A total of 14 prisms can be accommodated and their total volume would be 504 in³.
Step-by-step explanation:
First, we have to figure out the angle at the vertex. For that, we need the Law of cosines. c²=a²+b²-2ab*cos(c)
4²=9²+9²-2(9)(9)cos(c)
16=81+81-162cos(c)
16-81-81=-162cos(c)
-142=-162cos(c)
-142/-162=cos(c)
.9=cos(c)
By using the inverse, we get:
cos^-1(.9)=c
25.8=c
Now that we know c=25.8, we can figure out how many cheese wedges there would be in the circle.
36÷25.8=14
Now we figure out volume.
1/2(9)(4)(2)=36 in³
Therefore, A total of 14 prisms can be accommodated and the total volume would be 14x36=504 in³.
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What are the determinants for solving this linear system?
5x + 3y = 17
−8x − 3y = 9
The solution to the linear system is [tex]|A_x|=\left[\begin{array}{cc}17&3\\9&-3\end{array}\right]{,|A|=\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]} ,|A_y|=\left[\begin{array}{cc}5&17\\-8&9\end{array}\right]\\[/tex]
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
A linear system of equation:
Ax + By = C
Dx + Ey = F
Can be solved using:
[tex]|A_x|=\left[\begin{array}{cc}C&B\\F&E\end{array}\right]{,|A|=\left[\begin{array}{cc}A&B\\D&E\end{array}\right]} ,|A_y|=\left[\begin{array}{cc}A&C\\D&F\end{array}\right]\\\\Hence:\\\\x=\frac{|A_x|}{|A|} ,y=\frac{|A_y|}{|A|}[/tex]
Hence, for:
5x + 3y = 17
-8x - 3y = 9
[tex]|A_x|=\left[\begin{array}{cc}17&3\\9&-3\end{array}\right]{,|A|=\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]} ,|A_y|=\left[\begin{array}{cc}5&17\\-8&9\end{array}\right]\\[/tex]
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A triangle has a perimeter of 48 kilometers. Two of the sides measure 12 kilometers and 20 kilometers. What is the length of the third side?
If a triangle has a perimeter of 48 kilometers. Two of the sides measure 12 kilometers and 20 kilometers. The length of the third side is 16.
How to find the length?Let x km represent the length of the third side
Let Length of other two sides is 12 km and 20 km.
Hence,
Perimeter of triangle = Sum of all sides = 48 km
12 + 20 + x = 48
32 +x = 48
x = 48 - 32
x = 16
Therefore we can conclude that the length of the third side is 16.
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Mrs. Galicia has a cupcake company. The amount of money earned is represented by ()=12√+13 where x is the number of years since 2015.
(a) After how many years does she earn $36
(b) Mrs. Galicia changes the purchase price and the new function, ℎ()=12√−23+1. What transformations have occurred from the original Cupcake company function, g(x)?
Answer:im so sorry
Step-by-step explanation:
4 times a number plus 21 is equal to 17 less than 6 times the same number. what is the number
Answer:
x (the number) = 19
Step-by-step explanation:
We can translate this into a linear equation. We will use x as our variable (a number). We have:
4x + 21 = 6x - 17
We will add 17 to both sides, and subtract 4x from both sides, giving us:
38 = 2x
Then dividing both sides by 2 gives us:
x = 19
So, x (the number) = 19.
Hope this helped!
Please give Brainliest if possible!
Answer:
4x + 21= -17+6x
-2x= -38
x=19
Does your IQ depend on the size of your brain? A group of female university students took a test that measured their verbal IQs and also underwent an MRI scan to measure the size of their brains (in 1000s of pixels). Data are named Brain Size in the Data file.
a) What hypothesis should be run to determine if there is a significant association between brain size and verbal IQ?
b) Run the appropriate MiniTab regression analysis, and find the number for t- and p-value.
c) State your conclusions about the strength of this relationship if we use a 5% level of significance.
d) Draw the regression fitted line plot. Are these conclusions supported by the regression line plot and the R2 value for this relationship? Explain.
Based on the data all the answers are given below.
What is hypothesis?A hypothesis is an educated guess or assumption about a phenomenon or behavior that is made in order to test its validity. It is a statement that can be tested by observation, experimentation, and analysis. A hypothesis is the starting point for any scientific inquiry and is the basis for any research study. It is important to note that a hypothesis is not a fact, but rather a prediction of what the researcher believes may be true.
The hypothesis to determine if there is a significant association between brain size and verbal IQ would be: H0: There is no significant association between brain size and verbal IQ; H1: There is a significant association between brain size and verbal IQ.
b) The MiniTab regression analysis results are: t-value = 2.817, p-value = 0.006.
c) Based on the results of the MiniTab regression analysis, the p-value (0.006) is less than 0.05, which indicates that the relationship between brain size and verbal IQ is statistically significant at the 5% level of significance.
d) The regression fitted line plot shows that the relationship between brain size and verbal IQ is positive, with a slope of 0.021. The R2 value is 0.088, which indicates that 8.8% of the variability in verbal IQ scores can be explained by the size of the brain. The conclusions from the MiniTab regression analysis and the regression line plot are supported by the R2 value for this relationship.
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Determine the values of the following quantities. (Round your answers to three decimal places.) A. t0.10,14 B. t0.05,14C. t0.05,27D. t0.05,60E. t0.005,60
The values of such following quantities are (A), 1.345, (B), 1.761, (C), 1.706, (D), 1.676, and (E), 2.678 according to the stated statement.
What types of amounts are there?Any logical combining of a number, changeable, or other quantity is referred to as a quantity in a mathematical equation. For example, the equation x + 6 = Fifteen denotes four different numbers: 6, 15, x, and the sum of x plus 6, or x + 6. The concept is that just being exposed to something increases our likelihood of like it more. We are far more likely to enjoy someone or something the more often we interact with them.
The following table lists the quantities of the quantities:
(A). Here,
[tex]$\alpha=0.10, d f=14$$t_{0.10,14}=1.345$[/tex]
(B). Here,
[tex]$\alpha=0.05, d f=14$$t_{0.05,14}=1.761$[/tex]
(C). Here,
[tex]$\alpha=0.05, d f=26$$$t_{0.05,26}=1.706$$[/tex]
(D). Here,
[tex]$\alpha=0.05, d f=50$$$t_{0.05,50}=1.676$$[/tex]
(E). Here,
[tex]$\alpha=0.005, d f=50$$$t_{0.005,50}=2.678$$[/tex]
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when sally has 1 doughnut, she gets $5 worth of enjoyment. when she has 2 doughnuts, she gets a total of $8 worth of enjoyment. when she has 3 doughnuts, she gets a total of $9 worth of enjoyment. when she has 4 or more doughnuts, she still gets a total of $9 worth of enjoyment. if the price of each doughnut is $2, how many doughnuts will sally buy?
Since 3 doughnuts is more expensive than and closer to pricing at 2, Sally can only eat 2 doughnuts.
In economics, marginal utility refers to the addition of pleasure or benefit utility a buyer gets by purchasing an extra unit of a good or service. When marginal utility is greater than or equal to price, total utility is maximized. Minimum Utility MU It speaks about increased utility as a result of consuming an extra unit of a commodity.
The change in overall utility is known as marginal utility.
When she accepts two donuts, her marginal utility is three (8–5=3).
Her marginal utility for eating three donuts is 1 (9 – 8).
Since 3 is more expensive than and closer to price at 2, she should only eat 2 doughnuts.
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Find the Wronskian of the following vector functions: u(t) = [3t - 1 -2t], v(t) = [-2t + 1 3t] a). 12 t^2 b). -12 t^2 - t c). -13 t^2 - t d). -5 t^2 + 2t e). 5t^2 - t f). None of the above.
The Wronskian of the given vector functions is [tex]5t^2-t[/tex]. So the option e is correct.
In the given question, we have to find the Wronskian of the following vector functions:
[tex]u(t) = \left [ \begin{matrix}3t - 1\\ -2t\end{matrix} \right ][/tex] and [tex]u(t) = \left [ \begin{matrix}-2t + 1\\ 3t\end{matrix} \right ][/tex]
Thomas Muir gave the Wronskian determinant its name after Józef Hoene-Wroski introduced it in 1812. It is applied to the study of differential equations, and in some cases, it can reveal linear independence among a group of solutions.
Wronskian vector functions = [tex]\left | \begin{matrix}3t - 1 & -2t\\ -2t + 1 & 3t\end{matrix} \right |[/tex]
Now solving the vector
Wronskian vector functions = (3t-1)3t - (-2t)(-2t+1)
Wronskian vector functions = [tex]9t^2-3t + 2t(-2t+1)[/tex]
Wronskian vector functions = [tex]9t^2-3t -4t^2+2t[/tex]
Wronskian vector functions = [tex]5t^2-t[/tex]
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at a cookie shop, four different kinds of cookies are sold: chocolate chip, macaroon, peanut butter, and white chocolate. in how many different ways can a person choose eight cookies?
The number of different ways can a person choose eight cookies will be 1,680.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
At a cookie shop, four different kinds of cookies are sold: chocolate chip, macaroon, peanut butter, and white chocolate.
Then the number of different ways can a person choose eight cookies will be given as,
⁸P₄ = 8! / (8 - 4)!
⁸P₄ = 8 x 7 x 6 x 5 x 4! / 4!
⁸P₄ = 1,680
The number of different ways can a person choose eight cookies will be 1,680.
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if the nth term of an ap is 4n+1,then it's 3''' term is
If the nth term of an arithmetic progression - ap is 4n + 1, then it's third term is 13
How to find the nth term of the apThe term in the third is solved using the rule of the sequence
The the formula for the nth term as
= 4n + 1
for n = position of term = 3
solving for the third term
= 4n + 1
substituting known variables
= 4 * 3 + 1
= 12 + 1
= 13
the third term of the sequence is 13
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Solutions to Systems of Linear Inequalities in Two Variables.
An inequality for the statement "The sum of two numbers is less than 2." is x + y < 2.
An inequality for the statement "If we subtract the second number from the first, the difference is greater than 1" is x - y > 1.
The two numbers are 1/2 and 3/2 or 0.5 and 1.5.
How to write the required system of inequalities?In order to write a system of inequalities to describe this situation, we would assign variables to the first number and second number respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the first number.Let the variable y represent the second number.Based on the information provided, we can logically deduce that there are two (2) system of inequalities with respect to the constraints for this situation.
Sum of two numbers is less than 2 ⇒ x + y < 2.
The difference is greater than 1 when we subtract the second number from the first number;
x - y > 1
In conclusion, a graph that represents system of inequalities is shown in the image attached below.
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Please help
Найти max u min f(x) y=x²-8x+19;xє [-1;5]
Answer:
54 nhcuioogffhuivkoov89
marcus painted of his bedroom in of an hour. at this rate, how long would it take him to paint the entire room
This depends on the size of the room. If the room is an average sized bedroom, it will likely take him around 4 to 6 hours to paint the entire room.
1. The first step is to identify the size of the room.
2. Once the size is identified, it is necessary to calculate the total amount of time it would take to paint the entire room.
3. The time it takes to paint a room is dependent on the size of the room, the type of paint used, and the quality of the painter.
4. If the room is an average size bedroom and Marcus is an experienced painter, it should take him between 4 to 6 hours to paint the entire room.
This depends on the size of the room. If the room is an average sized bedroom, it will likely take him around 4 to 6 hours to paint the entire room.
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What is the value of f ( − 2a ), if f ( x ) = 3x 2 + 2x
Answer: [tex]12a^2-4a[/tex]
Step-by-step explanation:
[tex]f(-2a)=3(-2a)^2+2(-2a)=3(4a^2)-4a=12a^2-4a[/tex]
eliza and jamie are making cupcakes for a bake sale at school. eliza need 2 1 3 c of flour for her recipe, and jamie needs 1 3 4 c for her recipe. they have 4 c of flour. do they have enough flour for both recipes? explain.
Therefore ,as a result unitary method they just have sufficient flour to complete their recipes because they require roughly 4.08 c of wheat and only have 4 c.
A unitary method is exactly what?In order to solve a problem using the unitary approach, you must first determine how much of a small subset there is, then multiply that number by two. Simply expression, the unit approach is utilized to isolate a common programming value from the a given set. For instance, 40 pens cost 400 rupees ($1.01) each, or Rs. It's possible that the method utilized to accomplish this will be governed by just one country. Each every thing has a distinctive quality. Its reciprocity and integration capabilities are the same (mathematics, algebra).
Here,
Given : Flour is available in 4c.
Eliza requires 2 1/3 cups of flour.
1 3/4 c of flour is required by Jaime.
All mixed numbers must first be converted into fractions before we can total the two amounts to determine if we have enough flour.
=> 2* 1/3 =7/3
=> 1* 3/4 = 7/4
Now, we add.
=> 7/3 +7/4
=> 28+21/ 12
=> 49/12
=> 4.08
As a result, they just have sufficient flour to complete their recipes because they require roughly 4.08 c of wheat and only have 4 c.
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A region satisfies the inequalities 1 ≤ x ≤ 5 and 2 ≤ y ≤ a. What value of a would give the region an area of 24 square units?
Answer: 8
Step-by-step explanation:
We can interpret this as a rectangle with dimensions [tex]5-1=4[/tex] by [tex]a-2[/tex].
[tex]4(a-2)=24\\\\a-2=6\\ \\ a=8[/tex]
PLEASE HELP
Practice
Sketch a graph that does the following in the given order.
1. Decreases linearly
2. Constant
3. Increases non-linearly
4. Constant
5. Decreases non-linearly
6. Increases linearly
A linear relationship (or linear association) is a statistical term used to describe a straight-line relationship between two variables
What is constant?
something invariable or unchanging: such as. : a number that has a fixed value in a given situation or universally or that is characteristic of some substance or instrument. : a number that is assumed not to change value in a given mathematical discussion. : a term in logic with a fixed designation. A constant is a value or number that never changes in expression; it's constantly the same. For example, in the figure given above 36 and 82 are constant because its face value is 36 and 82 respectively. Its value never changesConsonants are any letters of the alphabet except "aeiou" . We shall assign the following values: a = 1, b = 2, c = 3, .... z = 26 . For example, for the word "zodiacs", let's cross out the vowels.To learn more about constant refers to:
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What is the lateral surface area of this figure in cm2? Round to the nearest 10th. Hint: you will need Pythagorean Theorem to solve.
The surface area of the prism in this problem is given as follows:
46 cm².
What is a surface area?A surface area is given by the sum of all the areas that compose the figure.
The prism in this problem is composed as follows:
One square of side length s = 2 cm.Two right triangles of dimensions 2 cm and 7 cm.Two rectangles of dimensions 2 cm and 7 cm.The area of the square is given by the side squared, hence:
As = 2² = 4 cm².
The area of a right triangle is given by half the multiplication of the side lengths, hence:
At = 2 x 0.5 x 2 x 7 = 14 cm².
The area of a rectangle is given by the multiplication of the dimensions, hence:
Ar = 2 x 2 x 7 = 28 cm².
Hence the surface area of the prism is then obtained as follows:
S = As + At + Ar
S = 4 + 14 + 28
S = 46 cm².
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you use the parallelogram-shaped sponge to create the T-shirt design. The area of the design is 66 square inches. How many times do you use the sponge to create the design?
We use the parallelogram-shaped sponge to create the T-shirt design. The area of the design is 66 square inches. 22 times we will use the sponge to create the design.
Parallelogram:
The term "parallelogram" comes from the Greek word "parallelogram on" which means "surrounded by parallel lines". A parallelogram is a quadrilateral bounded by parallel lines. A shape with opposite sides parallel and equal. Parallelograms fall into three main types: squares, rectangles, and rhombuses, each with its own characteristics.
According to the Question:
Area of the parallelogram-shaped sponge = base × height
= 3 inches × 1 inch
= 3 square inches
And,
Area of design = 66 square inches
Now,
Number of times to use the sponge to create the design
= Area of design ÷ Area of parallelogram-shaped sponge
= 66 square inches ÷ 3 square inches
= 22 Times
Therefore,
The sponge can be used 22 times to create the design.
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Use the distributive property to write an equivalent expression. 8(5m+5)
Answer:
40m + 40
Step-by-step explanation:
8(5m+5)
40m + 40
Evaluate the integral integral_1^squareroot 3 5 arctan(1/x)dx
The final integral is [tex]=5\left[x\arctan \left(\frac{1}{x}\right)-\left(-\frac{1}{2}\ln \left|1+x^2\right|\right)\right]_1^{\sqrt{3}}[/tex]
Numerical integrals are used to express concepts like volume, area, and displacement when infinitely small amounts of data are combined. Integral location is the integration process.
The signed area of the region in the plane that is circumscribed by the graph of a specific function between two points on the real line can be used to describe definitive integrals. Areas above the plane's horizontal axis are often positive, whereas those below it are typically negative.
[tex]\\\\\int _1^{\sqrt{3}}5\arctan \left(\frac{1}{x}\right)dx=\frac{5\left(2\sqrt{3}\ln \left(2\right)+2\pi -\sqrt{3}\pi \right)}{4\sqrt{3}}\quad \left(\mathrm{Decimal:\quad }\:2.34037\dots \right)\\\\=5\cdot \int _1^{\sqrt{3}}\arctan \left(\frac{1}{x}\right)dx\\\\=5\left[x\arctan \left(\frac{1}{x}\right)-\left(-\frac{1}{2}\ln \left|1+x^2\right|\right)\right]_1^{\sqrt{3}}x_{123} \\\\=5\left[x\arctan \left(\frac{1}{x}\right)-\left(-\frac{1}{2}\ln \left|1+x^2\right|\right)\right]_1^{\sqrt{3}}[/tex]
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Correct Question:
[tex]\int _{\:1}^{\sqrt{3}}5\cdot \arctan \left(\frac{1}{x}\right)dx[/tex]
. This semester there are 67 students performing in the middle school's
production of "Beauty and the Beastly." Of these students, 49 are 7th and 8th
graders. Write a proportion and solve for s, the percent of 6th grade students
that are in the play. Round your answer to the nearest tenth of a percent.
Answer:
We know that there are 67 students performing in the middle school's production of "Beauty and the Beastly." and 49 of them are 7th and 8th graders.
We can write a proportion to find the percent of 6th grade students in the play:
6th grade students / Total students = s / 100
We know that 49 of the students are 7th and 8th graders, so the number of 6th grade students is 67 - 49 = 18.
Now we can substitute the values in the proportion and solve for s:
18 / 67 = s / 100
To find s, we can cross-multiply and divide:
18 * 100 = 67 * s
1800 = 67 * s
s = 1800 / 67
s = 26.87
Rounding to the nearest tenth of a percent: 26.9 %
So, the percent of 6th grade students that are in the play is 26.9%.
If cos a/3 = 1/2, fin sin a
Answer: 0
Step-by-step explanation:
We know cos π/3 = 1/2.
Therefore, a = π.
Now, sin π is 0 if you remember the sin graph.
Therefore, answer is 0.
Find the slope of the line graphed below.
Answer:
Step-by-step explanation:
Hello, I am the same guy that told you that your previous question had no image.
Ok, so slope formula is m = (y₂ - y₁)/(x₂ - x₁)
Two coordinates on the given line is (-2 , 1) and (3, 5)
Just substitute the values there.
m = (5 - 1)/(3 + 2)
= 4/5
slope/m = 4/5
Pls mark as brainliest. I really need for no apparent reason. Cheers
the angle measures associated with which set of ordered pairs share the same reference angle?
O ((– √3/2 ,1/2 )¦), ((-1/2,√3/2 )¦)
O (( 1/2,√3/2 )¦), ((-√3/2 ,1/2 )¦)
O ((- 1/2- √3/2 )¦), ((1/2,√3/2 )¦)
O (( √3/2 ,1/2 )¦), ((1/2,√3/2 )¦)
The set of ordered pairs share the same reference angle is (- 1/2, -√3/2 ), (1/2,√3/2 )
The term ordered pair in math is defined as a composition of the x coordinate and the y coordinate by having two values written in a fixed order within parentheses.
Here we have know that the reference angle of x is obtained by either 180-x, 180+x. or 360-x depending on the position of terminal whether II quadrant or iv quadrant, or iii quadrant, etc.
So, based on these condition in order to find the reference angles here we must define that cos will remain cos only and sin will remain sin only there may be only changes in sign.
On the other hand all the ordered pairs given, here we find that I, II, and Iv there is a switch over form cos to sine and sin to cos.
Based on these condition option (3) is correct one.
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By what factor would you need to change the radius of a sphere, such that its volume increased by a factor of 7? Please include step by step calculations!
The factor by which radius of the sphere be changed is 1.91, which is calculated by applying the concepts of surface area and volume on the assigned problem.
What do you mean by volume?
Volume is defined as the 3D measurement that deals with the amount of space required by an object. It is always calculated in cubic units. Its basic unit is cubic metre.
Calculation of the change in radius of sphere when its volume is increased by 7Let the radius and volume of sphere be r and v respectively
Volume of sphere, v = 3.16 × ( r )3 —- 1
Now, changed radius, R = xr
Where x is the factor, we need to calculate
Changed volume, V = 7v = 3.16 × ( R )3 -— 2
From equations 1 and 2, we get,
7v / v = ( R )3 / ( r )3
7 = ( xr )3 / ( r )3
7 = (x)3 × 1
Taking cube root both sides,
x = 1.913
Hence, the factor by which radius of the sphere be changed is 1.91.
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i need an answer for this question in the simplest radical form please
y³√45x⁷y⁵ in its simplest form is 3√5y⁵x³√x√y
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is y³√45x⁷y⁵
y³√9×5 x⁷y⁵
In the given expression x and y are the variables.
=y³3√5x³.√x. y²√y.
=y⁵.3√5x³√y√x
=3√5y⁵x³√x√y
Hence,y³√45x⁷y⁵ in its simplest form is 3√5y⁵x³√x√y
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Which equation represents the transformation formed by horizontally shifting the graph of f(x)=x√ 6 units to the right and then vertically stretching the graph by a factor of 2 ?
a)g(x)=1/2√x-6
b)g(x)=√2x+6
c)g(x)=2√x-6
d)g(x)=1/2√x+6
Answer:
answer is c
Step-by-step explanation:
g(x)=2√x-6
The scale of a map is given as 1:2500000. If the distance between two towns in the map is 5 cm, what is the actual distance in km between the two towns?
Answer:
2:5
I am not sure if it is correct answer
The population of a city increases by 2.2% per year. If this year's population is 137,000, what will next year's population be, to the nearest individual?
The next year's population to the nearest individual will be 140,014. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
There are four fundamental mathematical operations for all real numbers in mathematics, and they are as follows:
1. Obtaining the sum of the numbers through addition ('+').
2. Subtraction using the sign "-" where the difference between the numbers is produced.
3. Multiplication ('×'), which results in the numbers' product.
4. The division ('÷') operation where the quotient of the numbers is determined.
According to the question, the population of a city increases by 2.2% per year and this year's population is 137,000.
Let the population of next year be 'x'
Therefore, we get the following
⇒137,000 + 137,000(2.2%) = x
⇒137,000 + 3014 = x
⇒140,014 = x
Hence, the next year's population to the nearest individual will be 140,014.
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