The value of the integral ∫(1+3x) dx is equal to 14.
What is integration?Integration is a process of adding up small elemental volumes to find the larger volume.
Given is to find the integral -
∫(1+3x)
We can find the equivalent values as -
∫(1+3x) dx = ∫1 dx + ∫3x dx
∫(1+3x) dx = x + 3x²/2
For the limit x = 1 to x = 3, we can write -
∫(1+3x) dx = (3 + 27/2) - (1 + 3/2)
∫(1+3x) dx = 33/2 - 5/2 = 14
Therefore, the value of the integral ∫(1+3x) dx is equal to 14.
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What is the solution to this question?
Answer:
Step-by-step explanation:
To solve the equation (-1)/(x-5) = 2/(x+4), we can start by cross-multiplying:
(-1)(x+4) = 2(x-5)
Expanding both sides and simplifying, we get:
-x - 4 = 2x - 10
Bringing all the x terms to one side and all the constant terms to the other, we get:
3x = 6
Dividing both sides by 3, we get:
x = 2
So the solution to the equation is x = 2. However, we need to check if this value of x makes the denominators of the original equation non-zero. Plugging x = 2 into the original equation, we get:
(-1)/(2-5) = 2/(2+4)
Simplifying, we get:
1/3 = 1/3
Since both sides are equal, the solution x = 2 satisfies the original equation. Therefore, the only solution to the equation is x = 2.
Answer: x = 2
Step-by-step explanation:
[tex]\boldsymbol{\sf{The\:exercise\:is \longmapsto \ \dfrac{-1}{x-5}=\dfrac{2}{x+4} }}[/tex]
We cross multiply.
-(x + 4) = 2(x - 5)
We apply the multiplicative law of distribution.
-x -4 = 2(x - 5)
-x - 4 = 2x - 10
We rearrange the unknown terms to the left side of the equation.
-x - 2x = -10 + 4 <===Combine as terms===> -3x = -10 + 4
We calculate -10 + 4 = -6.
-3x = -6
We divide both sides of the equation by the coefficient of the variable.
[tex]\boldsymbol{\sf{x=\dfrac{-6}{-3} \iff \ x=\dfrac{6}{3} }}[/tex]
x = 2
7. According to new research in 2021, Puerto Rican Reggaeton star Bad Bunny again took the title of
most-streamed artist in the world on Spotify. He received over 9.1 billion streams (9, 100, 000, 000)
without releasing a new album last year.
Use this number of streams with your equation to calculate how much money Bad Bunny may have
made via Spotify. (Worlds Most Streamed Songs (Spotify), 2021)
The requried, Bad Bunny may have made around $34.6 million from his 9.1 billion streams on Spotify in 2021.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
As of 2021, Spotify's average payout per stream is about $0.0038, which means that an artist earns approximately 0.38 cents per stream.
So, to calculate Bad Bunny's potential earnings from 9.1 billion streams on Spotify, we can use the following equation:
Earnings = Number of Streams x Payout per Stream
Earnings = 9,100,000,000 x $0.0038
Earnings = $34,580,000
Therefore, based on this rough estimate, Bad Bunny may have made around $34.6 million from his 9.1 billion streams on Spotify in 2021. It's important to note that this is just an estimate and that the actual amount he earned could be higher or lower depending on the factors mentioned earlier.
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Fill in the blanks:
1) if tan x=0, then tan(-x)= ___
2) If sin x= 0.3, then sin(-x)= ____
3) If cos x= 0.3, then cos(-x)= ____
4) If tan x= -2, the tan (pi+x)= ____
The values are :
tan(-x) = 0sin(-x) = -0.3cos(-x) =0.3tan(pie + x) = 2What is trigonometry ?
Trigonometry is a branch of mathematics that deals with the relationships and properties of angles and the trigonometric functions such as sine, cosine, and tangent. It is based on the study of the geometric properties of triangles and is used extensively in fields such as physics, engineering, architecture, and astronomy.
In trigonometry, the relationships between the sides and angles of a triangle are expressed using the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios between the sides of a right triangle, where one angle is 90 degrees. Trigonometric functions can also be defined for any angle, not just those in a right triangle, using the unit circle or other methods.
Trigonometry has many practical applications, such as in navigation, surveying, and the design of structures such as bridges and buildings. It is also used extensively in science and engineering, particularly in fields such as physics, mechanics, and electromagnetics.
If tan x = 0, then tan(-x) = 0.
The tangent function is an odd function, which means that tan(-x) = -tan(x). However, since tan x = 0, this means that -tan(x) = 0 as well. Therefore, tan(-x) = 0.
If sin x = 0.3, then sin(-x) = -0.3.
The sine function is an odd function, which means that sin(-x) = -sin(x). Since sin x = 0.3, this means that -sin(x) = -0.3. Therefore, sin(-x) = -0.3.
If cos x = 0.3, then cos(-x) = 0.3.
The cosine function is an even function, which means that cos(-x) = cos(x). Since cos x = 0.3, this means that cos(-x) = 0.3 as well.
If tan x = -2, then tan(pi+x) = tan(pi + atan(-2)) = tan(2.0344 + pi) = -2.
To find tan(pi + x), we need to use the identity tan(a + pi) = -tan(a). In this case, a = atan(-2), which is the inverse tangent of -2. Using a calculator or a table, we can find that a is approximately 2.0344 radians. Therefore, tan(pi + x) = -tan(2.0344) = -(-2) = 2.
Hence, values are
tan(-x) = 0sin(-x) = -0.3cos(-x) =0.3tan(pie + x) = 2To know more about trigonometry visit :
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Suppose that the distance a car travels varies directly with the amount of gasoline it uses. A certain car uses 12 gallons of gasoline to travel 288 miles. How
many miles can the car travel if it has 9 gallons of gasoline?
Answer:
Step-by-step explanation:
225 miles because you have to divide 100 by 4 that would give me 25 MPG and be asked, how many miles can the car travel using? Nine gallons of gasoline? So that would be right here, And that's at 225 Miles that it can travel with nine gallons of gasoline.
Write an equation for the word problem below
Sarah is renting a water filtration system from her water company. It has a startup fee of $36 plus $6 per month. If Sarah has a budget of $300, how many months can she rent the system?
Answer:
The Equation is (300-36)÷6.
Step-by-step explanation:
$300-$36=$264 (The budget after paying the set up fee)
$264/6=44 months. That's how many months she can rent.
So the equation would be (300-36)÷6.
(Sorry if this is wrong!)In a completely randomized experimental design involving six treatments, 11 observations were recorded for each of the six treatments. The following information is provided.
SSTR = 400 (Sum Square Between Treatments)
SST = 700 (Total Sum Square)
The mean square within treatments (MSE) is _____.
a. 5 b. 400 c. 80 d. 300
The mean square within treatments (MSE) is 5 when in a completely randomized experimental design involving six treatments, 11 observations were recorded for each of the six treatments.
What is mean?Mean is a measure of central tendency which represents the average value of a set of numbers. It is calculated by adding up all the values in the set and then dividing the sum by the total number of values in the set.
Here,
To find the mean square within treatments (MSE), we need to use the formula:
MSE = SSE / df
where SSE is the sum of squares within treatments and df is the degrees of freedom within treatments.
Since we are given SSTR and SST, we can find SSE using the formula:
SSE = SST - SSTR
Substituting the given values, we get:
SSE = 700 - 400 = 300
The total number of observations is:
n = 6 treatments × 11 observations/treatment = 66 observations
The degrees of freedom within treatments is:
df = n - number of treatments = 66 - 6 = 60
Therefore, the mean square within treatments is:
MSE = SSE / df
= 300 / 60
= 5
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a study was conducted that resulted in the following relative frequency histogram. determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.
If the bars of a histogram roughly follow a symmetrical bell or hill shape, then the distribution is approximately normally distributed.
What is Histogram?Histogram a diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.
Given is relative frequency histogram.
The histogram is not given, so will discussion the property that tells whether the histogram indicates a normal distribution or not.If the bars roughly follow a symmetrical bell or hill shape, then the distribution is approximately normally distributed.Therefore, if the bars of a histogram roughly follow a symmetrical bell or hill shape, then the distribution is approximately normally distributed.
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Completely factor the polynomial 2x³ + 54
Answer:
Step-by-step explanation:
2x³+54=2(x³+27)=2(x³+3³)
a³+b³=(a+b)(a²-ab+b²)
complete it
what is the solution to the equation
The requried solution of the two linear equations is given as x = (b - d)/a-c and y = a (d - c)/(a-c).
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
The question seems to be incomplete so the solution is a standard solution by assuming a standard linear equation.
The given equation,
ax + y = b - - - - - (1)
cx + y = d - - - - -(2)
Subtract equation 2 from 1
ax - cx + y - y = b - d
x(a - c) = b - d
x = b - d / a - c
Now,
Put x in equation 1
a (b - d) / (a - c) + y = b
y = b - a(b - d)/(a - c)
y = ab - ac -ab + ad/(a - c)
y = a (d - c)/(a - c)
Thus, the requried solution of the two linear equation are given as x = (b - d)/a-c and y = a (d - c)/(a - c).
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The question seems to be incomplete,
The solution given is standard solution for the simultaneous equations.
What does the index value of 99.2 in 1980 mean? Explain your reasoning.
The index value of 99.2 in 1980 mean Gas in 1980 cost 0.992 times as much as gas in 1990, because the ratio of the gas price index in 1980 to the gas price index in 1990 is 0.992, the correct option is D.
What is the ratio?
Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We are given that;
Years, prices, prices as a percentage of 1990 price, price index 1990=100
Now,
The given table shows the average gasoline prices per gallon for various years, as well as the price index for each year, with 1990 being the reference year with a price index of 100. The price index measures the change in the price of gasoline relative to the price in 1990. Therefore, the price index value of 99.2 for 1980 means that the average gasoline price in 1980 was 0.992 times the price of gasoline in 1990.
It is important to note that the gas price index does not directly measure the cost per gallon of gas. Rather, it is a measure of the change in gasoline prices over time, with a reference year (in this case, 1990) used as a baseline.
Therefore, by ratio the answer will be Gas in 1980 cost 0.992 times as much as gas in 1990, because the ratio of the gas price index in 1980 to the gas price index in 1990 is 0.992.
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The rim of the volcanic crater shown below is a circle. The diameter is 620 m. What is the circumference of the rim of the crater in kilometres (km)?
Can somebody please help me
find the value of x
If f(1)=9f and f(n)=−2f(n−1)−1 then find the value of f(4)
Answer:
f(4)= 36
f(4) = 7n-7
Step-by-step explanation:
f(4)= 9(4)
36= f(4)
f(4) = - 2(4)(n-1)-1
8(n-1) - 1
7 (n-1)
7n-7 = f(4)
if you have to go to school 3 days from tuesday what day will you go back to school
Answer:
Three days from Tuesday is Friday.
Assume that military aircraft use ejection seats designed for men weighing between 132. 4132. 4 lb and 217217 lb. If women's weights are normally distributed with a mean of 168. 7168. 7 lb and a standard deviation of 48. 848. 8 lb, what percentage of women have weights that are within those limits
The percentage of women with weights that are within the limits is:
60.93%
What percentage of women have weights that are within those limits?Can be calculated using the normal distribution formula. First, we need to find the z-scores for both the lower and upper limits:
z-score for lower limit = (132.4 - 168.7) / 48.8 = -0.74
z-score for upper limit = (217 - 168.7) / 48.8 = 0.99
Next, we can use a z-table to find the corresponding probabilities for these z-scores:
Probability for lower limit = 0.2296
Probability for upper limit = 0.8389
Finally, we can subtract the lower probability from the upper probability to find the percentage of women with weights that are within those limits:
Percentage = 0.8389 - 0.2296 = 0.6093
Therefore, approximately 60.93% of women have weights that are within the limits of 132.4 lb and 217 lb.
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Consider the parabola given by the equation:
f
(
x
)
=
4
x
2
+
8
x
−
1
Find the following for this parabola:
A) The vertex:
B) The vertical intercept is the point
C) Find the coordinates of the two
x
intercepts of the parabola and write them as a list, separated by commas:
It is OK to round your value(s) to to two decimal places.
The value following are
vertex: (6, -9)
y-intercept: (0, 27)
X = 3, 9
Finding Vertex (Part A)
Consider the formula -b/2a. This formula gives you the x-coordinate of the vertex.
[tex]y = 1x^2 - 12x + 27[/tex]
a = 1
b= -12
c =27
-b/2a = - (-12)/2(1) = 12/2 = 6 (x-coordinate of vertex)
When solving for the y-coordinate of the vertex you will need to substitute your 'x" back into the equation.
[tex]y = 1(6)^2 - 12(6) + 27[/tex]
y = 36 - 72 + 27 = -9 (y-coordinate of vertex)
--------------------------------------------------------------------------
Y- Intercept (Part B)
When looking for the y-intercept your "x" must always be 0.
Substitute 0 in every "x" in the equation.
y =[tex]1(0)^2 - 12(0) + 27[/tex]
y = 27
y-intercept: (0, 27)
-----------------------------------------------------------------------------
X- Intercepts (Part C)
To find the values of the "x" factor.
[tex]y = 1x^2[/tex] - 12x + 27
[tex]0 = 1x^2[/tex] - 12x + 27
0 = (x - 3 )(x - 9 )
(x-3) = 0 (x-9) = 0
x = 3 x = 9
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Help me with number 7 please
Answer:
Are we supposed to give the answer in fractions?
Find the number of years necessary for an investment to double at each of these rates of simple interest. Round to the nearest tenth if necessary.
Interest Rate: 11%
It would take approximately 6.5 years for an investment to double at a simple interest rate of 11%.
According to given information :To find the number of years necessary for an investment to double at a simple interest rate of 11%, we can use the following formula:
n = 72 / r
where n is the number of years required for the investment to double, and r is the interest rate.
Plugging in the values, we get:
n = 72 / 11
n ≈ 6.5 years (rounded to the nearest tenth)
Therefore, it would take approximately 6.5 years for an investment to double at a simple interest rate of 11%.
What is simple interest ?Simple interest is a type of interest that is calculated on the principal amount of a loan or investment. It is a fixed percentage of the original amount borrowed or invested, and it is not compounded over time.
The formula for calculating simple interest is:
I = P * r * t
where I is the interest, P is the principal amount, r is the interest rate, and t is the time period.
For example, if you borrow $1,000 for two years at a simple interest rate of 5%, the interest you would pay is calculated as follows:
I = 1,000 * 0.05 * 2
I = $100
So, you would have to pay back the $1,000 principal plus $100 in interest, for a total of $1,100.
Simple interest is commonly used in short-term loans or investments, and it is usually easier to calculate and understand than compound interest, which takes into account the effect of earning interest on previously earned interest.
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A circular device has a diameter of 4.5 inches. What is the radius of the device?
Answer:
Hello there! If the circular device has a diameter of 4.5 inches, the radius of the device would be 2.25 inches.
Step-by-step explanation:
The diameter of the circle is a line segment that not only passes through the center of the circle, but also has endpoints that are on the circle and opposite sides to each other. The radius, on the other hand, is half the distance of the diameter, or the distance from any point on the circle to the center of the circle. I've attached a picture below to show you what that would look like, if you're a visual learner.
Since we know the diameter of the circular device is 4.5 inches, and we know that the radius of a circle is half the length of the diameter of that same circle, that means the radius of the circular device would be [tex]\frac{4.5}{2}[/tex] or 2.25 inches long.
Have a great day! Feel free to let me know if you have any more questions :)
You accidentally dial one number on your phone's keypad. Find the probability that the number you dialed is greater than 9.
Answer:
0
Step-by-step explanation:
What is probability?Probability (also known as chance) is the number that indicates how likely an event is to occur. If something has a low probability, it is unlikely to happen. If something has a high probability, it is likely to happen.
If we look at a phone keypad, you will see the numbers 0-9, but you will never see a number greater than 9.
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the numbers, but none are greater than 9.
The stem and leaf plot shows the number of laps around a track
that several teams walked as part of a fund-raiser for the library.
The teams that walked more than 50 laps raised an extra $100 for
the library.
What fraction of the teams raised this extra money?
The fraction of the teams that raised the extra money, given the number of teams laps needed to be walked, is D. 1 / 3
How to find the fraction ?To find the fraction of teams that raised the extra money, you need to count the number of teams who were able to walk more than 50 laps. The number of teams who walked more than 50 laps walked:
53, 63, 63, and 65 miles so 4 teams did so.
The total number of teams is the number of leafs which is 12 teams.
The fraction of teams who raised the extra money is :
= 4 teams / 12 total teams
= ( 4 ÷ 4 ) / ( 12 ÷ 4 )
= 1 / 3
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g(-9)=
Evaluate the function
From the graph, the value of the function g(-9) is 1
Evaluating a function from the graphFrom the question, we are to evaluate the function using the given information from the graph.
The given function is g(-9)
To evaluate the function, g(-9), from the graph, we will locate the point where x = -9 on the cartesian plane and then we will trace the point straight to the function graph. From the point on the function graph, we will read the value on the y-coordinate of the point by tracing a straight line to the y-axis.
From the graph,
The value of g(-9) is 1
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When testing for current in a cable with 10 color-coded wires, the author used a meter to test 2 wires at a time. How many different tests are required for every possible pairing of 2 wires?
what is combination ?
In mathematics, a combination is a way of selecting items from a collection, such that the order of selection does not matter. The combination formula gives the total number of ways to choose k items from a set of n distinct items without regard to the order in which they are chosen.
The combination formula is given by:
n choose k = n! / (k! * (n-k)!)
Explanation:
If we have 10 color-coded wires, we can choose 2 wires out of them in (10 choose 2) ways.
(10 choose 2) is a combination formula given by:
(10 choose 2) = 10! / (2! * (10-2)!)
= (10 * 9) / 2
= 45
This means that we need to perform 45 tests to cover all possible pairings of 2 wires from 10 color-coded wires.
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Pippin went to a game room that charged $4 admission, plus $0. 25 per token. The equation which represents his total cost is y = 0. 25x + 4. What are the ordered pairs for the equation when you use these x-values: 5, 10, 20?.
Answer:
5 = $ 5.25. 10= $ 6.50. 20= $9.00
Step-by-step explanation:
if this is wrong you can completely write me a really rude email or message or something
A factory selling cell phones has a marginal cost function C(x)=0.01x2−3x+229, where x represents the number of cellphones, and a marginal revenue function given by R(x)=429−2x. Find the area between the graphs of these curves and x =0. What does this area represent?
The area between -
C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 is 492097.4 square
units.
What is function?A function is a relation between a dependent and a independent variable. Mathematically we can write the function as -
y = f(x)
Given is that a factory selling cell phones has a marginal cost function C(x) = 0.01x² - 3x + 229, where {x} represents the number of cellphones, and a marginal revenue function given by R(x) = 429 - 2x.
We can write the area between -
C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 as -
Area = ∫C(x) dx + ∫{C(x) - R(x)} dx
We can write the area with limits as -
Area =
∫(0.01x² - 3x + 229) dx {limits from 229 to 429}
+
∫(0.01x² - 3x + 229 - 429 + 2x) dx {limits from 429 to 629}
Area = 71548.7 + 420548.7
Area = 492097.4 square units
Therefore, the area between -
C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 is 492097.4 square
units.
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Ocupó la respuesta de la página 153 del ejercicio 4?
On dividing 153 by 4, we get the value as 38[tex]\frac{1}{4}[/tex].
What is algebraic expression?An algebraic expression is a combination of terms both constants and variables. For example -
2x + 3y + z
3x + y
Given is to find the equivalent value for the division as -
"153 ÷ 4"
On dividing 153 by 4, we can write the result as follows -
{x} = 153/4
{x} = 38.25
{x} = 38[tex]\frac{1}{4}[/tex]
Therefore, On dividing 153 by 4, we get the value as 38[tex]\frac{1}{4}[/tex].
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{Question in english -
What is the remainder when 153 is divided by 4?}
Plot the following points in the Cartesian plane.
{(3,6),(−8,2),(−9,−4),(2,−8)}
What is cartesian plane ?
A Cartesian plane (also known as a coordinate plane or rectangular coordinate system) is a two-dimensional plane formed by two perpendicular number lines, referred to as the x-axis and the y-axis, that intersect at a point called the origin. The x-axis is a horizontal line, and the y-axis is a vertical line.
Explanation:
To plot the following points in the Cartesian plane:
{(3,6),(-8,2),(-9,-4),(2,-8)}
First, we draw the x and y axes to form a Cartesian plane.
Then, for each point, we plot the x and y coordinates on the graph. The x coordinate indicates the horizontal position of the point on the x-axis, while the y coordinate indicates the vertical position of the point on the y-axis.
The point (3,6) is plotted as a dot on the Cartesian plane located 3 units to the right of the origin on the x-axis and 6 units above the origin on the y-axis.
The point (-8,2) is plotted as a dot located 8 units to the left of the origin on the x-axis and 2 units above the origin on the y-axis.
The point (-9,-4) is plotted as a dot located 9 units to the left of the origin on the x-axis and 4 units below the origin on the y-axis.
The point (2,-8) is plotted as a dot located 2 units to the right of the origin on the x-axis and 8 units below the origin on the y-axis.
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is 5 yards and 2 feet greater than 200 in
A regular pentagon has an area of 118.25 square meters, and each side of the pentagon measures 4.3 meters.
What is the length of an apothem of the pentagon?
Enter your answer in the box.
m
The length of the apothem of the pentagon is approximately 11 meters.
What is a polygon?Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,
Examples of polygons, equilateral triangles, squares, pentagons etc.
Here, we have,
To solve this problem, we can use the formula for the area of a regular pentagon:
A = (5/2) × s × a
Where A is the area of the pentagon, s is the length of one side, and a is the apothem (the distance from the center of the pentagon to the midpoint of a side).
We know that the area of the pentagon is 118.25 square meters and the length of one side is 4.3 meters. We can substitute these values into the formula and solve for the apothem:
118.25 = (5/2) × 4.3 × a
Divide both sides by (5/2) x 4.3:
a = 118.25 / ((5/2) × 4.3)
= 118.25 / 10.75 ≈ 11 meters
Therefore, the length of the apothem of the pentagon is approximately 11 meters.
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The population of a city increases by 0.5% per year. If this year's population is 201,000, what will next year's population be, to the nearest individual?
Next year's population is 202,005
How to calculate the quantity of next year's population?
The population of a city increases by 0.5% per year
This year's population is 201,000
Next year's population can be calculated as follows
201,000 × 0.5/100
= 201,000 × 0.005+1
= 201,000 × 1.005
= 202,005
Hence next year's population is 202,005
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