(i) Relative growth rate, k = 48 million people/ year
(ii) Population in 2020 is given by 5920 million people.
Given that in 1950, the population of world was 2560 million.
In 1960, the population of world was 3040 million people.
Also it is mentioned that, world population grows in constant relative proportion.
So, the difference between time = 1960 – 1950 = 10 years
The growth in population = 3040 mil – 2560 mil = 480 million
So the relative growth rate of population is = 480/10 = 48 million/year
Now N be the new population, k be the relative population growth rate, all figures in millions. And t be the time in years passes since 1950.
Then the mathematical model is,
N = 2560 + kt
So for 2020, t = 2020-1950 = 70
k = 48
So, N = 2560+48*70 = 5920
So the population in 2020 is 5920 million people.
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A plane is 80 miles south and 95 miles east of an airport. How far is the plane from the airport? What bearing should be plane take to fly directly to the airport?
Answer:
124.2 miles
∠310.1°
Step-by-step explanation:
You want to know the bearing and distance to the airport from a plane that is 95 miles east and 80 miles south of it.
DistanceThe Pythagorean theorem or the distance formula can be used to find the distance to the airport.
d = √((x2 -x1)² +(y2 -y1)²)
d = √((95 -0)² +(-80 -0)²) = √(9025 +6400) = √15425
d ≈ 124.197 . . . . miles
The plane is about 124.2 miles from the airport.
BearingThe reference angle with respect to the +y axis can be found using the tangent relation.
Tan = Opposite/Adjacent
tan(α) = 95/80 = 19/16
α = arctan(19/16) ≈ 49.9° . . . . . . CCW from +y axis
The bearing angle is measured clockwise from the +y axis (north), so is ...
bearing = 360° -49.9° = 310.1°
The bearing to the airport is 310.1°.
__
Additional comment
Some navigators would refer to the bearing as N 49.9° W.
Less commonly, it might be referred to as W 40.1° N. Usually, N and S are the reference directions, with the modification being E or W from there. The less common usage might be chosen if an angle less than 45° is wanted.
The bearing is often reported to the nearest degree, without any degree symbol, as N50W.
. Use the distance formula to find the distance between the points (5,6) and (10,12). You
can leave the answer as a square root if it is not a perfect square.
The distance between the two points (5,6) and (10,12) is [tex]\sqrt{61}[/tex]
What is the distance between two points formula?
The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a standard formula to calculate the distance between two points. This equation can calculate the separation between any two locations on an x-y plane.
Solution explained:
First, Write the distance formula:
[tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]
Now,
Substitute (5,6) and (10,12) into [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex] :
[tex]\sqrt{(10 - 5)^{2} + (12 - 6)^{2}}[/tex] Calculate
[tex]\sqrt{(5)^{2} + (6)^{2}}[/tex] Calculate
[tex]\sqrt{25 + 36}[/tex] Calculate
Hence. the distance between points (5,6) and (10,12) is [tex]\sqrt{61}[/tex].
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Two glasses of milk and 3 snack bars have a total of 67 carbohydrates (carbs), and 4 glasses of milk and 2 snack bars have a total of 74 carbs. Determine how many carbs are in one glass of milk and in one snack bar.
5. A road has a 6% downgrade (meaning for every 100 feet you could go horizontally, you go down 6
feet). What is the angle the road makes?
The angle the road makes is 3.43°
What is an angle?
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Here, we have
A 6% downgrade means that for every 100 units of horizontal run.
The vertical height decreases by 6 units.
The grade has a downward angle of
tan⁻1(6/100) = 3.43°
Hence, the angle the road makes is 3.43°
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Huey lost 80 marbles. He was to find 45% of them. How many marbles did Huey find
Answer:
OK, so we know that 50% of the 80 marbles is 40, but we are supposed to find 45% of it, so basically it is 36 marbles he has found, I hope this is right!
Love from Ella
Extra Credit
Where does this function cross the x-axis?
y = 25x² - 49
Answer:
Step-by-step explanation:
45
1 Test (1.4, 2.1 - 2.8)
K
Solve the equation P=n+k+ m for n.
n=
(Simplify your answer.)
In the given equation, the value of n is (p - k - m).
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given an equation, p = n + k + m
Solving for n, we get
n = p - k - m
Hence, In the given equation, n = p - k - m
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A linear function f has values f(-9)=-2 and f(-3)=-6 . The y-intercept of a linear function g is six greater than the y-intercept of f , and the x-intercept of g is the same as the x- intercept of f . Write equations that represent f and g.
The equations for the functions are f(x) = (-2/3)x - 8 and g(x) = (-2/3)x - 2
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is a point on the line.
Using the two given points for f, we can find the slope:
m = (y2 - y1) / (x2 - x1)
m = (-6 - (-2)) / (-3 - (-9))
m = -4 / 6
m = -2/3
Let's use the point (-9, -2):
y - (-2) = (-2/3)(x - (-9))
y + 2 = (-2/3)(x + 9)
Multiplying both sides by 3 to get rid of the fraction:
3y + 6 = -2x - 18
3y = -2x - 24
y = (-2/3)x - 8
So the equation for f is:
f(x) = (-2/3)x - 8
To find the equation for g, we can use the fact that the y-intercept is 6 greater than the y-intercept of f. So if the y-intercept of f is b, then the y-intercept of g is b + 6.
f(x) = (-2/3)x - 8
0 = (-2/3)x - 8
2/3 x = -8
x = -12
The x-intercept of both f and g is -12.
Now we can use the y-intercept and x-intercept to write the equation for g. The slope of g is the same as the slope of f, which is -2/3.
y - (b + 6) = (-2/3)(x - (-12))
y - b - 6 = (-2/3)(x + 12)
Multiplying both sides by 3 to get rid of the fraction:
3y - 3b - 18 = -2x - 24
3y = -2x + 3b - 6
y = (-2/3)x + (3/3)b - 2
y = (-2/3)x + b - 2
So the equation for g is:
g(x) = (-2/3)x + b - 2
We know that the x-intercept of g is -12, so we can plug that in and solve for b:
0 = (-2/3)(-12) + b - 2
0 = 8 + b - 2
b = -6
So the y-intercept of g is -6 + 6 = 0.
Therefore, the equation for g is:
g(x) = (-2/3)x - 2
Hence , the equations for f and g are: f(x) = (-2/3)x - 8 and g(x) = (-2/3)x - 2
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Select the correct answer. Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18, which equation represents this situation, and how old is Tina? A. The equation that represents this situation is t − 3 = 18. Tina is 21. B. The equation that represents this situation is t + 3 = 18. Tina is 15. C. The equation that represents this situation is 3 − t = 18. Tina is 21. D. The equation that represents this situation is -3 − t = 18. Tina is 15.
The equation that represents this situation is t − 3 = 18. Tina is 21. The correct option is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18.
The equation will be written as,
C = T - 3
18 = T-3
T = 18 + 3
T = 21 years
Therefore, the equation that represents this situation is t − 3 = 18. Tina is 21. The correct option is A.
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every week roger pays for a movie ticket and a soda out of his allowance. last week, roger's allowance was aa dollars. the cost of his movie ticket was 20\ % of the difference between aa and the cost of his soda, while the cost of his soda was 5\%5% of the difference between aa and the cost of his movie ticket. to the nearest whole percent, what fraction of aa did roger pay for his movie ticket and soda?
Answer:
23%
Step-by-step explanation:
We can create two equations:
\[m = \frac{1}{5}(A - s)\]\[s = \frac{1}{20}(A - m)\]
Substituting we get:
\[m = \frac{1}{5}(A - \frac{1}{20}(A - m))\]which yields:
\[m = \frac{19}{99}A\]
Now we can find s and we get:
\[s = \frac{4}{99}A\]
Since we want to find what fraction of $A$ did Roger pay for his movie ticket and soda, we add $m$ and $s$ to get:
\[\frac{19}{99}A + \frac{4}{99}A \implies \boxed{\text{(D)}\ 23\%}\]
Shelley is searching online for airline tickets. Two weeks ago, the cost to fly from Boston to Hartford was $220. Now the cost is $355. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
The percentage increase is 61.36%. If the airline charges an additional $50 baggage fee, the new percentage increase will be 45.68%.
What is the percent increase?A percentage increase denotes how much a percentage has risen over time. To get at this figure, discover the difference between the original and final values, then deduct it to get the actual sum of the decrease.
The idea of Percentage increase is simply the amount of increase from the original(initial) to the final figure expressed in terms of 100 parts of the original. E.g. A 10% increase implies that if the original value is divided into 100 parts, the value has increased by an extra 10 parts. So, if the initial value rose by 16%, the value would rise by 16 for every 100 units, and so on.
The formula for calculating the percentage increase can be expressed as:
[tex]\%\ increase= \frac{new \ value - original \ value}{original \ value}\times 100[/tex]
[tex]\%\ increase= \frac{355- 220}{220}\times 100[/tex]
[tex]\%\ increase= \frac{135}{220}\times 100[/tex]
[tex]\mathbf{=61.36\%}[/tex]
[tex]New \ \%\ increase= \frac{new \ value - original \ value}{original \ value}\times 100[/tex]
[tex]New \ \%\ increase= \frac{405- 220}{405}\times 100[/tex]
[tex]New \ \%\ increase= \frac{185}{405}\times 100[/tex]
[tex]New \ \%\ increase=\mathbf{45.68\%}[/tex]
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a sample of student opinion at a big ten university selects an srs of 200 of the 30,000 undergraduate students and a separate srs of 100 of the 5,000 graduate students. what is the term for this kind of sample?
The term for this kind of sample is cluster sampling
Given
that, At a major ten university, 200 of the 30,000 undergraduate students and 100 of the 5,000 graduate students are chosen to represent a sample of student opinion.
What is cluster sampling ?
Cluster sampling involves breaking up a population into smaller units called clusters. Then, they randomly select a sample from each of these clusters. Cluster sampling is a probability sampling technique that is frequently used to examine large populations, especially those that are widely geographically dispersed.
Researchers frequently refer to pre-existing groups like cities or schools when referring to clusters. With an SRS of 200 students and an SRS score of 100, clusters have been utilized in this instance. Cluster sampling is the name given to this type of sample as a result.
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A helicopter leaves A and flies 40 miles due east. Then the helicopter flies
10 miles due south and arrives at B. Work out the bearing of B from A.
The bearing of the helicopter from B to A is 75.96 degrees
How to determine the bearing of the helicopter from B to AInformation from the question
A helicopter leaves A and flies 40 miles due east
the helicopter flies
10 miles due south
Work out the bearing of B from A = ?
The bearing from B to A is worked using SOH CAH TOA
The direction of movements describes a right angle triangle of
opposite = 40 miles
adjacent = 10 miles
The bearing is calculated using tan, TOA let the angle be x
tan x = Opposite / Adjacent
tan x = 40 / 10
tan x = 4
x = arc tan 4
x = 75.96 degrees
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along a river is to be fenced. suppose that no fence is needed along the river, the fence on the side opposite the river costs $40 per foot, and the fence on the other sides costs $10 per foot. if the field must contain 64,800 square feet, what dimensions will minimize costs?
The dimensions required to minimize the cost of fencing is 180ft and 360 ft.
According to question
The cost of fence on opposite side of river is $40.
The cost of fence on other sides of river is $10.
Total yield = 64800 sq. feet
Let the length of fence on the opposite side of fence be x and width of fence on the other side be y.
Area of fence = xy = 64800 sq feet
⇒ [tex]y = \frac{64800}{x}[/tex]
Let C be the cost of making fence.
For cost to be minimum, dC/dx should be equal to zero.
C = 40x + 10y * 2
⇒ C = [tex]40x + 10(\frac{64800}{x})*2[/tex]
⇒ [tex]\frac{dC}{dx} = 40 + 20 * 64800 * \frac{-1}{x^{2} } = 0[/tex]
⇒ [tex]40x^{2} = 20 * 64800[/tex]
⇒ [tex]x^{2} = 32400[/tex]
⇒ [tex]x = 180[/tex]
⇒ [tex]y = \frac{64800}{180} = 360[/tex]
So, the dimensions needed will be 180 ft and 360 ft.
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given the equation y(t)= -14t + 500, what is y (25)
The value of the equation y(t) at y(25) is 150
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Equations can be linear, quadratic or polynomials.
if y(t) = -14t + 500
The y(25) means substitute t = 25 into the equation
y(25) = -14(25) + 500
y(25) = -350 + 500
y(25) = 150
In conclusion, the value of y(25) is 150
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Theo mows a lawn. After working for 1 3/5 hours, he has mowed 7/9 of the lawn. Can Theo mow the lawn in 2 hours if he continue to mow at the same rate?
Yes, he can mow the lawn in 2 hours.
What is work done?We can define the work done as, a work done in a given period of time.
Given that, Theo mows a lawn. After working for 1 3/5 hours, he has mowed 7/9 of the lawn
In [tex]1\frac{3}{5}[/tex] hours he mows 7/9 part of lawn
Therefore, in 8/5 hours he is mowing 7/9 part of lawn
In 1 hour = 7/9*5/8 = 35/72
In 2 hours = 35/72*2 = 35/36 ≈ 1
Hence, Yes, he can mow the lawn in 2 hours.
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Multiply.
4 1/3 x 2 3/4
7 1/12
8 1/4
11 11/12
i dont know
Serena just started working at the local salon. She is paid $9.85 per hour and earns, on
average, $58.50 in tips each day. Roseline just started working at a bank. Since she
does not receive tips, she earns $16.35 an hour. The system of equations
{y=9.85x+58.50 y=16.35x can be used to represent the amount of money earned, y,
each day for working x hours.
Determine the number of hours Serena and Roseline have to work to earn the same
amount of money.
The number of hours Serena and Roseline have to work to earn the same amount of money will be 9 hours.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Serena recently began working at the nearby salon. By and large, $58.50 in tips every day. Roseline recently began working at a bank. Since she doesn't get tips, she procures $16.35 60 minutes. The arrangement of conditions {y = 9.85x + 58.50 and y = 16.35x} can be utilized to address how much cash is procured, y, every day for working x hours.
The number of hours Serena and Roseline have to work to earn the same amount of money will be given as,
16.35x = 9.85x + 58.5
6.5x = 58.5
x = 9 hours
The number of hours Serena and Roseline have to work to earn the same amount of money will be 9 hours.
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Which of the following graphs represents the equation y−4.5=2.5(x−5)?
The graph that represents the equation y - 4.5 = 2.5(x - 5) is the third graph
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, y - 4.5 = 2.5(x - 5).
y - 4.5 = 2.5x - 12.5.
y = 2.5x - 8.
Now, to determine the graph we'll choose some random values of x for which we'll have different values of y.
When x = - 1 , y = - 10.5 ⇒ (-1, -10.5 ).
When x = 0 , y = - 8 ⇒ (0, - 8).
When x = 1 , y = -5.5 ⇒ (1, -5.5).
When x = 2 , y = -3 ⇒ (2, -3).
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Kendrick needed 10 gallons of gas last week. This week, Kendrick ended up needing 40%
less. How much gas is that?
Answer:
6 gallons
Step-by-step explanation:
40% of 10 is 4 gallons less
10 - 4 = 6 gallons
based on the graph what is the rate of the change for an airplane approaching an airport for landing
Answer:
(8, 9 000)
Step-by-step explanation:
6. The equation S = 50+45w represents the savings, S, after w weeks working and
depositing money into a savings account at the bank.
Determine whether there is a proportional relationship between S and w. Explain or
show your reasoning.
The relationship is not a proportional relationship between S and w.
Saving, S, after w weeks, is represented by the equation
S = 50+45w
If y is proportional to x, then
y ∝ x
y =kx
where k is the constant of proportionality.
Here, no constant term and (0,0) satisfies this equation.
The given equation is
S = 50+45w
Here, we have a constant term.
For S=0 and w=0,
0=50+45×0
0=50
Which is not true as 0 ≠ 50.
Since there is a constant term 50 and the equation is not valid for (0,0), therefore, the given relationship is not a proportional relationship.
I hope this answer helps.
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1. The slope of the line
y = x + 17 is ___.
2. The slope of the line
y = x - 7/9 is ___.
Answer:
1. 1
2. 1
Step-by-step explanation:
Step 1
recall the eqn of a line y = mx + c
where m is the slope
step 2
compare you eqn given with the eqn y = mx + c
y = mx + c
y = 1 x + 17
then m = 1 which is slope.
both qns follows the same procedure
ana and bonita are born on the same date in different years, nn years apart. last year ana was 55 times as old as bonita. this year ana's age is the square of bonita's age. what is nn?
Ana and Bonita were born nn year apart and its value of nn is 12.
Here we have to find nn which difference in the year in which Ana and Bonita were born.
Let x be the age of Ana and y be the age of Bonita.
It is given that last year Ana was 5 times as old as Bonita so from this statement we get the first equation:
x - 1 = 5(y -1)
x -1 = 5y - 5
5y -x = 4--------(1)
The second statement is Ana is square of Bonita's age. From this we get another equation:
x = y²-----------(2)
Putting equation 2 in equation 1 we get:
5y - y² = 4
y² - 5y +4 = 0
y² - 4y - y + 4 = 0
y(y-4) -1(y -4) = 0
(y - 4)(y -1) = 0
y = 4,1
As x = y²
x = 4² = 16 or x = 1² =1
We cannot take 1 as there is a difference in their age
So we get x = 16 and y =4
So the difference in their age = 16-4= 12
Therefore we get the value of nn as 12.
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Solve these using the balance method show steps of working out pls I’ll brainlist/5star it’s urgent!!!!!!
1) 5x - 4 = 31
2) 7(x+5) = 49
3) 3x + 7 = -2x + 22
4) x+8 = 6
3
y=5/x. Make x the subject of the formula
Solve in terms of x.
[tex]y=\frac{5}{x}[/tex]
Multiply by x on both sides to remove it from the denominator.
xy =5
Divide by y to get x by itself
[tex]x=\frac{5}{y}[/tex]
Answer:
x=5/y
Step-by-step explanation:
y=5/x
cross multiplying
yx=5
x=5/y
how would you change the exponential growth model if the per capita death rate increased?group of answer choicesi would not change anything about the exponential growth model.i would decrease the initial population size.i would increase r.i would decrease r.
Using the concepts of statistics, we got that if the per capita death rate increased, then the exponential growth model would decrease the initial population size.
We know very well, the set up of a differential equation relating instantaneous population growth with respect to the time to the per capita population growth rate and the current population size at an arbitrary time is as follows:
dN / dt = rN
Now, we are told that the constant, r, is per capita population growth rate. N is current size of the population at some time. "r" is the "organisms added per reproductive period" divided by total population at that time. For instance, if the 10 rabbits are born per month and the current population is 100 rabbits, then r value = 0.1.
Hence, the exponential growth model would decrease the initial population size if the per capita death rate increased.
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help meeeeeeeeeeeeeeeeee please
Answer:
x= 3.4
x+2= 5.4
x+3= 6.4
Step-by-step explanation:
Just figured it out :)
If the public debt of a country in 2009 was $11,982,000,000,000and the
budget for 2010 was in deficit by $101,347,000,000 , what was the public debt
in 2010? Do not include commas in your answer.
If a country's public debt in 2009 was $11,982,000,000,000 and its budget for 2010 was $101,347,000,000 in deficit, the public debt in 2010 is $12083347000000.
What is public debt?Government obligations, particularly those evidenced by securities, to pay certain sums to holders at some future time. Private debt, which includes the obligations of individuals, businesses, and nongovernmental organizations, is distinct from public debt. A debt-to-GDP ratio compares a country's total debt to its economic productivity. Divide a country's debt by its GDP to calculate the debt-to-GDP ratio. Governments can use public debt to raise funds to expand their economies or pay for services. Politicians would rather increase the national debt than raise taxes. The national debt includes public debt, and when the national debt reaches 77% or more of GDP, the debt begins to slow growth.As given
if the public debt of a country in 2009 was $11,982,000,000,000 and the budget for 2010 was in deficit by $101,347,000,000 .
Total public debt in 2010 = Public debt in 2009 + Amount by which 2010 budget deficit .
= $ 11982000000000 + 101347000000
= $ 12083347000000
Therefore the public debt in 2010 is $12083347000000.
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rewrite 16r^2s^2 as a power of a product
Answer: 16r²s²=(4rs)²
Step-by-step explanation:
[tex]16r^2s^2=\\\\4^2r^2s^2=\\\\(4rs)^2[/tex]