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 midpoint of each square footage range.
Multiply each midpoint by its corresponding frequency and sum the products: ∑ ( Midpoint × Frequency ) = 1220750 .
Calculate the total frequency: ∑ Frequency = 500 .
Divide the sum of the products by the total frequency and round to the nearest integer: 500 1220750 ≈ 2442 .
Explanation
Understand the problem and provided data We are given a frequency table of housing data and asked to find the mean square footage. The table provides square footage ranges and their corresponding frequencies. To calculate the mean, we need to find the midpoint of each range, multiply it by the frequency, sum these products, and then divide by the total frequency.
Calculate the midpoints of each range First, let's calculate the midpoint of each square footage range:
0-499: 2 0 + 499 = 249.5
500-999: 2 500 + 999 = 749.5
1000-1499: 2 1000 + 1499 = 1249.5
1500-1999: 2 1500 + 1999 = 1749.5
2000-2499: 2 2000 + 2499 = 2249.5
2500-2999: 2 2500 + 2999 = 2749.5
3000-3499: 2 3000 + 3499 = 3249.5
3500-3999: 2 3500 + 3999 = 3749.5
4000-4499: 2 4000 + 4499 = 4249.5
4500-4999: 2 4500 + 4999 = 4749.5
Multiply midpoints by frequencies Next, we multiply each midpoint by its corresponding frequency:
249.5 × 5 = 1247.5
749.5 × 17 = 12741.5
1249.5 × 33 = 41233.5
1749.5 × 121 = 211689.5
2249.5 × 119 = 267690.5
2749.5 × 83 = 228208.5
3249.5 × 45 = 146227.5
3749.5 × 41 = 153729.5
4249.5 × 26 = 110487
4749.5 × 10 = 47495
Sum the products Now, we sum these products: 1247.5 + 12741.5 + 41233.5 + 211689.5 + 267690.5 + 228208.5 + 146227.5 + 153729.5 + 110487 + 47495 = 1220750
Calculate the total frequency We calculate the total frequency by summing all the frequencies: 5 + 17 + 33 + 121 + 119 + 83 + 45 + 41 + 26 + 10 = 500
Calculate the mean To find the mean, we divide the sum of the products by the total frequency: Mean = 500 1220750 = 2441.5
Round to the nearest integer and conclude Finally, we round the mean to the nearest integer: 2441.5 ≈ 2442 . Therefore, the mean square footage is approximately 2442.
Examples
Understanding mean values is very useful in real estate. For example, a real estate agent can use the mean square footage of houses in a neighborhood to give potential buyers an idea of what to expect. This can also be used to compare different neighborhoods or to track changes in housing sizes over time. Knowing the average size helps in pricing strategies and understanding market trends.
To find how many electrons flow through an electric device delivering a current of 15.0 A for 30 seconds, we first calculate the charge using the formula Q = I × t to get 450 C. Then, dividing this charge by the charge of an electron (approximately 1.6 × 1 0 − 19 C ), we find that approximately 2.81 × 1 0 21 electrons flow through the device.
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