Suppose we express the amount of land under cultivation as the product of four factors:Land = (land/food) x (food/kcal) x (kcal/person) x (population)
The annual growth rates for each factor are:
1. the land required to grow a unit of food, -1% (due to greater productivity per unit of land)
2. the amount of food grown per calorie of food eaten by a human, +0.5%
3. per capita calorie consumption, +0.1%
4. the size of the population, +1.5%.
Required:
At these rates, how long would it take to double the amount of cultivated land needed? At that time, how much less land would be required to grow a unit of food?
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following annual growth rates:
land/food = - 1%
food/kcal = 0.5%
kcal/person = 0.1%
population = 1.5%
Σ annual growth rates = (-1 + 0.5 + 0.1 + 1.5)% = 1.1% = 0.011
Exponential growth in Land :
L = Lo * e^(rt)
Where Lo = Initial ; L = increase after t years ; r = growth rate
Time for amount of cultivated land to double
L = 2 * initial
L = 2Lo
2Lo = Lo * e^(rt)
2 = e^(0.011t)
Take the In of both sides
In(2) = 0.011t
0.6931471 = 0.011t
t = 0.6931471 / 0.011
t = 63.01 years
Land per unit of food at t = 63.01 years
L = Fo * e^(rt)
r = growth rate of land required to grow a unit of food = 1% = 0.01
L/Fo = e^(-0.01* 63.01)
L/Fo = e^(−0.6301)
= 0.5325385 = 0.53253 * 100% = 53.25%
Land per unit now takes (100% - 53.25%) = 46.75%
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The equivalent form of f(x) + g(x), if f(x) = x² + 2x + 1 and g(x) = 3(x + 1)² is
4x² + 8x + 4, so option C is correct.
What is a function?
In the case of a function from one set to the other, each element of X receives exactly one element of Y. The function's domain and co-domain are respectively referred to as the sets X and Y as a whole.
Given:
f(x) = x² + 2x + 1 and g(x) = 3(x + 1)²
Calculate the equivalent form as shown below,
f(x) + g(x) = x² + 2x + 1 + 3(x + 1)²
Simplify the above equation,
f(x) + g(x) = x² + 2x + 1 + 3(x² + 2x + 1)
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f(x) + g(x) = 4x² + 8x + 4
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Answer:
You need to sell approximately 119 paper cups to sell all of the lemonade.
Step-by-step explanation:
Answers
1 yard = 3 feet.
100 yards x 3 = 300 feet.
300 feet x 3/4 = 225 feet.
The answer is 225 feet.
Answer:
225 ft hope it helps
Answers
The peregrine falcon flies in the time it takes the eagle to fly 40 miles is 64 miles away.
What is the average speed?
The average speed is the total distance traveled by the object in a particular time interval.
The average speed is a scalar quantity.
The average speed of a golden eagle is 30 mph and the average speed of a peregrine falcon is 48 mph.
The time to fly 40 miles (that time is x):
miles hours
30 ⇒ 1
40 ⇒ x
We use the ruleof three which is to multiply the cross quantities on the table and divide by the remaining quantity:
x = 40(1)/30
x = 4/3 hour
it takes the eagle 4/3 flies to fly 40 miles.
Now we use the velocity of the falcon: 48mph, which can also be represented as:
miles hours
48 ⇒ 1
and we need the distance in miles that the falcon flies in 4/3 hours :
miles hours
48 ⇒ 1
x ⇒ 4/3
Again we use the rule of three (multiply cross quantities and divide by the remainingquantity)
x = (48)× (4/3)
x = 64 miles
Hence, the peregrine falcon flies in the time it takes the eagle to fly 40 miles is 64 miles away.
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Answer:
64
Step-by-step explanation:
64 miles
Answers
Answer:
26.11% of women in the United States will wear a size 6 or smaller
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
In the United States, a woman's shoe size of 6 fits feet that are 22.4 centimeters long. What percentage of women in the United States will wear a size 6 or smaller?
This is the pvalue of Z when X = 22.4. So
has a pvalue of 0.2611
26.11% of women in the United States will wear a size 6 or smaller
Answers
The perimeter of the given figure is 29.7 ft while the area is 63.25 ft².
What is area?
The area is the amοunt οf space within the perimeter οf a 2D shape. It is measured in squareunits, such as cm², m², etc.
Yοu can think οf area as the area inside a given shape οr space. It refers tο hοw much space is taken up. The larger the shape, the larger the area and perimeter οf the shape will be. Nοt tο be cοnfused with vοlume, area οnly refers tο space taken up by a flat οr 2Dοbject.
The perimeter is sum of all sides
Here,
sum of all sides = 1/2 × 2πr + 6 + 8
= 1/2 × (2×3.14×5) + 6 + 8
= 29.7 ft
Area = 1/2 × πr² + 1/2 × 8 × 6
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= 63.25 ft²
Thus, the perimeter of the given figure is 29.7 ft while the area is 63.25 ft².
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