79 results

population - all the inhabitants of a particular town, area, or country.

250 students have iPhones. This is one third of the population. How many students are there in total

250 students have iPhones. This is one third of the population. How many students are there in total?
Let the population be p. We're given:
1/3p = 250
Cross multiply:
p = 250 * 3
p = [B]750[/B]

3 boys share 100 in the ratio 1:2:2. how much each boy will get?

3 boys share 100 in the ratio 1:2:2. how much each boy will get?
Given the ratio 1 : 2 : 2, calculate the expected number of items from a population of 100
A ratio of 1 : 2 : 2 means that for every of item A, we can expect 2 of item B and 2 of item c
Therefore, our total group is 1 + 2 + 2 = 5
[SIZE=5][B]Calculate Expected Number of Item A:[/B][/SIZE]
Expected Number of Item A = 1 x 100/5
Expected Number of Item A = 100/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=100&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item A = 20/1
Expected Number of Item A = [B]20[/B]
[SIZE=5][B]Calculate Expected Number of Item B:[/B][/SIZE]
Expected Number of Item B = 2 x 100/5
Expected Number of Item B = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item B = 40/1
Expected Number of Item B = [B]40[/B]
[SIZE=5][B]Calculate Expected Number of Item C:[/B][/SIZE]
Expected Number of Item C = 2 x 100/5
Expected Number of Item C = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item C = 40/1
Expected Number of Item C = [B]40[/B]
[B]Final Answer:[/B]
(A, B, C) =[B] (20, 40, 40)[/B] for 1:2:2 on 100 people

A bacteria population increases every hour. At 12pm there are 5 cells. At 1pm there are 10 cells. At

A bacteria population increases every hour. At 12pm there are 5 cells. At 1pm there are 10 cells. At 2pm there are 20 cells. At 3pm there are 40 cells. If this pattern continues, how many cells will there be at 7pm?
The bacteria cells double each hour in the example above.
From 3pm to 7pm, we have 4 hours, meaning 4 doubling periods. Which is 2 * 2 * 2 * 2 or 2^4.
So we have:
40 * 2^4
40 * 16 = [B]640 cells[/B]

A bunny population is doubling every 2 years. There are currently 45 bunnies. How many will there be

A bunny population is doubling every 2 years. There are currently 45 bunnies. How many will there be in 10 years?
Find the number of doubling periods:
Number of Doubling periods = Time / Doubling period
Number of Doubling periods = 10/2
Number of Doubling periods = 5
Create a function to determine the amount of bunnies after each doubling period:
B(n) = 45 * 2^n
Since we calculated 5 doubling periods, we want B(5):
B(5) = 45 * 2^5
B(5) = 45 * 32
B(5) = [B]1,440[/B]

A city doubles its size every 48 years. If the population is currently 400,000, what will the popula

A city doubles its size every 48 years. If the population is currently 400,000, what will the population be in 144 years?
Calculate the doubling time periods:
Doubling Time Periods = Total Time / Doubling Time
Doubling Time Periods = 144/48
Doubling Time Periods = 3
Calculate the city population where t is the doubling time periods:
City Population = Initital Population * 2^t
Plugging in our numbers, we get:
City Population = 400,000 * 2^3
City Population = 400,000 * 8
City Population = [B]3,200,000[/B]

A city has a population of 240,000 people. Suppose that each year the population grows by 7.25%. Wha

A city has a population of 240,000 people. Suppose that each year the population grows by 7.25%. What will the population be after 9 years?
Let's build a population function P(t), where t is the number of years since right now.
P(t) = 240,000(1.0725)^t <-- 7.25% as a decimal is 0.0725
The question asks for P(9)
P(9) = 240,000(1.0725)^9
P(9) = 240,000(1.87748)
P(9) = [B]450,596[/B]

A city has a population of 240,000 people. Suppose that each year the population grows by 8%. What w

A city has a population of 240,000 people. Suppose that each year the population grows by 8%. What will the population be after 5 years?
[U]Set up our population function[/U]
P(t) = 240,000(1 + t)^n where t is population growth rate percent and n is the time in years
[U]Evaluate at t = 0.08 and n = 5[/U]
P(5) = 240,000(1 + 0.08)^5
P(5) = 240,000(1.08)^5
P(5) = 240,000 * 1.4693280768
[B]P(5) = 352638.73 ~ 352,639[/B]

A city has a population of 260,000 people. Suppose that each year the population grows by 8.75% . W

A city has a population of 260,000 people. Suppose that each year the population grows by 8.75% . What will the population be after 12 years? Use the calculator provided and round your answer to the nearest whole number.
Using our [URL='http://www.mathcelebrity.com/population-growth-calculator.php?num=acityhasapopulationof260000people.supposethateachyearthepopulationgrowsby8.75%.whatwillthepopulationbeafter12years?usethecalculatorprovidedandroundyouranswertothenearestwholenumber&pl=Calculate']population growth calculator,[/URL] we get P = [B]711,417[/B]

A city’s population in the 1987 was 125,524. In 2007 the population was 436,884. Determine the popul

A city’s population in the 1987 was 125,524. In 2007 the population was 436,884. Determine the population rate of increase or decrease
[U]Find the population change:[/U]
Population Change = New Population - Old Population
Population Change = 436,884 - 125,524
Population Change = 311,360
[U]Since the population change increased, we calculate the rate of increase:[/U]
Rate of increase = 100% * Population Change / Starting Population
Rate of increase = 100% * 311,360 / 125,524
Rate of increase = 100% * 2.48
Rate of increase = [B]248%[/B]

A colony of 100 bacteria doubles in size every 34 hours. What will the population be 68 hours from n

A colony of 100 bacteria doubles in size every 34 hours. What will the population be 68 hours from now
T(0) = 100
T(34) = 100 * 2 = 200
T(68) = 200 * 2 = [B]400[/B]

A colony of 995 bacteria doubles in size every 206 minutes. What will the population be 618 minutes

A colony of 995 bacteria doubles in size every 206 minutes. What will the population be 618 minutes from now?
Calculate the doubling time periods:
Doubling Time Periods = Total Minutes From Now / Doubling Period in Minutes
Doubling Time Periods = 618/206
Doubling Time Periods = 3
Calculate the new population using the doubling time formula below where t is the number of doubling periods:
Population = Initial Population * 2^2
Population = 995 * 2^3
Population = 995 * 8
Population = [B]7,960[/B]

a confidence interval for a population mean has a margin of error of 0.081

a confidence interval for a population mean has a margin of error of 0.081

A hypothetical population consists of eight individuals ages 14,15,17,20,26,27,28, and 30 years. Wh

A hypothetical population consists of eight individuals ages 14,15,17,20,26,27,28, and 30 years. What is the probability of selecting a participant who is at least 20 years old?
At least 20 means 20 or older, so our selection of individuals is:
{20, 26, 27, 28, 30}
This is 5 out of a possible 8, so we have [URL='http://www.mathcelebrity.com/perc.php?num=5&den=8&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']5/8 of 0.625, which is 62.5%[/URL]

A Petri dish contains 2000. The number of bacteria triples every 6 hours. How many bacteria will exi

A Petri dish contains 2000. The number of bacteria triples every 6 hours. How many bacteria will exist after 3 days?
Determine the amount of tripling periods:
[LIST]
[*]There are 24 hours in a day.
[*]24 hours in a day * 3 days = 72 hours
[*]72 hours / 6 hours tripling period = 12 tripling periods
[/LIST]
Our bacteria population function B(t) where t is the amount of tripling periods. Tripling means we multiply by 3, so we have:
B(t) = 2000 * 3^t
with t = 12 tripling periods, we have:
B(12) = 2000 * 3^12
B(12) = 2000 * 531441
B(12) = [B]1,062,882,000[/B]

A population grows at 6% per year. How many years does it take to triple in size?

A population grows at 6% per year. How many years does it take to triple in size?
With a starting population of P, and triple in size means 3 times the original, we want to know t for:
P(1.06)^t = 3P
Divide each side by P, and we have:
1.06^t = 3
Typing this equation into our search engine to solve for t, we get:
t = [B]18.85 years[/B]
Note: if you need an integer answer, we round up to 19 years

A population of 200 doubles in size every hour. What is the rate of growth of the population after 2

A population of 200 doubles in size every hour. What is the rate of growth of the population after 2.5 hours?
Time 1: 400
Time 2: 800
Time 3: 1200 (Since it's only 1/2 of a period)

A population of wolves on an island starts at 5 if the population doubles every 10 years, what will

A population of wolves on an island starts at 5 if the population doubles every 10 years, what will be the population in 90 years?
If the population doubles every 10 years, we have 90/10 = 9 doubling periods.
Our population function P(t) is where t is the doubling period
P(t) = 5(2^t)
The problem asks for P(9):
P(9) = 5(2^9)
P(9) = 5(512)
P(9) = [B]2,560[/B]

A professor assumed there was a correlation between the amount of hours people were expose to sunlig

A professor assumed there was a correlation between the amount of hours people were expose to sunlight and their blood vitamin D level. The null hypothesis was that the population correlation was__
a. Positive 1.0
b. Negative 1.0
c. Zero
d. Positive 0.50
[B]c. Zero[/B]
Reason: Since the professor wanted to assume a correlation (either positive = 1.0 or negative = -1.0), then we take the other side of that assumption for our null hypothesis and say that there is no correlation (Zero)

A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population sta

A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval estimate of the mean lifetime.
[B]2902 < u < 3098[/B] using our [URL='http://www.mathcelebrity.com/normconf.php?n=100&xbar=3000&stdev=500&conf=95&rdig=4&pl=Large+Sample']confidence interval for the mean calculator[/URL]

A random sample of 144 with a mean of 100 and a standard deviation of 70 is known from a population

A random sample of 144 with a mean of 100 and a standard deviation of 70 is known from a population of 1,000. What is the 95% confidence interval for the unknown population?
[URL='http://www.mathcelebrity.com/normconf.php?n=144&xbar=100&stdev=70&conf=95&rdig=4&pl=Large+Sample']Large Sample Confidence Interval Mean Test[/URL]
[B]88.5667 < u < 111.4333[/B]

A random sample of n = 10 flash light batteries with a mean operating life X=5 hr. And a sample stan

A random sample of n = 10 flash light batteries with a mean operating life X=5 hr. And a sample standard deviation S = 1 hr. is picked from a production line known to produce batteries with normally distributed operating lives. What's the 98% confidence interval for the unknown mean of the working life of the entire population of batteries?
[URL='http://www.mathcelebrity.com/normconf.php?n=10&xbar=5&stdev=1&conf=98&rdig=4&pl=Small+Sample']Small Sample Confidence Interval for the Mean test[/URL]
[B]4.1078 < u < 5.8922[/B]

A super deadly strain of bacteria is causing the zombie population to double every day. Currently, t

A super deadly strain of bacteria is causing the zombie population to double every day. Currently, there are 25 zombies. After how many days will there be over 25,000 zombies?
We set up our exponential function where n is the number of days after today:
Z(n) = 25 * 2^n
We want to know n where Z(n) = 25,000.
25 * 2^n = 25,000
Divide each side of the equation by 25, to isolate 2^n:
25 * 2^n / 25 = 25,000 / 25
The 25's cancel on the left side, so we have:
2^n = 1,000
Take the natural log of each side to isolate n:
Ln(2^n) = Ln(1000)
There exists a logarithmic identity which states: Ln(a^n) = n * Ln(a). In this case, a = 2, so we have:
n * Ln(2) = Ln(1,000)
0.69315n = 6.9077
[URL='https://www.mathcelebrity.com/1unk.php?num=0.69315n%3D6.9077&pl=Solve']Type this equation into our search engine[/URL], we get:
[B]n = 9.9657 days ~ 10 days[/B]

A town has a population of 12000 and grows at 5% every year. What will be the population after 12 ye

A town has a population of 12000 and grows at 5% every year. What will be the population after 12 years, to the nearest whole number?
We calculate the population of the town as P(t) where t is the time in years since now.
P(t) = 12000(1.05)^t
The problem asks for P(12)
P(12) = 12000(1.05)^12
P(12) = 12000(1.79585632602)
P(12) = [B]21550[/B] <- nearest whole number

A town has a population of 25,000 and grows at 7.7% every 4 months. What will be the population afte

A town has a population of 25,000 and grows at 7.7% every 4 months. What will be the population after 6 years?
[LIST]
[*]1 year = 12 months
[*]12 months / 4 months = 3 compounding periods per year
[*]3 compounding periods per year * 6 years = 18 compounding periods
[/LIST]
So we have our population growth as follows:
25,000(1.077)^18
25,000 * 3.8008668804
95,021.67 ~ [B]95,021[/B]

A town has a population of 50,000. Its rate increases 8% every 6 months. Find the population after 4

A town has a population of 50,000. Its rate increases 8% every 6 months. Find the population after 4 years.
Every 6 months means twice a year. So we have 4 years * twice a year increase = 8 compounding periods.
Our formula for compounding an initial population P at time t is P(t) at a compounding percentage i:
P(t) = P * (1 + i)^t
Since 8% is 0.08 as a decimal and t = 4 *2 = 8, we have:
P(8) = 50000 * (1.08)^8
P(8) = 50000 * 1.85093
P(8) = 92,546.51
Since we can't have a partial person, we round down to [B]92,545[/B]

A towns population is currently 500. If the population doubles every 30 years, what will the populat

A towns population is currently 500. If the population doubles every 30 years, what will the population be 120 years from now?
Find the number of doubling times:
120 years / 30 years per doubling = 4 doubling times
Set up our growth function P(n) where n is the number of doubling times:
P(n) = 500 * 2^n
Since we have 4 doubling times, we want P(4):
P(4) = 500 * 2^4
P(4) = 500 * 16
P(4) = [B]8,000[/B]

A wildlife reserve has a population of 180 elephants. A group of researchers trapped 60 elephants an

A wildlife reserve has a population of 180 elephants. A group of researchers trapped 60 elephants and recorded their vital statistics. Of the trapped elephants, 12 were female. If that rate holds true for the entire population of 180 elephants, how many female elephants are on the wildlife reserve?
Set up a proportion of female to trapped elephants:
12/60 = f/180
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=12&num2=f&den1=60&den2=180&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we see that f = [B]36[/B]

A ________ ________ is the value of a statistic that estimates the value of a parameter.

A ________ ________ is the value of a statistic that estimates the value of a parameter.
[B]Point Estimate[/B].
A point [B]estimate[/B] is a single [B]value[/B] (statistic) used to [B]estimate[/B] a population [B]value[/B]([B]parameter[/B])

Bangladesh, a country about the size of the state of Iowa, but has about half the U.S population, ab

Bangladesh, a country about the size of the state of Iowa, but has about half the U.S population, about 170 million. The population growth rate in Bangladesh is assumed to be linear, and is about 1.5% per year of the base 170 million. Create a linear model for population growth in Bangladesh. Assume that y is the total population in millions and t is the time in years.
At any time t, the Bangladesh population at year t is:
[B]y = 170,000,000(1.015)^t[/B]

Confidence Interval of a Proportion

Free Confidence Interval of a Proportion Calculator - Given N, n, and a confidence percentage, this will calculate the estimation of confidence interval for the population proportion π including the margin of error. confidence interval of the population proportion

Confidence Interval/Hypothesis Testing for the Difference of Means

Free Confidence Interval/Hypothesis Testing for the Difference of Means Calculator - Given two large or two small distriutions, this will determine a (90-99)% estimation of confidence interval for the difference of means for small or large sample populations.

Also performs hypothesis testing including standard error calculation.

Also performs hypothesis testing including standard error calculation.

Construct a confidence interval of the population proportion at the given level of confidence. x = 1

Construct a confidence interval of the population proportion at the given level of confidence.
x = 120, n = 300, 99% confidence
Round to 3 decimal places as needed
[B]0.327 < p < 0.473[/B] using our [URL='http://www.mathcelebrity.com/propconf.php?bign=300&smalln=120&conf=99&pl=Proportion+Confidence+Interval']proportion confidence interval calculator[/URL]

Currently 16 out of every 25 American adults drink coffee every day. In a town with a population of

Currently 16 out of every 25 American adults drink coffee every day. In a town with a population of 7900 adults, how many of these adults would you expect to drink coffee ever
We'd multiply 16/25 times 7900:
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=7900&frac2=16/25&pl=Multiply']fraction multiplication calculator by type 16/25 of 7900[/URL], we get:
[B]5056[/B]

data below consists of the pulse rates (in beats per minute) of 32 students. Assuming σ = 10.66,

The data below consists of the pulse rates (in beats per minute) of 32 students. Assuming σ = 10.66, obtain a 95.44% confidence interval for the population mean.
80 74 61 93 69 74 80 64
51 60 66 87 72 77 84 96
60 67 71 79 89 75 66 70
57 76 71 92 73 72 68 74

Determine ux and sigma(x) from the given parameters of the population and sample size u = 76, sigma

Determine ux and sigma(x) from the given parameters of the population and sample size
u = 76, sigma = 28, n = 49
ux = ?
sigma(x) = ?
[B]u = ux = 76[/B]
sigma(x) = sigma/sqrt(n) so we have
28/sqrt(49) = 28/7 = [B]4[/B]

Eight-ninths of the population p

Eight-ninths of the population p
[B]8p/9[/B]

F Test Statistic

Free F Test Statistic Calculator - Calculates the F-test statistic for two populations

Find Mean 106 and standard deviation 10 of the sample mean which is 25

Do you mean x bar?
mean of 106 inches and a standard deviation of 10 inches and for sample of size is 25. Determine the mean and the standard deviation of /x
If so, x bar equals the population mean. So it's [B]106[/B].
Sample standard deviation = Population standard deviation / square root of n
10/Sqrt(25)
10/5
[B]2[/B]

Find Mean and standard deviation

Sample Mean = Population Mean
Sample Mean = [B]75[/B]
Sample Standard Deviation = Population Standard Deviation / Sqrt(n)
Sample Standard Deviation = 16/sqrt(64)
Sample Standard Deviation = 16 / 8
Sample Standard Deviation = [B]2[/B]

Find Requested Confidence Value

The data below consists of the pulse rates (in beats per minute) of 32 students. Assuming σ = 10.66, obtain a 95.44% confidence interval for the population mean.
80 74 61 93 69 74 80 64
51 60 66 87 72 77 84 96
60 67 71 79 89 75 66 70
57 76 71 92 73 72 68 74

For a population with μ = 60 and σ = 12, what is the z-score that corresponds to a score of 66?

For a population with μ = 60 and σ = 12, what is the z-score that corresponds to a score of 66?
[URL='https://www.mathcelebrity.com/probnormdist.php?xone=66&mean=60&stdev=12&n=1&pl=P%28X+%3C+Z%29']Using our z-score calculator[/URL], we get a probability:
[B]0.691462[/B]

Height and weight are two measurements used to track a child's development. TheWorld Health Organiza

Height and weight are two measurements used to track a child's development. The World Health Organization measures child development by comparing the weights of children who are the same height and the same gender.
In 2009, weights for all 80 cm girls in the reference population had a mean μ = 10.2 kg and standard deviation σ = 0.8 kg. Weights are normally distributed. X ~ N(10.2, 0.8).
Calculate the z-scores that correspond to the following weights and interpret them.
a. 11 kg

b. 7.9 kg

c. 12.2 kg a. [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+11&mean=10.2&stdev=8&n=+1&pl=1" target="_blank']Answer A[/URL] - Z = 0.1 b. [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+7.9&mean=+10.2&stdev=+8&n=+1&pl=1']Answer B[/URL] - Z = -0.288 c. [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+12.2&mean=+10.2&stdev=+8&n=+1&pl=1']Answer C[/URL] - Z = 0.25

b. 7.9 kg

c. 12.2 kg a. [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+11&mean=10.2&stdev=8&n=+1&pl=1" target="_blank']Answer A[/URL] - Z = 0.1 b. [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+7.9&mean=+10.2&stdev=+8&n=+1&pl=1']Answer B[/URL] - Z = -0.288 c. [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+12.2&mean=+10.2&stdev=+8&n=+1&pl=1']Answer C[/URL] - Z = 0.25

HELP SOLVE

A sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test about the mean, µ, of the population from which the sample was drawn
x = 3.26 , S = 0.55, σN= 9, H0: µ = 2.85, Ha: µ > 2.85 , α = 0.01

HELP SOLVE

sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given significance level.
x = 3.7, n = 32, σ = 1.8, H0: µ = 4.2 , Ha: µ ≠ 4.2 , α = 0.05

HELP SOLVE

A sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given significance level.
x = 20.5, n = 11, σ = 7, H0: µ = 18.7 , Ha: µ ≠ 18.7 , α = 0.01

HELP SOLVE

Perform a one-sample z-test for a population mean. Be sure to state the hypotheses and the significance level, to compute the value of the test statistic, to obtain the P-value, and to state your conclusion.
Five years ago, the average math SAT score for students at one school was 475. A teacher wants to perform a hypothesis test to determine whether the mean math SAT score of students at the school has changed. The mean math SAT score for a random sample of 40 students from this school is 469. Do the data provide sufficient evidence to conclude that the mean math SAT score for students at the school has changed from the previous mean of 475? Perform the appropriate hypothesis test using a significance level of 10%. Assume that Η = 73.

If 23.8% of a population is 8,212,000. What is the total population?

If 23.8% of a population is 8,212,000. What is the total population?
This can be written as [I]23.8% of x is 8212000
[/I]
We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=23.8&den1=8212000&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type this expression into our search engine[/URL] and we get:
[B]1,954,456[/B]

In 1910, the population of math valley was 15,000. If the population is increasing at an annual rate

In 1910, the population of math valley was 15,000. If the population is increasing at an annual rate of 2.4%, what was the population in 1965?
1965 - 1910 = 55 years of growth.
P(1965) = 15,000 * (1.024)^55
P(1965) = 15,000 * 3.68551018049
P(1965) = 55282.652707 ~ [B]55,283[/B]

In 2010, the population of Greenbow, AL was 1,100 people. The population has risen at at rate of 4%

In 2010, the population of Greenbow, AL was 1,100 people. The population has risen at at rate of 4% each year since. Let x = the number of years since 2010 and y = the population of Greenbow. What will the population of Greenbow be in 2022?
P(x) = 1,100(1.04)^x
x = 2022 - 2010
x = 12 years
We want P(12):
P(12) = 1,100(1.04)^12
P(12) = 1,100(1.60103221857)
P(12) = [B]1,761.14 ~ 1,761[/B]

In 2016 the geese population was at 750. the geese population is expected to grow at a rate of 12% e

In 2016 the geese population was at 750. the geese population is expected to grow at a rate of 12% each year. What is the geese population in 2022?
12% is also 0.12. We have the population growth function:
P(t) = 750(1.12)^t
2022 - 2016 is 6 years of growth. We want P(6).
P(6) = 750(1.12)^6
P(6) = 750(1.9738)
[B]P(6) = 1,480.36 ~ 1,480[/B]

In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both

In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like either tea or coffee
We don't want to count duplicates, so we have the following formula
Tea Or Coffee = Tea + Coffee - Both
Tea Or Coffee = 40 + 30 - 10
Tea Or Coffee = [B]60[/B]

In order to test if there is a difference between means from two populations, which of following ass

In order to test if there is a difference between means from two populations, which of following assumptions are NOT required?
a. The dependent variable scores must be a continuous quantitative variable.
b. The scores in the populations are normally distributed.
c. Each value is sampled independently from each other value.
d. The two populations have similar means
[B]a and d
[/B]
[I]because b and c [U]are[/U] required[/I]

In the year 2000, the population of Rahway, New Jersey, was 26500. Express this number in scientific

In the year 2000, the population of Rahway, New Jersey, was 26500. Express this number in scientific notation
26,500 in [URL='https://www.mathcelebrity.com/scinot.php?num=26500&pl=Convert+to+Number']scientific notation is found using our scientific notation calculator[/URL]:
[B]2.65 x 10^4[/B]

Of the worlds 7.5 billion people, 1.2 billion people live on less than 4 per day. Calculate the perc

Of the worlds 7.5 billion people, 1.2 billion people live on less than 4 per day. Calculate the percent of the worlds population who lives on less than 4 per day?
We want the percentage 1.2/7.5.
[URL='https://www.mathcelebrity.com/perc.php?num=1.2&den=7.5&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Type this fraction into our search engine[/URL], choose percentage, and we get:
[B]16%[/B]

On January 1st a town has 75,000 people and is growing exponentially by 3% every year. How many peop

On January 1st a town has 75,000 people and is growing exponentially by 3% every year. How many people will live there at the end of 10 years?
[URL='https://www.mathcelebrity.com/population-growth-calculator.php?num=atownhasapopulationof75000andgrowsat3%everyyear.whatwillbethepopulationafter10years&pl=Calculate']Using our population growth calculator[/URL], we get:
[B]100,794[/B]

Ordered and Unordered Partitions

Free Ordered and Unordered Partitions Calculator - Given a population size (n) and a group population of (m), this calculator determines how many ordered or unordered groups of (m) can be formed from (n)

Pleasantburg has a population growth model of P(t)=at2+bt+P0 where P0 is the initial population. Sup

Pleasantburg has a population growth model of P(t)=at^2+bt+P0 where P0 is the initial population. Suppose that the future population of Pleasantburg t years after January 1, 2012, is described by the quadratic model P(t)=0.7t^2+6t+15,000. In what month and year will the population reach 19,200?
Set P(t) = 19,200
0.7t^2+6t+15,000 = 19,200
Subtract 19,200 from each side:
0.7t^2+6t+4200 = 0
The Quadratic has irrational roots. So I set up a table below to run through the values. At t = 74, we pass 19,200. Which means we add 74 years to 2012: 2012 + 74 = [B]2086[/B]
t 0.7t^2 6t Add 15000 Total
1 0.7 6 15000 15006.7
2 2.8 12 15000 15014.8
3 6.3 18 15000 15024.3
4 11.2 24 15000 15035.2
5 17.5 30 15000 15047.5
6 25.2 36 15000 15061.2
7 34.3 42 15000 15076.3
8 44.8 48 15000 15092.8
9 56.7 54 15000 15110.7
10 70 60 15000 15130
11 84.7 66 15000 15150.7
12 100.8 72 15000 15172.8
13 118.3 78 15000 15196.3
14 137.2 84 15000 15221.2
15 157.5 90 15000 15247.5
16 179.2 96 15000 15275.2
17 202.3 102 15000 15304.3
18 226.8 108 15000 15334.8
19 252.7 114 15000 15366.7
20 280 120 15000 15400
21 308.7 126 15000 15434.7
22 338.8 132 15000 15470.8
23 370.3 138 15000 15508.3
24 403.2 144 15000 15547.2
25 437.5 150 15000 15587.5
26 473.2 156 15000 15629.2
27 510.3 162 15000 15672.3
28 548.8 168 15000 15716.8
29 588.7 174 15000 15762.7
30 630 180 15000 15810
31 672.7 186 15000 15858.7
32 716.8 192 15000 15908.8
33 762.3 198 15000 15960.3
34 809.2 204 15000 16013.2
35 857.5 210 15000 16067.5
36 907.2 216 15000 16123.2
37 958.3 222 15000 16180.3
38 1010.8 228 15000 16238.8
39 1064.7 234 15000 16298.7
40 1120 240 15000 16360
41 1176.7 246 15000 16422.7
42 1234.8 252 15000 16486.8
43 1294.3 258 15000 16552.3
44 1355.2 264 15000 16619.2
45 1417.5 270 15000 16687.5
46 1481.2 276 15000 16757.2
47 1546.3 282 15000 16828.3
48 1612.8 288 15000 16900.8
49 1680.7 294 15000 16974.7
50 1750 300 15000 17050
51 1820.7 306 15000 17126.7
52 1892.8 312 15000 17204.8
53 1966.3 318 15000 17284.3
54 2041.2 324 15000 17365.2
55 2117.5 330 15000 17447.5
56 2195.2 336 15000 17531.2
57 2274.3 342 15000 17616.3
58 2354.8 348 15000 17702.8
59 2436.7 354 15000 17790.7
60 2520 360 15000 17880
61 2604.7 366 15000 17970.7
62 2690.8 372 15000 18062.8
63 2778.3 378 15000 18156.3
64 2867.2 384 15000 18251.2
65 2957.5 390 15000 18347.5
66 3049.2 396 15000 18445.2
67 3142.3 402 15000 18544.3
68 3236.8 408 15000 18644.8
69 3332.7 414 15000 18746.7
70 3430 420 15000 18850
71 3528.7 426 15000 18954.7
72 3628.8 432 15000 19060.8
73 3730.3 438 15000 19168.3
74 3833.2 444 15000 19277.2

Population Doubling Time

Free Population Doubling Time Calculator - Determines population growth based on a doubling time.

Population Growth

Free Population Growth Calculator - Determines population growth based on an exponential growth model.

population MEAN OF ENVIRONMENTAL SPECIALIST SALARY IS $62000.A RANDOM SAMPLE OF 45 SPECIALIST IS DRA

population MEAN OF ENVIRONMENTAL SPECIALIST SALARY IS $62000.A RANDOM SAMPLE OF 45 SPECIALIST IS DRAWN FROM THE POPULATION. WHAT IS THE LIKELIHOOD THAT THE MEAN SALARY SAMPLE IS $59000. ASSUME SIGMA IS $6000.
Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=59000&mean=62000&stdev=6000&n=45&pl=P%28X+%3C+Z%29']Z-Score calculator[/URL], we get the probability as [B]0.0004[/B].

Ratios

Free Ratios Calculator - * Simplifies a ratio of a:b

* Given a ratio in the form a:b or a to b, and a total population amount, this calculator will determine the expected value of A and B from the ratio.

* Given a ratio in the form a:b or a to b, and a total population amount, this calculator will determine the expected value of A and B from the ratio.

Sample Size Reliability for μ

Free Sample Size Reliability for μ Calculator - Given a population standard deviation σ, a reliability (confidence) value or percentage, and a variation, this will calculate the sample size necessary to make that test valid.

Sample Size Requirement for the Difference of Means

Free Sample Size Requirement for the Difference of Means Calculator - Given a population standard deviation 1 of σ_{1}, a population standard deviation 2 of σ_{2} a reliability (confidence) value or percentage, and a variation, this will calculate the sample size necessary to make that test valid.

Solve the problem

a confidence interval for a population mean has a margin of error of 0.081. Determine the length of the confidence interval

Suppose a city's population is 740,000. If the population grows by 12,620 per year, find the populat

Suppose a city's population is 740,000. If the population grows by 12,620 per year, find the population of the city in 7 years
Set up the population function P(y) where y is the number of years since now:
P(y) = Current population + Growth per year * y
Plugging in our numbers at y = 7, we get:
P(7) = 740000 + 12620(7)
P(7) = 740000 + 88340
P(7) = [B]828,340[/B]

Suppose a city's population is 740,000. If the population grows by 12,620 per year, find the populat

Suppose a city's population is 740,000. If the population grows by 12,620 per year, find the population of the city in 7 years.
We setup the population function P(y) where y is the number of years of population growth, g is the growth per year, and P(0) is the original population.
P(y) = P(0) + gy
Plugging in our numbers of y = 7, g = 12,620, and P(0) = 740,000, we have:
P(7) = 740,000 + 12,620 * 7
P(7) = 740,000 + 88,340
P(7) = [B]828,340[/B]

Survival Rates

Free Survival Rates Calculator - Given a set of times and survival population counts, the calculator will determine the following:

Survival Population l_{x}

Mortality Population d_{x}

Survival Probability p_{x}

Mortality Probability q_{x}

In addition, the calculator will determine the probability of survival from t_{x} to t_{x + n}

Survival Population l

Mortality Population d

Survival Probability p

Mortality Probability q

In addition, the calculator will determine the probability of survival from t

The average precipitation for the first 7 months of the year is 19.32 inches with a standard deviati

The average precipitation for the first 7 months of the year is 19.32 inches with a standard deviation of 2.4 inches. Assume that the average precipitation is normally distributed.
a. What is the probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months?
b. What is the average precipitation of 5 randomly selected years for the first 7 months?
c. What is the probability of 5 randomly selected years will have an average precipitation greater than 18 inches for the first 7 months?
[URL='https://www.mathcelebrity.com/probnormdist.php?xone=18&mean=19.32&stdev=2.4&n=1&pl=P%28X+%3E+Z%29']For a. we set up our z-score for[/URL]:
P(X>18) = 0.7088
b. We assume the average precipitation of 5 [I]randomly[/I] selected years for the first 7 months is the population mean μ = 19.32
c. [URL='https://www.mathcelebrity.com/probnormdist.php?xone=18&mean=19.32&stdev=2.4&n=5&pl=P%28X+%3E+Z%29']P(X > 18 with n = 5)[/URL] = 0.8907

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognit

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the bran. How many adults must he survey in order to be 90% confident that his estimate is within seven percentage points of the true population percentage?
[IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] = 0.5
1 - [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] = 0.5
margin of error (E) = 0.07
At 90% confidence level the t is,
alpha = 1 - 90%
alpha = 1 - 0.90
alpha = 0.10
alpha / 2 = 0.10 / 2 = 0.05
Zalpha/2 = Z0.05 = 1.645
sample size = n = (Z[IMG]https://ci4.googleusercontent.com/proxy/mwhpkw3aM19oMNA4tbO_0OdMXEHt9juW214BnNpz4kjXubiVJgwolO7CLbmWXXoSVjDPE_T0CGeUxNungBjN=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Calpha[/IMG] / 2 / E )2 * [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] * (1 - [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] )
= (1.645 / 0.07)^2 *0.5*0.5
23.5^2 * 0.5 * 0.5
552.25 * 0.5 * 0.5
= 138.06
[B]sample size = 138[/B]
[I]He must survey 138 adults in order to be 90% confident that his estimate is within seven percentage points of the true population percentage.[/I]

The doubling time of a population of flies is 8 hours by what factor does a population increase in 2

The doubling time of a population of flies is 8 hours.
a) By what factor does a population increase in 24 hours?
b) By what factor does the population increase in 2 weeks?
a) If the population doubles every 8 hours, then it doubles 3 times in 24 hours, since 24/8 = 3.
So 2 * 3 = 6. The increase factor is [B]6[/B]
b) Since a) is one full day, we now need to know how much it doubles in 14 days, which is 2 weeks. We take our factor of 6 for each day, and multiply it by 14: 14 * 6 = [B]84[/B]

The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a) What i

The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
a) What is the probability that a randomly person has an IQ between 85 and 115?
b) Find the 90th percentile of the IQ distribution
c) If a random sample of 100 people is selected, what is the standard deviation of the sample mean?
a) [B]68%[/B] from the [URL='http://www.mathcelebrity.com/probnormdist.php?xone=50&mean=100&stdev=15&n=1&pl=Empirical+Rule']empirical rule calculator[/URL]
b) P(z) = 0.90. so z = 1.28152 using Excel NORMSINV(0.9)

(X - 100)/10 = 1.21852 X = [B]113[/B] rounded up c) Sample standard deviation is the population standard deviation divided by the square root of the sample size 15/sqrt(100) = 15/10 =[B] 1.5[/B]

(X - 100)/10 = 1.21852 X = [B]113[/B] rounded up c) Sample standard deviation is the population standard deviation divided by the square root of the sample size 15/sqrt(100) = 15/10 =[B] 1.5[/B]

The population of a town doubles every 12 years. If the population in 1945 was 11,005 people, what w

The population of a town doubles every 12 years. If the population in 1945 was 11,005 people, what was the population in 1981?
Calculate the difference in years:
Difference = 1981 - 1945
Difference = 36
Calculate doubling periods:
Doubling periods = Total years / Doubling time
Doubling periods = 36/12
Doubling periods = 3
Population = Initial Population * 2^doubling periods
Population = 11005 * 2^3
Population = 11005 * 8
Population = [B]88,040[/B]

The population of a town is currently 22,000. This represents an increase of 40% from the population

The population of a town is currently 22,000. This represents an increase of 40% from the population 5 years ago. Find the population of the town 5 years ago. Round to the nearest whole number if necessary.
To get the population 5 years ago, we'd discount the current population of 22,000 by 40%. We can write a 40% discount as 1.4.
Population 5 years ago = 22,000/1.4
Population 5 years ago = 15,714.29
Rounding to the nearest whole number, we get [B]15,714[/B]

The population of goats on a particular nature reserve t years after the initial population was sett

The population of goats on a particular nature reserve t years after the initial population was settled is modeled by p(t) = 4000 - 3000e^-0.2t. How many goats were initially present?
[U]Initially present means at time 0. Substituting t = 0, p(0), we get:[/U]
p(0) = 4000 - 3000e^-0.2(0)
p(0) = 4000 - 3000e^0
p(0) = 4000 - 3000(1)
p(0) = 4000 - 3000
[B]p(0) = 1000[/B]

The population of Kansas is two-fifths the population of California

The population of Kansas is two-fifths the population of California
Assumptions:
[LIST]
[*]Let p be the population of Kansas
[*]Let c be the population of California
[/LIST]
We have:
[B]k = 2c/5[/B]

The population of Westport was 43,000 at the beginning of 1980 and has steadily decreased by 1% per

The population of Westport was 43,000 at the beginning of 1980 and has steadily decreased by 1% per year since. Write an expression that shows the population of Westport at the beginning of 1994 and solve.
1994 - 1980 = 14 years.
Using our [URL='https://www.mathcelebrity.com/population-growth-calculator.php?num=thepopulationofwestportwas43000hassteadilydecreasedby1%for14years&pl=Calculate']population calculator[/URL], we get:
[B]37,356[/B]

There are 3,742,450 men, 3,177,805 women and 21,508 children in a village. Find the total population

There are 3,742,450 men, 3,177,805 women and 21,508 children in a village. Find the total population of the village.
Total population = Men + Women + Children
Total population = 3,742,450 + 3,177,805 + 21,508
Total population = [B]6,941,763[/B]

You are selling fertilizer to female farmers in Ghana. There are 22,600,000 people in Ghana, and 60%

You are selling fertilizer to female farmers in Ghana. There are 22,600,000 people in Ghana, and 60% are of working age. Within that working-age group, women account for 53%. Of the working-age females, 42% of them are employed in farming. What is the total number of potential customers for your fertilizer?
[U]Our sample population is found by this product:[/U]
Female farmers of working age in Ghana = Total people in Ghana *[I] Working Age[/I] * Women of working Age * Farmers
Since 60% = 0.6, 53% = 0.53, and 42% = 0.42, we have
Female farmers of working age in Ghana = 22,600,000 * 0.6 * 0.53 * 0.42
Female farmers of working age in Ghana = [B]3,018,456[/B]

Zombies are doubling every 2 days. If two people are turned into zombies today, how long will it tak

Zombies are doubling every 2 days. If two people are turned into zombies today, how long will it take for the population of about 600,000 to turn into zombies?
Let d = every 2 days. We set up the exponential equation
2 * 2^d = 600,000
Divide each side by 2:
2^d = 300000
To solve this equation for d, we [URL='https://www.mathcelebrity.com/natlog.php?num=2%5Ed%3D300000&pl=Calculate']type it in our math engine[/URL] and we get
d = 18.19 (2 day periods)
18.19 * days per period = 36.38 total days
Most problems like this ask you to round to full days, so we round up to [B]37 days[/B].