The recursive formula is an = a(n-1) +4. A recursive formula is one that defines each term in a sequence by using the term before it (s)
What is recursive formula?A recursive formula is one that defines each term in a sequence by using the term before it (s). The following parameters are defined by the recursive formulas: The sequence's first term. The pattern rule for obtaining any term from its preceding term. A recursive formula is composed of two parts: a statement of the first term and a statement of the formula that connects successive terms. The sequence is as follows: 10, 15, 20, 25, 30, 35,... Look for a recursive formula. This is an arithmetic sequence (the same number, 5, is added to each term to get to the next term).The sequence's first term
The pattern rule for obtaining any term from its preceding term
Recursive Arithmetic Sequence Formula
To find the nth term of an arithmetic sequence, use the recursive formula:
an = an-1 + d for n ≥ 2
Where
an is the nth term of a A.P.
d is the common difference.
Given:
14, 18, 22, 26, 30, …
a1 = 14
and, d = 18-14
d = 4
a2 = a1 + 4
a2 = 14 + 4 = 18
Similarly, going this way
an = a(n-1) +4
Hence, the recursive formula is an = a(n-1) +4
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-2(4 + 3y) = -2(4 + y)
Answer:
Step-by-step explanation:
-8-6y=-8-2y
+2y +2y
-8-4y=-8
+8 +8
-4y=0
Y=0
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The length and width of a rectangle that maximises the enclosed area are 162.5 yards. The maximum area is 26,406.25 square yards.
In the given question we have to find the maximum area of the rectangular area.
A farmer with 650 meters of fencing wants to enclose a rectangle plot that border on a river.
As we know that the perimeter of rectangle
P= 2(l+b)
Let length of the rectangle is x yards and width is y yards.
So the equation should be
2(x+y) = 650
Divide by 2 on both side we get
x+y = 325................(1)
From the area of rectangle is
A = xy
From the equation the value of y is 325-x.
Now putting the value of y
A = x(325-x)
A = 325x-x^2
On differentiating
dA/dx = 325-2x
Putting dA/dx=0
325-2x=0
Subtract 325 on both side we get
-2x= -325
Divide by -2 on both side we get
x = 162.5 yards
Now putting the value of x in the y=325-x
y=325-162.5
y=162.5 yards
So the maximum area is
A= 162.5*162.5
A= 26,406.25 square yards
Hence, the length and width of a rectangle that maximises the enclosed area are 162.5 yards. 26,406.25 square yards is the maximum area.
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Janet attends state university and lives in an on campus dorm suite with 5 friends. They share cost of the monthly upgraded cable bill for their suite. Below is a listing of the bills for their freshman year. 9. Round the following value
Σ
619
X₁
to the nearest dollar.
Interpret the answer in the context of the problem.
Answer:
Step-by-step explanation: Step 1
1 of 2
step 1.2659 ;[26 Discovery Group
October 20
Last
Trade Time
Chg
Open
52-week High
52-week Low
Sales in 100s
High
Low
$38.50
4:00 P.M. ET
$1.56
$37.22
$76.19
$22.78
19,700
$40.10
$36.77
\begin{matrix} \text{Discovery Group} & \text{}\\ \text{October 20} & \text{}\\ \text{Last} & \text{\$42.00}\\ \text{Trade Time} & \text{4:00 P.M. ET}\\ \text{Chg} & \text{\$1.50}\\ \text{Open} & \text{\$42.50}\\ \text{52-week High} & \text{\$76.19}\\ \text{52-week Low} & \text{\$22.78}\\ \text{Sales in 100s} & \text{23,600}\\ \text{High} & \text{\$42.50}\\ \text{Low} & \text{\$42.00}\\ \end{matrix}
Discovery Group
October 20
Last
Trade Time
Chg
Open
52-week High
52-week Low
Sales in 100s
High
Low
$42.00
4:00 P.M. ET
$1.50
$42.50
$76.19
$22.78
23,600
$42.50
$42.00
Can anyone write the equation of the graph?
What is the product of (4i-5)(4i+5)
The product of (4i-5)(4i+5) is -41.
What are complex numbers?
Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted i, also known as the imaginary unit, and satisfies the equation i² = - 1.
Here, we have
Given function
= (4i-5) (4i+5)
After applying the product rule, we get
= 16i² + 20i - 20i - 25
= 16i² - 25
after putting i² value, we get
= 16(-1) - 25
= -41
Hence, the product of (4i-5)(4i+5) is -41.
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ind the perimeter or circumference and area of each igure. Round to the nearest tenth. 4. 6. 2.5 cm 14 yd 2 cm 3.5 cm 3 cm 5. 7. 3 cm 4 ft 5 cm 4 cm
For figure 4, The perimeter is 9 cm and the area is 3.5 square cm.
For figure 5, The circumference is 8π ft. and the area is 16π square ft.
For figure 6, The perimeter is 56 yards and the area is 196 square yards.
For figure 7, The perimeter is 12 cm and the area is 6 square cm.
What is the perimeter?
Perimeter is the distance measured around the edge of any geometrical shape.
The perimeter of a square having side "a" is = 4 ×a.
The perimeter of a triangle having sides "a", "b", and "c" is = a+b+c.
What is the Circumference of a circle?
In geometry, the circumference is the perimeter of a circle.
To find the circumference of a circle, we can use the formula.
Circumference of a circle = 2×π×r
Where "r" is the radius of a circle.
What is the Area of a circle?
In geometry, the area of a circle is the space occupied by the circle.
To find the area of a circle having radius "r", we can use the formula.
Area of a circle = π×r².
What is the Area of a triangle?
The area of a triangle is defined as the space enclosed within the three given sides of a triangle.
The formula for finding the area of a triangle for a given height "h" and base "b" is
Area of a Triangle = [tex]\frac{1}{2} *b *h[/tex]
What is the area of a square?
The area of a square is defined as the space occupied by the square.
To find the area of a square having side "a" is
Area of a Square = (a)²
For figure 4,
The sides of the given triangle are 2.5 cm, 3 cm, and 3.5 cm.
The height of the triangle is given as 2 cm.
Then, the perimeter of a triangle = 2.5 + 3 + 3.5
= 9 cm.
and the area of a triangle [tex]=\frac{1}{2}*3.5*2[/tex]
= 3.5 square cm.
For figure 5,
The radius of the given circle is 4 ft.
so, the Circumference of a circle = 2×π×r
= 2×π×4
= 8π ft.
and the area of the circle = π×r²
= π×(4)²
= 16π square ft.
For figure 6,
The side of the given square is 14 yd.
so, the perimeter of a square = 4×side
= 4×14
= 56 yards.
and the area of a square = (side)²
= (14)²
= 196 square yards.
For figure 7,
The sides are 3 cm, 5 cm, and 4 cm.
so, the perimeter of a triangle = 3+5+4
= 12 cm.
The height of a triangle is 3 cm and the base is 4 cm.
and the area of a triangle = [tex]\frac{1}{2}[/tex] × h × b
= [tex]\frac{1}{2}[/tex] × 3 × 4
= 6 square cm.
Hence,
For figure 4, The perimeter is 9 cm and the area is 3.5 square cm.
For figure 5, The circumference is 8π ft. and the area is 16π square ft.
For figure 6, The perimeter is 56 yards and the area is 196 square yards.
For figure 7, The perimeter is 12 cm and the area is 6 square cm.
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whats the quotient for 2.0 and 4.0
The solution to the quotient for 2.0 and 4.0 is 0.50
How to determine the quotient of the numbers?From the question, the mathematical statement is given as
The quotient for 2.0 and 4.0
The quotient of numbers is their division
This in other words mean that:
The quotient for a and b is a/b
Using the above highlights as a guide, we have
The quotient for 2.0 and 4.0 to be 2.0/4.0
Evaluate the quotients
So, we have the following representation
The quotient for 2.0 and 4.0 to be 0.50
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Write an equation for the transformation of y=x; vertical by a factor of 1/10
The equation the function after the transformation is g(x) = x/10
How to determine the transformation of the function?The equation of the function is given as
y = x
Express as a function
f(x) = x
The sequence of transformations is given as follows:
Vertically stretched by a factor of 1/10
When the above transformations are combined, we have:
Vertically stretched by a factor of 4: g(x) = 1/10f(x)
So, we have
g(x) = 1/10f(x)
Substitute x for f(x)
So, we have
g(x) = 1/10 * x
Evaluate
g(x) = x/10
Hence, the function g(x) is g(x) = x/10
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A probablity experiment is conducted in which the sample space of the experiment is S= (5. 6, 7, 8,9, 10, 11, 12, 13, 14, 15. 16}, event F={8,9,10,11,12,13), And event G = {12, 13, 14, 15} Assume that each outcome is equally likely. List the outcomes in F For G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule.
List the outcomes in F or G.
A. For G= {__}
(Use a comma to separate answers as needed)
Using the general addition rule, p(F or G) = 0.667.
What is sample space?
In probability theory, the set of all feasible outcomes or outcomes of an experiment or random trial is referred to as the sample space. The sample points, or potential ordered outcomes, are listed as elements in the set used to represent the sample space.
Let,
S = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
F = {8, 9, 10, 11, 12, 13}
G = {12, 13, 14, 15}
n(S) = number of elements in set S are 12.
n(F) = 6
n(G) = 4
n(F and G) = common elements in F and G = 2
n(F or G) = n(F) + n(G) - (F and G)
n(F or G) = 6 + 4 - 2
n(F or G) = 8
Now, using the general addition rule,
P(F or G) = P(F) + P(G) - P(F and G)
Here,
P(F) = n(F)/n(S) = 6/12 = 1/2
P(G) = n(G)/n(S) = 4/12 = 1/3
P(F and G) = n(F and G)/n(S) = 2/12 = 1/6
⇒ P(F or G) = 1/2 + 1/3 - 1/6
= 5/6 - 1/6
= 4/6
⇒ P(F or G) = 0.667
Hence, using the general addition rule, P(F or G) = 0.667.
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Last year, the student population at Haley Elementary School was 360 students. After rezoning this year, the student population is 10% smaller. HOW MANY STUDENTS ATTEND HALEY ELEMENTARY THIS YEAR?
Answer:
360 of 10%
360 x 10/100
36
now, 360 - 36 = 324
therefore, 324 students attended haley elementry this yr.
Heather is planning her birthday party at the rink. the graph below shows the total cost including the fee to rent the party room and the price for each guest.
130 for 2
140 for 4
150 for 6
how much for the party room
how much for each guest
what's the equation for the total cost for the party
how much for 15 people and the party room
Step-by-step explanation:
I skipped the answer line because they are pasted below.
Since there is a ten dollar difference for two people, each guest is 5 dollars. If each guest is 5 dollars, the party room is 120. If we want to create an equation, we have:
y=5x(each guest is 5 dollars)+120(the basic fee).
If we use 15 here, we have that it will be $195.
ANSWERS DOWN HERE:
1. $120
2. $5
3. y=5x+120
4. $195
the product of two numbers is 432.if GCF of the numbers is 12 then the greater number is ?
.i need the steps the answer is 36, Please help
The greater factor of 432, if 12 is the greatest common factor between the two factors is 36
What is greatest common factor?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 factors of 432 are 36,12, 24 ,18,4,108
But the two factors of 432 that has a multiple of 12 is 12 and 36
12× 36 = 432
The factors of 12 = 1,2,3,4,6,12
The factors of 36 = 1,2,3,4,6,9,12,18,36
the common factors are ; 1,2,3,4,6 and 12
therefore the greatest common factor = 12
since the GCF between 12 and 36 is 12, the second number will be 36
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Question 2
Which set of rational numbers is arranged from least to greatest?
O
O
O
O
-3.5, 4, 2, 3
11
-3.5, 4,3,2
113
2, 3.
1
4.-3.5
11
4.3.2, -3.5
11
10 pts
Answer:
The second option.
Step-by-step explanation:
We can figure this out by going down each option and checking if it works and is arranged from least to greatest.
The first option provides the numbers -3.5, -1/4, 2, 1/3 in that order.
This does not work because 1/3 is less than 1 which is less than 2. 1/3 should come before 2.
The second option provides the numbers -3.5, -1/4, 1/3, 2.
This option does work, because -3.5 is less than -1/4, -1/4 is less than 1/3 because it is negative, and 1/3 is less than 2.
If we look at this on a number line, the numbers that are smaller will appear farther to the left on the number line.
please help look at picture
What are the solutions of 8x2 = 6 + 22x? Check all of the boxes that apply.
x = -3
x = 3
x = 6
The solution of quadratic equation 8x² = 6 + 22x is x = 3 and x = -1/4
What is a Quadratic equation ?
A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.
Given expression is,
8x² = 6 + 22x
Rewrite this expression as,
8x² - 6 - 22x = 0
8x² - 22x - 6 = 0
Now, we get the form quadratic equation i.e, ax² + bx + c = 0
Solve the equation and find roots
8x² - 22x - 6 = 0
2(4x² - 11x - 3) = 0
4x² - 11x - 3 = 0
4x² - 12x + x - 3 = 0
Take common terms out,
4x(x - 3) + 1(x - 3) = 0
we get the brackets same that means we're on right way,
(4x + 1) (x - 3) = 0
split the values into two,
4x + 1 = 0 and x - 3 = 0
4x = -1 x = 3
x = -1/4
Therefore, the solution of quadratic equation 8x² = 6 + 22x is x = 3 and x = -1/4
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A mixture of 13% disinfectant solution is to be made from 11% and 17% disinfectant solutions. How much
of each solution should be used if 12 gallons of the 13% solution are needed?
There needs to be
gallons of 11% solution and
gallons of 17% solution.
The mixture of 13% disinfectant solution needs to be made with 8 gallons of 11% solution and 4 gallons of 17% solution respectively.
How to find the number of gallons of solution needed?Let
gallons of 11% solution = xgallons of 17% solution = yx + y = 12
0.11x + 0.17y = 0.13 × 12
x + y = 12
0.11x + 0.17y = 1.56
From (1)
x = 12 - y
Substitute into (2)
0.11x + 0.17y = 1.56
0.11(12 - y) + 0.17y = 1.56
1.32 - 0.11y + 0.17y = 1.56
- 0.11y + 0.17y = 1.56 - 1.32
0.06y = 0.24
divide both sides by 0.06
y = 0.24/0.06
y = 4
Substitute y = 4 into (1)x + y = 12
x + 4 = 12
x = 12 - 4
x = 8
So therefore, the gallons of 11% solution and
gallons of 17% solution needed are 8 and 4 gallons respectively.
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What is the volume of this figure?
O 6,720 cm³
O 5,760 cm³
O 3,840 cm³
O I don't know.
The volume of the given figure is 5760 [tex]cm^{3}[/tex].
According to the question,
We have the following information:
We have a figure where two cuboids are joined together. So, the volume of the figure will be the sum of the volume of these cuboids.
We know that the following formula is used to find the value of cuboid:
Volume of cuboid = Length*breadth*height
Volume of larger cuboid = 40*8*12
Volume of larger cuboid = 3840 [tex]cm^{3}[/tex]
Volume of smaller cuboid = 20*8*12
Volume of smaller cuboid = 1920 [tex]cm^{3}[/tex]
Volume of the figure = 3840+1920
Volume of the figure = 5760 [tex]cm^{3}[/tex]
Hence, the correct option is B (the second option).
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Answer:
5760
Step-by-step explanation:
the superintendent of schools in a small town in ohio made many policy changes to the way school administration worked in his district. a researcher at a nearby university wanted to look at what teachers in his district thought about the changes. the researcher made a list of all the schools in the district and used a random number generator to select a sample of five schools from the district. then the researcher interviewed every teacher at each of those five schools. which sampling method did the researcher use?
Answer:
The number to the ration
Step-by-step explanation:
Which equation show the relationship between the number of
hours, x, and the number of dogs groomed, y?
y = 15x
y = 5x
y = 30x
y=3x
The relation that can be formed by obersving the Cartesian Plane is y = 5x
What is Co-ordinate Geometry?
The study of geometry using coordinate points is known as coordinate geometry (or analytic geometry). It is possible to estimate the distance between two points, divide lines in a m:n ratio, identify the midpoint of a line, calculate the area of a triangle in the Cartesian plane, and so on using coordinate geometry.
Solution:
By analysing the given Cartesian Plane
it can be observed that the rate of change of y with respect to x
is 5 times
Therefore, the relation that can be formed by obersving the Cartesian Plane is y = 5x
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PLEASE HELP ASAP! (QUESTION IN IMAGE + 15 Points)
One angle of an isosceles triangle measures 128°. What measures are possible for the other two angles? Choose all that apply.
Answer:
Hmm I am not sure, but I think you should try 44 and 26!
Step-by-step explanation:
Reply back if its right :)
(x² + 8x + 1) ÷ (x −4)
Answer: x=4
Step-by-step explanation: simplify expression and divide polynomials
Construct the graph of the equation given by solving for the intercepts. Show all of the steps in finding the intercepts and then
plot the intercepts to create the graph. Label the intercepts, as well as the axis on the graph.
2x+3y=6
The slope and the intercepts of the graph are determined.
Given:
the equation is :
2x+3y=6
we first find the slope of the equation:
m = -a/b
m = -2/3
now solve the intercepts:
to find x intercept, substitute in 0 for y and solve for x.
⇒ 2x+3y=6
⇒ 2x+3(0)=6
⇒ 2x+0=6
⇒ 2x=6
⇒ x=6/2
⇒ x=3
hence we get (3,0)
now, to find y intercept, substitute in 0 for x and solve for y.
⇒ 2x+3y=6
⇒ 2(0)+3y=6
⇒ 0+3y=6
⇒ 3y=6
⇒ y=6/3
⇒ y=2
hence we get (0,2) as the intercepts.
Therefore we plot the required graph.
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Question 5 of 10
Which of the following graphs represents a function that has a positive
leading coefficient? Check all that apply.
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Find the value of k so that the system of equation has no solution
kx + 6y = 6
y = 2/3x - 4
The value of k so that the system of equation has no solution is k = -4
How to find the value of k so that the system of equation has no solution?Since we have the system of equations
kx + 6y = 6
y = 2/3x - 4
For the system of equations to have no solution, the determinant coefficient matrix must be zero.
Re-arranging the equations, we have
kx + 6y = 6
-2/3x + y = - 4
So, the coefficient matrix is
[tex]\left[\begin{array}{ccc}k&6\\-2/3&1\end{array}\right][/tex]
So, the determinant D = k × 1 - (-2/3) × 6
= k + 2/3 × 6
= k + 2 × 2
= k + 4
Since the determinant must be zero for the system of equations to have no solution, we have that
D = 0
k + 4 = 0
k = -4
So, the value of k = -4
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PLEASE PLEASE HELP NOW!!!!!
Givin: logam=x and logan=y
Prove: logamn=logam+logan
Drag the statements and reasons into the boxes to correctly complete the proof.
Answer:
2. ax=m and ay=n
4. mn=a(x+y)
6. power property of logarithms.
I took the quiz.
k12
i took the quiz this is the right answers
Wyatt is saving money for a PS5 but has to pay back
the $3 he owes his sister.
#5.
Drag the green points so that the shaded region covers
the range.
#6.
What is the range of this function? (Consider: How do
you think the arrow affects the range?)
Answer:
Step-by-step explanation:
dees
sec^2 54 - 1, can anyone please help me with question asap
The numeric value of the expression sec²(54º) - 1, using a trigonometric identity, is given as follows:
tan²(54º) = 1.8944.
How to solve the expression using a trigonometric identity?Before applying the trigonometric identity, we have to define the secant and the tangent of an angle, as follows:
The secant of an angle is given by the division of one by the cosine of the angle.The tangent is given by the division of the sine of the angle by the cosine of the angle.The identity that exists between the squares of these measures is given as follows:
tan²(x) + 1 = sec²(x).
Hence, isolating the tangent:
tan²(x) = sec²(x) - 1.
In this problem, the expression is given as follows:
sec²(54º) - 1
Applying the identity, the expression is given as follows:
sec²(54º) - 1 = tan²(54º).
Using a calculator, the numeric value of the expression is given as follows:
tan²(54º) = 1.8944.
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Write the function whose graph is the graph of y = x2, but is shifted to the left 2 units.
The function whose graph is shifted 2 units to the left is y = (x + 2)² .
In the question ,
it is given that the equation is given as y = x² .
we know that when the function y = x² is shifted " a units " to the left , the shifted function becomes y = (x + a)² ,
we have to find the equation of the graph that is shifted 2 units to the left ,
So , the value of a is 2 ,
and the equation becomes
y = (x + 2)²
so , the equation is y = (x + 2)² .
the graph is shown below .
Therefore, The function whose graph is shifted 2 units to the left is y = (x + 2)² .
The given question is incomplete , the complete question is
Write the function whose graph is the graph of y = x², but is shifted to the left 2 units ?
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simplify (55x + 46y) - (29x - 10y)
Answer:
26x-56y
Step-by-step explanation:
First you open the bracket and collect like terms
55x-29x-46y-10y
26x-56y
greta is opening a savings account. she starts with 100$ and plans to add 50$ each week. write an equation she can use to calculate the amount of money she will have after any number of weeks. how much money will she have after 1 year?
Money she will have after 52 weeks = rs.2,700
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
Unit rate of change here is =
⇒ Unit rate of change here is =
⇒ Unit rate of change here is = 50%
Part B
Equation to calculate the amount of money Greta will have after any number of weeks = ?
Money after 'x' number of weeks =
⇒ Money after 'x' number of weeks =
Part C
Money Greta will have after 1 year= ?
In a year there are 52 weeks
So, putting x = 52 in the solution of Part B
⇒ Money after 52 weeks =
⇒ Money after 52 weeks =
⇒ Money after 52 weeks = 2,700
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