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08 Jul 2024, 07:02
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Number of female voters in the year 2000: \(3300R\)
Ratio of female to male voters in the year 2020: \(R*\frac{100 + F}{100 + M}\)
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In the town of Xionia, elections were held every 5 years, between the year 2000 to the year 2020. During the 5 elections held in this period, the number of female voters increased while the number of male voters decreased from 3300 in the year 2000.
In the given expressions, F and M represent the percentage change in the number of female and male voters, respectively, over the 5 elections, and R represents the ratio of female to male voters in the year 2000. The percentage change in voters is calculated as \(\frac{\text{number of new voters – number of old voters}}{\text{number of old voters}}* 100\).
Select the expression that represents the Number of female voters in the year 2000, and select the expression that represents the Ratio of female to male voters in the year 2020. Make only two selections, one in each column.
In the given expressions, F and M represent the percentage change in the number of female and male voters, respectively, over the 5 elections, and R represents the ratio of female to male voters in the year 2000. The percentage change in voters is calculated as \(\frac{\text{number of new voters – number of old voters}}{\text{number of old voters}}* 100\).
Select the expression that represents the Number of female voters in the year 2000, and select the expression that represents the Ratio of female to male voters in the year 2020. Make only two selections, one in each column.
|
| Number of female voters in the year 2000 | Ratio of female to male voters in the year 2020 | |
| \(3300R\) | ||
| \(\frac{3300}{R}\) | ||
| \(\frac{1}{R}\) | ||
| \(R*\frac{100 + F}{100 + M}\) | ||
| \(R*\frac{100 - F}{100 + M}\) | ||
| \(R*\frac{100 + F}{100 - M}\) |
ShowHide Answer
Official Answer
Number of female voters in the year 2000: \(3300R\)
Ratio of female to male voters in the year 2020: \(R*\frac{100 + F}{100 + M}\)
09 Jul 2024, 01:30
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Bunuel
Experts' Global Explanation:
Let the number of female voters in the year 2000 be \(F_{2000}\).
Let the number of male voters in the year 2000 be \(M_{2000}\).
Let the number of female voters in the year 2020 be \(F_{2020}\).
Let the number of male voters in the year 2020 be \(M_{2020}\).
\(M = 3300\)
\(R = \frac{F_{2000}}{M_{2000}}\)
I.
\(R = \frac{F_{2000}}{M_{2000}}\)
\(F_{2000}=M_{2000}* R\)
\(F2000 = 3300 R\)
Since F is the percentage change in the number of females:
\(F = 100 * \frac{(F_{2020} – F_{2000}) }{ F_{2000}}\)
\(\frac{F * F_{2000}}{100} = F_{2020} – F_{2000}\)
\(\frac{F * F2000}{100} + F_{2000} = F_{2020}\)
\(\frac{(F * F_{2000} + 100F_{2000})}{100} = F_{2020}\)
\(\frac{F_{2000}(F + 100)}{100} = F_{2020}\)
\(F_{2020}/M_{2020}=\)
\(= \frac{\frac{F_{2000}(F + 100)}{100}}{\frac{M_{2000}(M + 100)}{100}}\)
\(= \frac{F_{2000}(F + 100)}{M_{2000}(M + 100)}\)
\(R*\frac{100 + F}{100 + M}\)
General Discussion
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08 Jul 2024, 07:42
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From the text, consider
f = The number of female voters in 2000
m = The number of male votes in 2000
and it is given that,
R = f/m
And m = 3300
So f = 3300R
This gives us the answer for the first column.
Now According to the question,
F = the %change in the population of females
M = the %change in the population of males
So the new ratio of population will be
[f + (F/100)*f] / [m + (M/100)*m]
If we take 'f' common from the numerator and 'm' common from the denominator, the fraction can be simplified to
[f*(100 + F)] / [m*(100 + M)]
And we know that f/m is R
So the total fraction becomes R*[F+100]/[M+100], which will be the answer for our second column.
f = The number of female voters in 2000
m = The number of male votes in 2000
and it is given that,
R = f/m
And m = 3300
So f = 3300R
This gives us the answer for the first column.
Now According to the question,
F = the %change in the population of females
M = the %change in the population of males
So the new ratio of population will be
[f + (F/100)*f] / [m + (M/100)*m]
If we take 'f' common from the numerator and 'm' common from the denominator, the fraction can be simplified to
[f*(100 + F)] / [m*(100 + M)]
And we know that f/m is R
So the total fraction becomes R*[F+100]/[M+100], which will be the answer for our second column.
