Answer: 0.004
Step-by-step explanation:
Chang invested his savings in two investment funds. the $3000 that he invested in fund a returned a 2% profit. the amount that he invested in fund b returned a 7% profit. how much did he invest in fund b, if both funds together returned a 4% profit?
Using algebraic expression and equation, he invested $2000 in fund b.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
Let x = amount he invested in fund b
If both funds together returned a 4% profit, then the sum of the profit in each investment is equal to 4% of the total investment.
$3000(0.02) + x(0.07) = (3000 + x)(0.04)
Solving for x,
$3000(0.02) + x(0.07) = (3000 + x)(0.04)
$60 + 0.07x = $120 + 0.04x
0.07x - 0.04x = $120 - $60
0.03x = $60
x = $2000
amount he invested in fund b = $2000
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please! Is for today!! HELP!!
The given pairs of lines have been identified as parallel, perpendicular lines or neither as explained below.
How to Determine if Two Lines are Parallel or Perpendicular?Two lines are parallel if they have the same slope (m), while they are perpendicular to each other if their slopes are negative reciprocal of each other.
The slope in a given equation of a line that is in slope-intercept form, y = mx + b, is represented as "m" in the equation.
1. y = 3x - 7 and y = 3x + 1 both have the same slope (m) of 3. They are parallel lines.
2. y = -2/5x + 3 and y = 2/5x + 8 both have the different slope (m), which are not negative reciprocal to each other. They are neither parallel nor perpendicular lines.
3. The slope of y = -1/4x is -1/4. The slope of y = 4x - 5 is 4. -1/4 is the negative reciprocal of 4. Therefore, the lines are perpendicular.
4. 2x + 7y = 28 can be rewritten as y = -2/7x + 4, the slope (m) is -2/7.
7x - 2y = 4 can be rewritten as y = 7/2x - 2, the slope (m) is 7/2.
-2/7 and 7/2 are negative reciprocals.
They are perpendicular lines.
5. The slope of y = -5x + 1 is -5.
x - 5y = 30 can be rewritten as y = 1/5x - 6, the slope is 1/5.
The lines are perpendicular.
6. 3x + 2y = 8 can be rewritten as y = -3/2x + 4, the slope (m) is -3/2.
2x + 3y = -12 can be rewritten as y = -2/3x - 4, the slope (m) is -2/3.
The lines are neither.
7. The slope of y = -4x - 1 is -4.
8x + 2y = 14 can be rewritten as y = -4x + 7, the slope is -4.
They are therefore parallel lines.
8. x + y = 7 can be rewritten as y = -x + 7, the slope (m) is -1.
x - y = 9 can be rewritten as y = x - 9, the slope (m) is 1.
The lines are perpendicular.
9. They have the same slope of 1/3. They are parallel lines.
10. They have different slopes that are not negative reciprocals, therefore, they are neither.
11. Their slopes are 1/2 and -2. Therefore, they are perpendicular lines.
12. They have the same slope of 3/4. They are parallel lines.
13. They have the same slope of 1. They are parallel lines.
14. Their slopes are -5/4 and 4/5. Therefore, they are perpendicular lines.
15. Their slopes are not negative reciprocals and are not the same, therefore, they are neither.
16. Their slopes are 1/2 and -2. Therefore, they are perpendicular lines.
17. They are both vertical lines, therefore they are neither.
18. x = 1 is a vertical line while y = -8 is a horizontal line that meets perpendicularly. Therefore, the lines are perpendicular.
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Write the following number in standard decimal form.
eleven and seventy-eight hundredths
Answer: 11.78
Step-by-step explanation:
For every 500 g of reactants, 3.1 g of catalyst were required. How much catalyst was
required for 900 g of reactants?
For every 500 g of reactants, 3.1 g of catalyst were required. The catalyst that was required for 900 g of reactant was 5.58g
What do you mean by a catalyst?The process of catalysis involves introducing a catalyst to chemical reaction to speed up the process. Catalysts are not destroyed during reaction and are unaffected by it. Very little amounts of catalyst are frequently sufficient when the reaction is swift and the catalyst recycles quickly; the velocity of the reaction is greatly influenced by mixing, surface area, and temperature. In most cases, catalysts interact with one or more reactants to produce intermediates that ultimately lead to the final reaction product, regenerating the catalyst in the process.
Homogeneous catalysis, in which all of the components are dispersed in the same phase as the reactant (often a gas or liquid), and heterogeneous catalysis, in which the components are not. It's common to think of enzymes and other biocatalysts as a a third category.
In all branches of the chemical business, catalysis is commonplace. 90% of all chemical compounds manufactured for commercial purposes are thought to use catalysts at some point during the manufacturing process.
500g of reactants = 3.1g of catalyst
1g of reactants = 3.1g of catalyst / 500g of reactants
900g of reactants = [tex]\frac{3.1}{500} * 900[/tex] = 5.58g
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multiply. what is the product (3 x 10^9) x (2 x 10^17) in scientific notation
Answer:
600000000000000000000000000[tex]x^{2}[/tex]
Santa and his elves had a workshop that allowed them to produce 22{,}912{,}546{,}99222,912,546,99222, comma, 912, comma, 546, comma, 992 toys each year.
The world population increased, so they built a new workshop. The new workshop allows them to produce 4{,}134{,}232{,}638{,}9374,134,232,638,9374, comma, 134, comma, 232, comma, 638, comma, 937 toys each year.
Approximately how many times as many toys can the new workshop produce each year compared to the old workshop?
Choose 1 answer:
Choose 1 answer:
The new workshop can produce as many as 180 toys each year compared to the old workshop
What is the approximation of a number?The approximation of numbers is the estimates of the said number.
This means that the approximation of a number is close to the said number, but it has a slight different value
How to determine the approximate number of times?The given parameters are:
Old capacity = 22,912,546,992 toys per year
New capacity = 4,134,232,638,937 toys per year
The approximate number of times is calculated as
Number of times = New capacity/Old capacity
Substitute the known values in the above equation
So, we have
Number of times = 4,134,232,638,937 toys per year/22,912,546,992 toys per year
Remove the units
So, we have
Number of times = 4,134,232,638,937/22,912,546,992
Evaluate the quotient
So, we have
Number of times = 180.435315217
Approximate
Number of times = 180
Hence. the approximate number of times is 180
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Robin’s favorite pound cake recipe needs 2 1/3 cups of flour. She plans to make 2 cakes for a picnic. She has 4 1/2 cups of flour in her cabinet. How much more flour does she need to make the 2 cakes
Answer: 1/6
Step-by-step explanation:
the minimum distance between earth and mars is about 33,900,000 miles how can this distance be expressed in scientific notation
Answer:
3.3⁷
Step-by-step explanation:
To make a scientific notation the whole number must be more than 1 and less that 9.9 repeating. To do this, move the decimal however many times it takes to make the whole number (the number before the decimal) more than one and less that 9.9 repeating. For the number 33,900,000, the decimal must be moved 7 times, which is why I added the 7 exponent. Also when making a number into a scientific notation, be sure to add the number after the whole number, placing it after the decimal.
What is the special angle pair relationship between 2 and 3?
The special angle pair relationship between ∠2 and ∠3 is same-side interior angles.
How to find angles?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, the angle pair relationship between angle 2 and 3 are same side interior angles.
The same-side interior angle theorem states that when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary.
Supplementary angles are those angles that sum up to 180 degrees. In other words, If the measures of two angles sum up to 180°, they are called supplementary angles.
Therefore, same side interior angles are supplementary angles.
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Given g(x) = 2x + 3, find g(3).
Answer:
g(3) = 9
Step-by-step explanation:
replace 3 in x
g(3) = 2(3) +3 = 6 + 3 = 9
Hope this helps
Find the measure of angles 1 and 2
I really need to get this done by today!
The unknown angles are as follows:
∠1 = 118°∠2 = 62°How to find measures of angles?The measures of angle 1 and 2 can be found as follows:
When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.
Therefore,
∠1 + ∠2 = 180(sum of angle on a straight line)
∠1 = 118(alternate angles)
118 + ∠2 = 180
∠2 = 180 - 118
∠2 = 62 degrees
Therefore,
∠1 = 118 degrees
∠2 = 62 degrees.
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Every year, Reba's family runs the sand castle contest during the Fun in the Sun beach festival. Reba's job is to deliver empty buckets to the teams. This year, Reba hands out the same number of buckets to each of the 12 teams in the contest. Each team gets 6 buckets.
Use an equation to find the total number of buckets Reba delivers.
If this year, Reba hands out the same number of buckets to each of the 12 teams in the contest. Each team gets 6 buckets. the total number of buckets Reba delivers is 72 buckets.
Total number of bucketsLet x represent the total number of buckets Reba delivers.
The equation to find the total number is:
x / 6 = 12
Let solve for x, to get the total number of buckets Reba delivers.
x = 12 × 6
x = 72 buckets
Therefore the total number of buckets is 72.
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Please help, thanks
Answer:
13. x = 3∛2
14 x = ± 4√6 = ± 4√2 √3
15. x = 2∛11
16 x = -4∛2
17 x = ± 10√3
18. x = ± 4 √3 √5
Step-by-step explanation:
13. x³ = 54
x = ∛4
Factor 54: 2 x 27
∛54 = ∛2 x ∛27
∛27 = 3
answer: 3∛2
14. x² = 96
x = ±√96
96 = 6 x 16
√16 = 4
√6
√96 = ± 4√6 = ± 4√2√3
15. x³ = 88
x = ∛88
88 = 8 x 11
∛88 = ∛8 x ∛11 = 2∛11
16. x³ = -128 means x has to be negative
x = -∛128
128 = 64 x 2
∛128 = ∛64 x ∛2 = 4∛2
So x = -4∛2
17. x² = 300
=> x = ± √300
300 = 100 x 3
√300 = √100 x √3 = 10√3
x = ± 10√3
18. x² = 240
x = ±√240
240 = 16 x 15
√240 = ± (√16 x √15)
= ± 4 √3 √5
Which number rounds to 32.6 when rounded to the nearest tenth?
1 32.58 2 32.65 3 32.68 4 32.75
We can find the remainder for the quotient using either substitution or synthetic division. Using either method, explain whether or not we can conclude that x - 5 is a factor of the polynomial f(x)=x^3-x^2-17x-15. (Your answer must include what that remainder value is and what it indicates
We may get the same conclusion using either approach, which is that x—5 is a factor of the polynomial.
This will be discussed in further detail below.
Can you explain what the polynomial is?Explain, taking into account the fact that, using either method, whether or not we can think of x-5 as a factor in the polynomial based on the given information.
Generally, the equation for the problem is mathematically given as
f(x)=x^3-x^2-17 x-15
Therefore, If (x-5) is factor of f(x) then at x=5 ,f(x)=0 then apply this
[tex]\begin{aligned}f(x) &=5^3-5^2-17 \times 5-15 \\&=125-25-85-15 \\&=0\end{aligned}[/tex]
In conclusion,Since f(x) is equal to 0 when x = 5, the factor of f is (x-5) (x).
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Write an equation of the line that passes through point (2, −4) and has the slope m=.5. y=
Answer:
Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.
Since slope is 5, equation is y = 5x + c.
Substitute (2,-4) into the equation to find c.
-4 = 5(2) + c
c = -14
Hence equation of line is y = 5x - 14
A) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over times, x measured in seconds. During what interval(s) of the domain is the water balloon's height staying the same?
A.0 ≤ x ≤ 2
B.2 ≤ x ≤ 5
C.5 ≤ x ≤ 6
D.6 ≤ x ≤ 8
B) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height increasing?
A.0 ≤ x ≤ 2
B.40 ≤ y ≤ 70
C.5 ≤ x ≤ 8
D.40 ≤ y ≤ 10
C) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height decreasing the fastest?
A.5 ≤ x ≤ 9.5
B.8 ≤ x ≤ 9.5
C.6 ≤ x ≤ 8
D.5 ≤ x ≤ 6
D) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Justify your answer from Part C.
A.5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing.
B.8 ≤ x ≤ 9.5 is the interval where the slope is the steepest.
C.6 ≤ x ≤ 8 is the interval where the balloon's height decreases the most.
D.5 ≤ x ≤ 6 is the interval where the slope is the steepest.
Please help as fast as possible <3
From the given linear function, we have that:
A. The function is constant on the following interval: B.2 ≤ x ≤ 5.
B. The function is increasing on the following interval: A.0 ≤ x ≤ 2.
C. The function is decreasing the fastest on the following interval: D.5 ≤ x ≤ 6.
D. The justification for the previous item is: D.5 ≤ x ≤ 6 is the interval where the slope is the steepest.
When a function is constant?A function is constant when it's graph is an horizontal line, hence in this problem the function is constant for two intervals.
2 ≤ x ≤ 5.10 ≤ x ≤ ∞.Hence, in item A, option B is correct.
When a function is increasing?A function is increasing on the intervals that y is increasing while x increases, that is, the function is moving right and up.
Hence, in item B, option A is correct.
When a function is decreasing?A function is decreasing on the intervals that y is decreasing while x increases, that is, the function is moving right and down.
The decrease is faster when the division of the change in the output by the change in the input has the lower value(greater absolute negative).
Hence:
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x² - 7x-18 = 0
What is the set of all values of x that satisfy the equation above?
A. (-9,2)
B. (-6, 3)
C. (6, 3)
D. (9,-2)
method 1.
[tex] {x}^{2} - 7x - 18 = 0[/tex]
simplify:
[tex](x - 9)(x + 2) = 0[/tex]
so the answer is (D) x =9 or x = -2
method 2.
if
[tex] {a}^{2}x+ bx + c = 0[/tex]
[tex]x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \: or \: \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
so
[tex]x = \frac{ - ( - 7) + \sqrt{ { - 7}^{2} - 4(1)(18)} }{2(1)} or\frac{ - ( - 7) - \sqrt{ { - 7}^{2} - 4(1)(18)} }{2(1)}[/tex]
[tex]x = \frac{ 7 + \sqrt{ 121 } }{2}or\frac{ 7 - \sqrt{ 121 } }{2}[/tex]
[tex]x = 9 \: \: \: \: or - 2[/tex]
what is 71.04 in expanded form
Answer:
(7 x 10) + (1 x 1) + (0/10) + (4/100)
70 + 1 + 0.04
70 + 1 + 4/100
Step-by-step explanation:
Here are all the expanded forms I can think of off the top of my head, sorry if this didn’t help much!
1. Shelley comparó el número de robles al número de arces como parte de un estudio sobre árboles de madera dura en una arboleda. Ella contó 9 árboles de arce por cada 5 árboles de roble. Más adelante en el año hubo un problema de insectos y muchos árboles murieron. Se plantaron nuevos árboles para asegurarse de que hubiera el mismo número de árboles que antes del problema de insectos. La nueva razón del número de árboles de arce al número de árboles de roble es 3:11. Después de plantar nuevos árboles, habia 132 robles. ¿Cuántos árboles de arce más había en la arboleda antes del problema de insectos que después del problema de insectos? Explica.
Answer:
Step-by-step explanation:
855555555555fhhhhhhhhhhhhhhhhg6
can y’all help me out with this worksheet?
Value of x [tex]\frac{36}{5}[/tex]
value of m∠3 = [tex]\frac{462}{5}[/tex]
Define angles.When two rays meet at a point, they make an angle. An "angle" is the term used to describe the "opening" between these two rays, and it is symbolized by the symbol. Angles are typically expressed as 60°, 90°, etc. and are measured in degrees. A figure made up of two rays meeting at the vertex of the angle can be referred to as an angle.
Given Data
m∠3 = 17x - 30
m∠6 = 12x +6
Angle pair - exterior alternate angle
For the value of x,
17x - 30 = 12x + 6
17x - 12x = 6 + 30
5x = 36
x = [tex]\frac{36}{5}[/tex]
For m∠3,
17x - 30
Equating value of x,
17([tex]\frac{36}{5}[/tex]) - 30
[tex]\frac{612-150}{5}[/tex]
[tex]\frac{462}{5}[/tex]
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Order from least to greatest .003 3.03 33.03 .303 .383 .030
Answer:
0.003, 0.03, 0.303, 0.383, 3.03, 33.03
Step-by-step explanation:
On a coordinate plane, a triangle has points R (negative 3, 4), T (negative 1, negative 4), and S (negative 4, negative 2).
What are the coordinates of the image of vertex R after a reflection across the y-axis?
(–4, 3)
(4, –3)
(–3, –4)
(3, 4)
Translation of negative 6 units x, negative 2 units y composition reflection across the x-axis
Reflection across the x-axis composition translation of negative 6 units x, negative 2 units y
Translation of negative 6 units x, negative 2 units y composition 90 degree rotation about point 0
90 degree rotation about point 0 translation of negative 6 units x, negative 2 units y
The reflection of the coordinate (-3, 4) over the y-axis is (3, 4).
Reflection of coordinatesThe Y-coordinates do not change when a point is reflected across the Y-axis. However, the X-coordinates are changed into their opposite signs.
Given the coordinates of the triangles RST as shown below;
R = (-3, 4)
S = (-1, -4)
T = (-4, -2)
If (x, y) for instance is reflected over the y-axis, the resulting coordinate will be (-x, y). Similarly, if the coordinate R (-3, 4) is reflected over the x-axis, the resulting coordinate point will be (3, 4)
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Which equation reveals the minimum or maximum value of f (x) without changing the form of the equation?
)A) ƒ (x) = (x+3)(x − 4)
(B) ƒ (x) = x² - 8x +15
(C)ƒ (x) = (x + 2)² − 1
(D) f(x) =x^2 +2x -1
The function has a minimum if the x2 coefficient is positive. If it is negative, the function has reached its limit. If you have the function 2x2+3x-5, for example, the function has a minimum because the x2 coefficient, 2, is positive. Divide the x term coefficient by twice the x2 term coefficient.
What exactly is an equation?A formal statement of the equality or equivalence of two mathematical or logical expressions. : a quantitative expression representing a chemical reaction using chemical symbols.A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. After solving this equation, we obtain the value of the variable x as x = 7.An equation is made up of expressions that have the same value. A formula is a two- or more-variable equation that represents a relationship between the variables.Hence, The function has a minimum if the x2 coefficient is positive. If it is negative, the function has reached its limit. If you have the function 2x2+3x-5, for example, the function has a minimum because the x2 coefficient, 2, is positive. Divide the x term coefficient by twice the x2 term coefficient.
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Lizzy is tiling a kitchen floor for the first time. She had a tough time at first and placed only 5 tiles the first day. She started to go faster, and by the end of day 4, she had placed 35 tiles. She worked at a steady rate after the first day. Use an equation in point-slope form to determine how many days Lizzy took to place all of the 100 tiles needed to finish the floor.
y - y1 = m (x - x1)
It will take 11 days to place all of the 100 tiles needed to finish the floor.
What is point slope form?The slope of a line and any points it contains determine the point-slope form of the line. When a point on the line and the slope are provided, the form's objective is to represent the equation of the complete line.
Given Data
She had a tough time at first and placed only 5 tiles the first day. She started to go faster, and by the end of day 4, she had placed 35 tiles.
Points are:
(1,5) (4,35)
Slope = [tex]\frac{30}{3}[/tex]
Slope = 10
y - y₁ = m(x -x₁)
y - 5 = m(x- 1)
For 100, it will need,
100 - 35 = 10(x-4)
65 = 10x - 40
105 = 10x
x = 10.5
It will take 11 days to place all of the 100 tiles needed to finish the floor.
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convert -5C into fehrenheit
okay soo.. Vance wants to determine if an old photo frame is still rectangular. The height of the frame is 8 inches, the base is 6 inches and the diagonal is 10 inches long. Is the old photo frame still rectangular? how do you know?
We can check this using Pythagoras' theorem.
Explain Pythagoras' theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It asserts that the area of the square with the hypotenuse (the side opposite the right angle) equals the sum of the areas of the squares with the other two sides. This theorem may be expressed as an equation linking the lengths of the legs a, b, and the hypotenuse c, which is known as the Pythagorean equation: a² + b² = c²
According to Pythagoras' theorem, as we see a² + b² = c²
6² + 8² = 10², so the photo frame is still a rectangle.
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help asap pls!!!!!!!!!
Answer:
z=70 y=98
Step-by-step explanation:
180-110=70=z
70+87+105=262
360-262=98=y
Whats x+7y=-39?
Please help me and show me how to work this whole thing out thank you so much!!!
Answer:
Step-by-step explanation:
Let's solve for x.
x+7y=−39
Step 1: Add -7y to both sides.
x+7y+−7y=−39+−7y
x=−7y−39
Let's solve for y.
x+7y=−39
Step 1: Add -x to both sides.
x+7y+−x=−39+−x
7y=−x−39
Step 2: Divide both sides by 7.
7y/7 = −x−39/7
y= −1/7x+−39/7
A career counselor decides to make monthly payments of $150 on credit card debt of $3,482.46 and discontinue using that credit card. Assuming the monthly interest rate is 1.55%, it will take the counselor approximately 30 months to repay the debt. How many fewer months would it take to repay the debt if the counselor makes monthly payments of $200? (Round your answer to the nearest month.)
The $150 monthly payment on the $3,482.46 credit card loan at 1.55% monthly interest rate gives the number of fewer months it would take to repay the loan if the monthly payment is $200 as 10 months
What is a monthly interest rate?A monthly interest rate is obtained from an annual interest rate by dividing it by 12.
The monthly payment formula is presented as follows;
[tex] \displaystyle{M = \frac{P \cdot r \cdot (1 + r)^{n} }{ (1 + r)^{n} - 1}} [/tex]
Where;
M = The monthly payments = $150
P = The loan amount = $3,482.46
r = The monthly interest rate = 1.55% = 0.0155
n = The number of periods (monthly payments) = 30
When the monthly payment, M = $150, it takes the career councilor approximately 30 months for the debt to be repaid.
When the monthly payment, M = $200, we have;
[tex]\displaystyle{200 \approx \frac{3482.46 \times 0.0155 \times (1 + 0.0155)^{n} }{ (1 + 0.0155)^{n} - 1}} [/tex]
Which gives;
[tex] \displaystyle{200 \times ((1 + 0.0155)^{n} - 1)= 3482.76 \times 0.0155 \times (1 + 0.0155)^{n}} [/tex]
[tex] \displaystyle{200 \times (1.0155)^{n} - 200 = 53.98278 \times (1.0155)^{n}} [/tex]
[tex]\displaystyle{ 146.017 \times (1.0155)^{n} = 200 }[/tex]
n•ln(1.0155) ≈ ln(1.3697)
[tex] n = \frac{ln(1.3697)}{ln(1.0155)} \approx 20.45[/tex]
The number of months it will take to pay back the loan using a monthly payment of $200 is therefore approximately 20 months
The number of fewer months it takes to repay the loan is therefore;
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