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What is the coefficient of $x^2y^6$ in the expansion of $\left(\frac{3}{5}x-\frac{y}{2}\right)^8$? Express your answer as a common fraction
**Step 1: Analyze the Problem Requirements** To find the coefficient of \( x^2y^6 \) in \( \left(\frac{3}{5}x - \frac{y}{2}\right)^8 \), we use the binomial theorem. The general term in the expansion of \( (a + b)^n \) is: \[ \text{Term} = \binom{n}{k} \cdot a^{n-k} \cdot b^k \] Here, \( a = \frac{3}{5}x \), \( b...
If a train travels 60 miles in 1.5 hours, what is its average speed in miles per minute?
To solve the problem of finding the average speed of a train in miles per minute given that it travels 60 miles in 1.5 hours, we'll go through the following steps: 1. **Analyze the problem requirements:** - The problem requires us to calculate the average speed. - The average speed is defined as the total dist...
how many a in banana?
Alright, let's break down the problem step by step. ### 1. Analyze the problem requirements We are asked to figure out how many "a"s are in the word "banana". But first, I need to confirm what we mean by "a" in "banana". Is it referring to the number of times the letter "a" appears in the word? That seems most likely...
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