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what time is the alabama game and what channel - Malaeb

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Solution: The variance of a dataset is defined as the average of the squared deviations from the mean. Given that there are 12 samples and the sum of the squares of the deviations is 144, we compute the variance as follows:

📌 Question: A preservation scientist studies the accumulation of microplastics in ocean depths. If the number of microplastic particles per liter at depth $ d $ meters follows the pattern $ P(d) = 3d + 7 $, how many total particles are found between 1 meter and 10 meters depth inclusive?

📌 Solution: We are given the function $ P(d) = 3d + 7 $, and we are to compute the total number of microplastic particles from depth $ d = 1 $ to $ d = 10 $. This requires summing $ P(d) $ over integer values from 1 to 10:

📌 Question: A geographer analyzing coastal erosion maps uses remote sensing data and finds that the area of lost land over 8 consecutive years forms an arithmetic sequence. If the total area lost over the 8 years is 448 square kilometers and the sum of the areas lost in the first and eighth years is 112 square kilometers, what is the common difference of the sequence?

📌 Solution: Let the first term of the arithmetic sequence be $ a $ and the common difference be $ d $. The sequence has 8 terms, so the sum $ S_8 $ is:

📌 The eighth term is $ a + 7d $, and the first term is $ a $, so their sum is:

📌 Now solve the system. From equation (2): $ 2a + 7d = 112 $. Multiply both sides by 4:

📌 This matches equation (1), so the equations are consistent. Now use $ 2a + 7d = 112 $ to express $ a $ in terms of $ d $:

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