - Abu Waleed Tea

Log In MyGlHyth Now: Unlock Your Free Personalized Health Dashboard – Act Fast! - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 $\boxed{\frac{59}{48}}$

📌 Question: A climate researcher in New York City analyzes energy usage data from three boroughs. Over one week, the total CO₂ emissions were proportional to the ratios $4:7:9$. If the second borough emitted 147 metric tons, how many metric tons did the third borough emit?

📌 Solution: The ratio of emissions is $4:7:9$. Let the common multiplier be $x$. Then the second borough emitted $7x = 147$ metric tons. Solving for $x$:

📌 x = \frac{147}{7} = 21

📌 Then the third borough emitted $9x = 9 \times 21 = 189$ metric tons.

📌 $\boxed{189}$

📌 Question: A museum curator divides a $12 \times 12$ meter exhibition hall into identical non-overlapping rectangular display zones of integer side lengths. What is the smallest possible number of such rectangles needed to exactly cover the floor if each rectangle must have area at least 18 square meters?

📌 Solution: The total area of the hall is $12 \times 12 = 144$ square meters. Each rectangle has area at least 18, so the maximum number of rectangles is $ \left\lfloor \frac{144}{18} \right\rfloor = 8 $, but we want the *minimum* number, so we seek the largest rectangle area that divides 144 and is $ \geq 18 $, and check if tiling with such rectangles covers the square.

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