An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the total number of coupons: 20 + 10 + 5 = 35 .
Determine the probability of drawing each coupon type: 35 20 for 1 month, 35 10 for 1.5 months, and 35 5 for 2 months.
Calculate the expected value by multiplying each probability by the corresponding extended membership in days: ( 35 20 × 30 ) + ( 35 10 × 45 ) + ( 35 5 × 60 ) .
The correct expressions are: 35 20 × 30 , 35 10 × 45 , and 35 5 × 60 .
Explanation
Understand the problem We are given a problem about calculating the expected value of extended membership in days. The fitness center has a contest where customers can draw coupons for extended membership. There are 20 coupons for 1 month, 10 coupons for 1.5 months, and 5 coupons for 2 months. We need to identify the correct expressions for A, B, and C, where A+B+C represents the expected value.
Calculate total number of coupons First, we need to calculate the total number of coupons.
Total number of coupons The total number of coupons is 20 + 10 + 5 = 35 .
Calculate probabilities Next, we calculate the probability of drawing each type of coupon.
Probabilities of each coupon The probability of drawing a 1-month coupon is 35 20 .
The probability of drawing a 1.5-month coupon is 35 10 .
The probability of drawing a 2-month coupon is 35 5 .
Calculate expected value Now, we calculate the expected value of the extended membership in days. Remember that 1 month = 30 days, 1.5 months = 45 days, and 2 months = 60 days.
Expected value expression The expected value E is given by: E = ( 35 20 × 30 ) + ( 35 10 × 45 ) + ( 35 5 × 60 ) So, A = 35 20 × 30 , B = 35 10 × 45 , and C = 35 5 × 60 .
Final Answer Therefore, the correct expressions are: 35 20 × 30 35 10 × 45 35 5 × 60
Examples
This type of expected value calculation is used in various real-life scenarios, such as calculating the potential return on investments or determining the average outcome of a game of chance. For instance, if you're deciding whether to invest in a stock, you can estimate the expected return by considering the probabilities of different market conditions and the potential gains or losses associated with each condition. Similarly, casinos use expected value calculations to ensure they make a profit on games like roulette or blackjack. In our fitness center example, the expected value helps the center understand the average amount of extended membership they're giving away per customer.
The electric device delivers a current of 15.0 A for 30 seconds, resulting in a total charge of 450 coulombs. This charge represents approximately 2.81 x 10^21 electrons flowing through the device. The calculation involved using the relationship between current, charge, and the charge of individual electrons.
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