An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
The sum of the proportions of all colors must equal 1.
Set up the equation: 0.24 + 0.20 + 0.15 + 0.12 + 0.15 + 0.10 + y = 1 .
Solve for y : y = 1 − ( 0.24 + 0.20 + 0.15 + 0.12 + 0.15 + 0.10 ) = 0.04 .
The proportion of cars that are yellow is 0.04 .
Explanation
Understand the problem We are given a relative frequency table showing the proportion of cars of different colors at a dealership. The colors listed are White, Black, Silver, Blue, Red, Green, and Yellow. We are given the proportions for all colors except Yellow, and we need to find the proportion of Yellow cars.
Set up the equation The sum of the proportions of all colors must equal 1, since the table represents all cars at the dealership. We can write this as: 0.24 + 0.20 + 0.15 + 0.12 + 0.15 + 0.10 + y = 1 where y is the proportion of Yellow cars.
Solve for y Now, we solve for y :
y = 1 − ( 0.24 + 0.20 + 0.15 + 0.12 + 0.15 + 0.10 ) y = 1 − 0.96 y = 0.04
State the final answer Therefore, the proportion of cars that are yellow is 0.04.
Examples
Understanding proportions is useful in many real-life situations. For example, if you are planning a party and want to estimate how many people will choose each type of food, you can use proportions based on previous parties. Similarly, businesses use proportions to understand market share and customer preferences, helping them make informed decisions about product development and marketing strategies. In this case, the car dealership uses proportions to understand the popularity of different car colors, which can influence their inventory choices.
The electric device delivers a current of 15.0 A for 30 seconds, resulting in a total charge of 450 C. This charge corresponds to approximately 2.81 x 10^21 electrons flowing through the device. Thus, a large number of electrons contribute to the electric current over this time period.
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