Use the point slope formula to find the linear equation with a slope of 1/3 and a point of (12, 5).

Ponyboy shivered as he recalled the Socs jumping him and asking if he was a greaser.

The statement is referencing a scene from the novel "The Outsiders" by S.E. Hinton. In the novel, Ponyboy is a member of a poor, lower-class gang called the "greasers." The Socs are the wealthier, more privileged gang in town. The scene described in the statement is likely one in which Ponyboy is confronted and beaten up by members of the Socs gang, who are asking him if he is a member of the greaser gang.

The scene highlights the tensions and conflicts between the two gangs and their different experiences growing up in different social classes.

"The Outsiders" is considered a young adult novel, so it can be read by kids who are at or near the target age range for that genre, typically around 12 to 18 years old. However, the themes and content of the novel may be mature for some younger readers, so it is always a good idea for parents or guardians to read the book first and determine if it is appropriate for their child.

Additionally, individual reading levels can vary greatly, so it is always best to assess a child's individual abilities and interests when determining if a particular book is suitable for them to read.

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For the given coordinates, the equation of line is y = 1, The coordinates of foot of perpendicular will be (0, 5)

Assume that ax + by + c = 0. is a continuous line. If a perpendicular line is drawn from any point on the plane to the provided straight line, the intersection of the two lines is referred to as the foot of the matching perpendicular.

Because a perpendicular line is created from point P to the y-axis, the distance between its intersection with the x-z plane remains constant.

Given,

the points of line are - (1, 1) and (5, 5).

equation of line = (y - yo) = m (x - xo)

⇒ y - 1 = [tex]\frac{5 - 1}{5 - 1}[/tex] (x - 1)

⇒ y = 1. is the equation of the line,

Let us consider the point (a,b) such that it is the foot of the perpendicular,

Now, as the line line joining the points (1,5) and (a,b) will be perpendicular to each other,

⇒ y - 1 = b - 5 / a - 1 (x - 1)

The slope of one line is the negative inverse of other line,

⇒ b - 5 / a -1 = 0

⇒ b = 5

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Answer:

600,000 is greater than 11,733.83. Or

600,000>11,733.83

Step-by-step explanation:

To compare the values of 600,000 and 11,733.83, we can simply look at the magnitude of the numbers.

600,000 is much larger than 11,733.83. This means that 600,000 is greater than 11,733.83

The greatest common factor of 5x⁷, 30x⁴, 10x³ is 5x³

The Greatest Common Factor is defined as the largest number that is a factor of two or more numbers. For example, the GCF of 24 and 36 is 12, because the largest factor that is shared by 24 and 36 is 12. 24 and 36 have other factors in common, but 12 is the largest.

The greatest common factor between 5, 10 and 30 is 5. This means out all of the common factors between 5,10 and 30 , 5 is the greatest

The greatest common factor between x⁷ and x⁴ and x³ is x³.

Therefore the greatest common factor between 5x⁷, 30x⁴, 10x³ is 5× x³ = 5x³

This means 5x³ is the highest factor that can go through 5x⁷, 30x⁴, 10x³

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The equation for the volume of a cylindrical shell is:

V = πr² * h * w, where r is the radius of the semicircle base, h is the height of the shell, and w is the width of the shell.

The volume of the solid can be found using the method of cylindrical shells. The volume of each cylindrical shell is equal to the product of the area of the base (a semicircle), the height of the shell, and the width of the shell (which is equal to the difference in the x-coordinates of the two vertices that define the height).

To find the total volume, we would sum up the volumes of all the cylindrical shells, from the top to the bottom of the solid.

The equation for the volume of a cylindrical shell is:

V = πr² * h * w, where r is the radius of the semicircle base, h is the height of the shell, and w is the width of the shell.

The height of the shell is given by the difference in the y-coordinates of the two points that define the height, and the width of the shell is given by the difference in the x-coordinates of these two points.

To find the total volume, we would integrate the volume of the cylindrical shell over the height of the solid. The limits of integration would be the y-coordinates of the bottom and top of the solid.

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The formula of standard deviation method is

[tex]P=\sqrt{\frac{ \sum(X-\mu)^2}{N}}[/tex]

[tex]S=\sqrt{\frac{ \sum(X-\bar{x})^2}{n-1}}[/tex]

What is the standard deviation?

A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

Standard deviation It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

population mean:

[tex]P=\sqrt{\frac{ \sum(X-\mu)^2}{N}}[/tex]

X- the value in the data distribution

[tex]\mu[/tex]  - the population mean

N- total number of observations

[tex]S=\sqrt{\frac{ \sum(X-\bar{x})^2}{n-1}}[/tex]

[tex]\bar{x}[/tex]  - the sample mean

n- total number of observations

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The sum or difference matched with its simplified form;

(7x³ -12x + 4) - (6x²- 8x - 3)

open parenthesis

= 7x³ -12x + 4 - 6x² + 8x + 3

= 7x³ - 6x² - 4x + 7

(5x³ - 3x + 7) - (2x³ + 6x² - x)

= 5x³ - 3x + 7 - 2x³ - 6x² + x

= 3x³ - 6x² - 2x + 7

(3x³ - 10x² + 2x) - (10x² + 7x - 10)

= 3x³ + 10x² + 2x - 10x² - 7x + 10

= 3x³ - 5x + 10

(5x³- 3x + 7) + (2x³ + 6x² - x)

= 5x³- 3x + 7 + 2x³ + 6x² - x

= 3x³ + 6x² - 4x + 7

Therefore, a given expression can be written Ina simplified form.

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The value of the operation sec theta plus cot theta using trigonometric ratios is; 2.465

The primary trigonometric ratios are;

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

sec x = 1/cos x

cosec x = 1/sin x

cot x = cos x/sin x

The parameters are;

sin θ = 0.6224

cos θ = 0.8820

Thus;

sec θ = 1/cos θ = 1/0.8820

cot θ = cos θ/sin θ = 0.8820/0.6624

Thus

sec θ  + cot θ = (1/0.8820) + (0.8820/0.6624)

= 2.465

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The solution is given below.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

The perimeter of a rectangle is 40 cm. The length is 14 cm.

Let x = width of the rectangle.

Ravi says he can find the width using the equation 2(x + 14) = 40.

Fran says she can find the width using the equation 2x + 28 = 40.

now, we get,

1. Divide both sides by 2

 2(x+14) = 40

 x+14 = 20

2. Isolate the x term by subtracting 14 from both sides

3. x = 6. The width of the triangle is 6 cm.

4. Isolate the x term by subtracting 28 from both sides

 2x + 28 = 40

 2x = 12

5. Divide both sides by 2

6. x = 6

7. The two equations have the same solution, because by the distributive rule, 2(x+14) = 2x+28.

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Given the following information, we can calculate the requested probabilities:

Probability that the customer is at least 20 but no older than 60:

Number of customers in the specified age range: 72 + 52 + 100 + 71 + 69 = 364

Total number of customers: 364 + 1 = 365

So, the probability is 364/365 = 0.997

Probability that the customer is either older than 40 or younger than 20:

Number of customers in the specified age range: 72 + 52 = 124

Total number of customers: 365

So, the probability is 124/365 = 0.338

Note: The chart doesn't provide information about customers who are older than 60 or younger than 20, so we can't calculate the probability for those ranges.

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"The function is increasing in the interval (-2.5,∞)".

To determine whether the function is increasing or decreasing we are going to use the derivative test.

f(x) = x² + 5x + 6

f'(x) = 0

2x + 5 = 0

x = -5/2

Intervals associated with this point are  (-∞,-2.5) and (-2.5,∞)

Now by checking in the interval  (-∞,-2.5)  at a point, let's say -3

Then,

f'(-3) = -1 so function is decreasing over this interval.

Now by checking in the interval  (-2.5,∞)  at a point, let's say 2

Then,

f'(2) = 1 so function is increasing over this interval.

Hence "The function is increasing in the interval (-2.5,∞)".

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The sign of the second derivative of a function can determine whether the function is increasing or decreasing. If the second derivative is positive, the function is concave up and therefore increasing.

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[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{(-3)}}} \implies \cfrac{4 +1}{-5 +3} \implies \cfrac{ 5 }{ -2 } \implies - \cfrac{ 5 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- \cfrac{ 5 }{ 2 }}(x-\stackrel{x_1}{(-3)}) \implies y +1 = - \cfrac{ 5 }{ 2 } ( x +3) \\\\\\ y+1=- \cfrac{ 5 }{ 2 }x-\cfrac{15}{2}\implies y=- \cfrac{ 5 }{ 2 }x-\cfrac{15}{2}-1\implies {\Large \begin{array}{llll} y=- \cfrac{ 5 }{ 2 }x-\cfrac{17}{2} \end{array}}[/tex]

The recursive formula for the arithmetic sequence in this problem is given as follows:

c(1) = -16.

c(n) = c(n - 1) - 17.

Arithmetic sequences are collections of numbers that share a consistent difference between them; that is, there is a constant amount of subtraction between any two entries in an arithmetic sequence.

The recursive formula for an arithmetic sequence is defined as follows:

c(n) = c(n - 1) + d.

In which d is the common difference of the arithmetic sequence.

The sequence in this problem is given as follows:

-16, -33, -50, -67,...

Then the common difference is obtained as follows:

d = -33 - (-16) = -33 + 16 = -17.

So, c(n) = c(n - 1) - 17.

c(1) = -16.

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The triangle that will be formed using the sides 12 mm , 16 mm and 20 mm will be a right trinagle.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

The characteristics of a right-angled triangle.

Let is consider the triangle is a right triangle so the base and height will be 12 mm and 16 mm respectivly.

Now using Pythagoras Theorem :

√(height² + base²) = hypotenuse

⇒√(12²+16²) = √(144+256) = √(400) = 20 mm = hypotenuse.

The triangle that will be formed using the sides 12 mm , 16 mm and 20 mm will be a right trinagle.

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The values of a and b such that y∼n(0,1) are a = ± (1/σ) and b = ± (μ/σ)

of a gaussian distribution.

Gaussian distribution (also known as normal distribution) is a bell-shaped curve, and it is assumed that during any measurement values will follow a normal distribution with an equal number of measurements above and below the mean value.

E(X) = μ, Var(X) = σ^2

Y = aX + b

We want E(Y) = 0 and Var(Y) = 1

E(Y) = a E(X) + b

0 = a μ + b

b = -a μ  --- (1)

Var(Y) = (a^2) Var(X)

1 = (a^2) σ^2

a^2 = 1/σ^2

a = ± 1/σ  --- (2)

From (1) and (2)

b = (± 1/σ) μ

So, a = ± (1/σ) and b = ± (μ/σ)

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The complete question is :

A random variable X ∼ N (µ, σ2 ) is Gaussian distributed with mean µ and variance σ 2 . Given that for any a, b ∈ R, we have that Y = aX + b is also Gaussian, find a, b such that Y ∼ N (0, 1)

Hence the formula of [tex]a ^2 + b^ 2 + c^ 2[/tex] is [tex]( a + b + c )^ 2 - 2 ( ab + bc + ca ) .[/tex]

Formulas are equations that compute values from your spreadsheet. A formula always starts with the equal sign (=).

Using a calculating operator and a constant, you can make a straightforward formula.

For instance, the equation =5+2*3 multiplies two numbers before adding one more to the outcome.

A formula is a rule or relationship in mathematics that utilizes letters to indicate amounts that might change; these amounts are known as variables. For instance, the triangular area calculation formula.

The word "formula" is pluralized to "formulas." A list of elements that are employed in various concoctions and potions is referred to as a formula, which can also refer to a specific mathematical calculation.

Because English might be erratic at times, newborns can also be fed formula.

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The function f(x,y) is defined for all (x,y) pairs that lie within the region d, which is bounded by the parabolas y= 2x2 and y= 1 x2. It returns the product of x and 2 to the power of y.

The function f(x,y) is a two-variable function defined on the region d, which is bounded by the parabolas y= 2x2 and y= 1 x2. In order to calculate the output of this function, we must first identify the values of x and y that lie within the region d. We can do this by graphing both parabolas and finding the intersection point, which is when x=1 and y=2. This tells us that any (x,y) pairs with x<1 and y<2 will be within the region d. Now that we have identified the region, we can calculate the output of the function by multiplying x and 2 to the power of y. For example, if x=0.5 and y=1, then f(x,y)= 0.52 = 0.25.

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Answer: 40 pages/hour

Step-by-step explanation:

12pages / 18min  *   60min/1hr

= 40pages / 1hr

OR

12 pages / 18min    SIMPLIFY

2pages / 3 min

Multiply both by 20 to get how many pages per 60 minutes.

The mean/standard error of the sampling distribution of the proportion is 0.0111.

Its root-mean The square root of the mean of the squares of all the values in a series calculated from the arithmetic mean is the square deviation, also referred to as the standard deviation and denoted by the symbol.

The standard deviation reveals the degree of data dispersion. It expresses how far away from the mean each observed value is.

Almost 95% of the values in any distribution will be within two standard deviations of the mean. The degree of data dispersion from the mean is described by the term "standard deviation" (or " σ").

The data tend to cluster around the mean when the standard deviation is low; when it is high, the data are more dispersed.

The formula to calculate the standard error of sampling distribution of sample proportion is:

[tex]$ SE(p) =\sqrt{\frac{p(1-p)}{n} }[/tex]

It is given that the bank believes that 8% of people who receive loans will not make payments on time. That is,

Population proportion, p =0.08

Sample size, n= 800

Using the formula defined :

[tex]$ SE(p) =\sqrt{\frac{0.08(1-0.08)}{600} }[/tex]

[tex]$ SE(p) =\sqrt{0.000123}[/tex]

SE(p) = 0.0111

Thus, the mean/standard error of sampling distribution of the proportion is 0.0111.

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Using the details given, the exponential growth at rate of 10% over 14 years is 26582.5

An exponential function is a mathematical function in which the variable appears as an exponent. It can be written in the form of y = ab^x, where a is the base, b is a constant, and x is the variable. This function has the property that y grows or decays at an exponential rate as x increases or decreases.

y = a(1 + r)^t

In the given problem, we have the data given as;

Substituting the values into the formula;

y = 7000(1 + 0.1)^14

y = 26582.5

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Answer:  3:10

Step-by-step explanation:

Answer:

6:20 or 3/10

Step-by-step explanation:

The minimum degree of a Taylor polynomial required to calculate to 3 decimal places depends on the complexity of the function being approximated.

A Taylor polynomial is a way of approximating a function with a polynomial. The polynomial is built based on the function's value and its derivatives at a specific point.

To calculate a Taylor polynomial to 3 decimal places, the degree of the polynomial required depends on the complexity of the function and the desired accuracy.

If the function is smooth, with no sudden changes, a lower degree polynomial may be sufficient to approximate the function to 3 decimal places.

A general rule is to use a polynomial of degree at least two times the number of decimal places desired. So, for 3 decimal places, a polynomial of degree 6 or higher is required.

However, it is important to note that the minimum degree required can be determined by experimenting with different degrees of polynomials and checking the accuracy of the approximation.

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The equation is unchanged when you replace x with --x AND y with -y.

Hence, according to the above hypothesis, our equation is origin symmetry.

Equation graphs may be symmetric with regard to the origin or with respect to one of the coordinate axes.

If the Cartesian plane were folded along the -axis, the area of the graph above the x-axis and the area below the x-axis would coincide. This is known as symmetry with regard to the -axis.

Similar concepts apply to symmetry with regard to the y-axis or the origin.

x-axis, not symmetry, the equation will be changed when we replace the y with -y.

y-axis, not symmetry,  the equation will be changed when we replace the x with -x.

origin symmetry , the equation is unchanged when you replace x with --x AND y with -y.

hence, according to the above hypothesis, our equation is origin symmetry.

The complete question is-

Use the algebraic tests to check for symmetry with respect to both axes and the origin. (Select all that apply.)

y=x3

x-axis symmetry

y-axis symmetry

origin symmetry

no symmetry

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1) The area of the board shown on the scale drawing is; 1800 cm².

2) The way that Adam can use the scale factor to find the area of the actual electronics board is; The scale factor 5:1 means that 1 cm in the drawing is 0.2 cm in reality. Thus, he would multiply both 36 and 50 and by 0.2 cm then add them to get 17.2.

3)  The area of the actual electronics board is; 17.2 cm².

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size maybe bigger or smaller.

1) The formula for area of a rectangle is;

Area = Length * Width

Thus;

Area of board = 36 * 50

Area = 1800 cm².

2) He can figure out that the scale factor 5:1 means that 1 cm in the drawing is 0.2 cm in reality. Thus, he would take 36 and 50 and multiply them both by 0.2 cm then add them to get 17.2, which is the actual area of the rectangle.

3) Actual area is 17.2 cm²

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Her sales are at least $1000 during that week.

Let x stand in for her sales.

The equation to determine her sales is as follows, based on the data in the question:

Hillary works at a video store. She earns $8. 50 per hour plus a 12% commission on all the weekly sales she makes.

he works 24 hours a week if she earns at least $324 during that week

(8.50 × 24) + (12% × x) ≥ 324

204 + (0.12 × x) ≥ 324

204 + 0.12x ≥ 324

0.12x ≥ 324 - 204

0.12x ≥ 120

x ≥ 120/0.12

x ≥ 1000

Her sales are at least $1000

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On solving the provided question, we can say thatarea of the figure = area of triangle + area of semi-circle = 12 + 14.13 = 26.13 yd sq.

The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.

area of semi-circle = 1/2 * [tex]\pi *r^2[/tex] = 0.5*3.14*3*3 = 14.13yd sq.

area of triangle = 1/2*b*h = 0.5*6*4 = 12sq. yd

area of the figure = area of triangle + area of semi-circle = 12 + 14.13 = 26.13 yd sq.

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The surface area of ​​this rectangular prism 290 square inches.

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.

The surface area of a solid is defined as the sum of the areas of each of its faces (or surfaces), hence the name.

The surface area of rectangular prism formula is

Surface Area = 2(lw+lh+wh)

Here, length=5 inches, width= 5 inches and height=12 inches

Now, surface area = 2(5×5+5×12+5×12)

= 2(25+60+60)

= 2×145

= 290 square inches

Therefore, the surface area of ​​this rectangular prism 290 square inches.

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The surface area of a rectangular prism is given by the expression 2(lh+bh+lb) where, l = length, h = height and b = width

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases.

Given that, what is the surface area of ​​this rectangular prism.

Let us consider a rectangular prism with l = length, h = height and b = width

Now, we will find its surface area,

Since, we know that, there are 6 rectangular faces in a rectangular prism

Therefore, for surface area of the rectangular prism will add the areas of all 6 faces,

Area of the faces = lb + bh + lh + lb + bh + lh (area of rectangle = length x width)

Area of the faces = 2(lb+bh+lh)

Hence, the surface area of a rectangular prism is given by the expression 2(lh+bh+lb) where, l = length, h = height and b = width

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According to the histogram, the expected mean exam score is approximately 6.5. This value is centered on the majority of scores, indicating that it is most likely the exam's average.

A histogram is a graph that shows data points arranged in user-defined ranges. By grouping a large number of data points into logical ranges or bins, the histogram, which looks like a bar graph, makes a data series easier to understand.

Histograms and bar charts both use columns to present a visual display, and the terms are frequently used interchangeably. However, technically speaking, a histogram depicts the frequency distribution of a data set's variables.

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Answer: 12

Step-by-step explanation:

you would first add up all of the numbers togeather, and it would give you 60. You then need to divide 60 by the amount of numbers which is 5. So you would do 60 divided by 5 to get 12.

she has to pay $736 per month, next year in rent.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, lian currently pays 640 per month to rent her apartment she has been told by her landlord that her rent will be increasing by 15% next year.

Her rent is now = 640 per month

Since, After a year her rent will increase by 15 %

Thus,

Her rent next year per month = 640(1 + 15%)

Her rent next year per month = 640(1 + 0.15)

Her rent next year per month = 640* 1.15

Her rent next year per month = 736

Therefore, she has to pay $736 per month, next year in rent.

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