Answer:
The year in which there are 30 m² of agricultural land available for each inhabitant is approximately 438.286 years
Step-by-step explanation:
The growth rate of the planet Magrathea = Double every 40 years
The start population of Magrathea = 20 million
The area of the Magrathea = 200 million km²
The area that can hose 200 Magratheans = 1 km²
The land used for agriculture = The land not used for housing
The equation for a population that doubles every 20 years is given as follows;
We have;
㏑2 = 40·㏑(1 + r)
㏑(1 + r) = ㏑(2)/40
1 + r = ㏑(2)/40
1 + r = e^(㏑(2)/40)
r = 1 - e^(㏑(2)/40) = 0.0174796921
30 m²
200·x
The area per individual = (1/200) km²
The total number
We have;
(x/200) km²) + (x × 0.00003 km²) = 200,000,000 km²
x × ((1/200) km² + 0.00003 km²) = 200,000,000 km²
x = 200,000,000 km²/(((1/200) km² + 0.00003 km²)) = 3.97614314 × 10¹⁰
The population at the time = 3.97614314 × 10¹⁰
We have;
3.97614314 × 10¹⁰/(2×10⁷) =
t = ㏑((3.97614314 × 10¹⁰/(2×10⁷)))/(㏑)) ≈ 438.286 years
The year in which there are 30 m² of agricultural land available for each inhabitant ≈ 438.286 years
For this problem, we are going to use the Remainder Theorem. This says that for to be a factor of a polynomial
, then
. Essentially, it says that
is a factor if when you substitute
into the polynomial you get a result of 0.
Thus, in our case, when we substitute into the polynomial, we should get an answer of 0 if
is a factor of the polynomial. Given this information, we can solve for
:
The solution is c = 3.
Answer:
Step-by-step explanation:
Hello!
The variable of interest is
X: volume of root beer in a Windsor Bottling Company can.
A sample of n=24 cans was taken and their contents measured, resulting:
X[bar]= 11.4 oz
S= 0.62 oz
Assuming that the variable has a normal distribution X~N(μ;σ²), the parameter of interest is the average contents of the root beer cans of the Windsor Bottling Company (μ)
The claim is that the population mean content of the cans is different from 12 oz, symbolically: μ ≠ 12
The statistical hypothesis (Null and alternative) have to be complementary, exhaustive and mutually exclusive. The null hypothesis is the "no change" hypothesis and always carries the "=" sign.
If the claim is μ ≠ 12, its complement is μ = 12, the expression carrying the "=" sign will be the null hypothesis and its complement will be the alternative hypothesis:
H₀: μ = 12
H₁: μ ≠ 12
α: 0.05
To test the population mean of this normal population, you have to apply a one sample t-test, with statistic:
This test is two-tailed, using the critical value approach, you have to determine two rejection regions. Meaning, you'll reject the null hypothesis to small values of the statistic or to high values of the statistic.
The decision rule is:
If ≤ -2.069 or if
≥ 2.069, then you reject the null hypothesis.
If -2.069 < < 2.069, then you do not reject the null hypothesis.
The value is less than the left critical value, the decision is to reject the null hypothesis.
Then you can say that with a 5% significance level, there is significant evidence to reject the null hypothesis, then the average amount of root beer of the Windsor Bottling Company is different from 12 oz, this means that the claim about the amount of root beer in the cans is correct.
I hope it helps!