To find the fraction of the cars that are both gray and electrically powered, you can follow these steps:
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Identify the fraction of gray cars: The problem states that \( \frac{2}{5} \) of the cars are gray.
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Identify the fraction of gray cars that are electrically powered: It is given that \( \frac{1}{3} \) of the gray cars are electrically powered. To find the fraction of the total number of cars that are both gray and electrically powered, multiply the fraction of gray cars by the fraction of gray cars that are electrically powered:
\[ \text{Fraction of cars that are gray and electrically powered} = \left(\frac{2}{5}\right) \times \left(\frac{1}{3}\right) \]
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Multiply the fractions:
\[ \frac{2}{5} \times \frac{1}{3} = \frac{2 \times 1}{5 \times 3} = \frac{2}{15} \]
Therefore, the fraction of the cars that are both gray and electrically powered is \( \frac{2}{15} \).