Of the cars in a used-car lot, 2/5 are the color gray. 1/3 of the gray cars are electrically powered vehicles. What fraction of the cars on the lot are both gray and electrified? Leave your answer in the simplest fraction form
Let N be the number of cars in the used-car lot.
There are (2/5)*N gray cars.
Of these, (1/3)*(2/5)*N = (2/15)*N cars are both gray and electrically powered.
Thus, the fraction of cars on the lot that are both gray and electrified is 2/15. Answer: \boxed{\frac{2}{15}}.
To find the fraction of cars on the lot that are both gray and electrified, we need to multiply the fraction of cars that are gray by the fraction of gray cars that are electrically powered.
The fraction of cars that are gray is 2/5.
The fraction of gray cars that are electrically powered is 1/3.
To multiply these fractions, we multiply the numerators together (2 x 1) and the denominators together (5 x 3).
Therefore, the fraction of cars on the lot that are both gray and electrified is (2/5) x (1/3) = 2/15.
So, 2/15 of the cars on the lot are both gray and electrically powered.
To find the fraction of the cars on the lot that are both gray and electrified, we need to multiply the fractions that represent the proportion of gray cars and the proportion of gray cars that are also electrically powered.
First, let's consider the fraction of gray cars. We know that 2/5 of the cars on the lot are gray. So, this means that the proportion of gray cars is 2/5.
Next, let's consider the fraction of gray cars that are electrically powered. We know that 1/3 of the gray cars are electrically powered. So, the proportion of gray cars that are also electrically powered is 1/3.
To find the fraction of the cars that are both gray and electrically powered, we multiply these two fractions:
(2/5) * (1/3) = 2/15.
Therefore, 2/15 of the cars on the lot are both gray and electrically powered.