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 cumulative population for each age group.
Determine the midpoint of the total population: 2 , 059 , 179/2 = 1 , 029 , 589.5 .
Identify the age group where the cumulative population exceeds the midpoint.
Conclude that the median age falls within the 35-49 age group.
Explanation
Understanding the Problem The problem asks us to estimate the median age in New Mexico in 2010 based on the provided population distribution by age groups. The median age is the age that divides the population into two equal halves, meaning 50% of the population is younger and 50% is older than the median age.
Calculating the Midpoint First, let's calculate the cumulative population for each age group to determine when we reach the midpoint of the total population. The total population is 2,059,179, so the midpoint is 2,059,179 / 2 = 1,029,589.5.
Cumulative Population Calculation Now, let's look at the cumulative populations:
Under 18: 518,672
Under 20 (Under 18 + 18-19): 518,672 + 61,169 = 579,841
Under 25 (Under 20 + 20-24): 579,841 + 142,370 = 722,211
Under 35 (Under 25 + 25-34): 722,211 + 267,245 = 989,456
Under 50 (Under 35 + 35-49): 989,456 + 393,362 = 1,382,818
Under 65 (Under 50 + 50-64): 1,382,818 + 404,106 = 1,786,924
Total Population: 1,786,924 + 272,255 = 2,059,179
Identifying the Median Age Group We are looking for the age group where the cumulative population exceeds 1,029,589.5. From the calculations above, we see that:
The cumulative population under 35 is 989,456, which is less than 1,029,589.5.
The cumulative population under 50 is 1,382,818, which is greater than 1,029,589.5.
This means the median age falls within the 35-49 age group.
Final Answer Therefore, a possible median age in New Mexico in 2010 could be any age between 35 and 49.
Conclusion The median age falls within the 35-49 age group.
Examples
Understanding population distributions and medians is crucial in urban planning. For instance, if a city knows its median age is increasing, it can plan for more senior centers and healthcare facilities. Conversely, a younger median age might prompt investment in schools and parks. This demographic insight guides resource allocation and policy decisions to meet the community's needs effectively.
Approximately 2.81 × 1 0 21 electrons flow through an electric device delivering a current of 15.0 A for 30 seconds. This was calculated using the relationship between current, charge, and time, followed by converting the total charge to the number of electrons. The charge of one electron is approximately 1.6 × 1 0 − 19 C .
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