In equation 7(5x + 2) = -4(6 - 5x), Using the Distributive Property, we get 35x + 14 = -24 + 20x. So, the correct option is D).
To solve the equation 7(5x + 2) = -4(6 - 5x), a good first step is to use the Distributive Property to simplify both sides of the equation. Distributing the 7 and -4 on the left and right sides, respectively, we get
35x + 14 = -24 - 20x.
Next, we can combine like terms by adding 20x to both sides to get 55x + 14 = -24. Then, subtracting 14 from both sides, we get 55x = -38. Finally, we can solve for x by dividing both sides by 55, giving us x = -38/55. Therefore, the solution to the equation is x = -38/55.
The evaluation process involves performing arithmetic operations in a logical order to simplify the equation step-by-step until a solution is reached. So, the correct answer is D).
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3. Each sample of water from a river has a 10% chance of contamination by a particular heavy metal. Find the probability that in 18 independent samples taken from the same river, only two samples were contaminated. [3 marks]
The probability that, out of 18 independent samples received from one river, just two were contaminated is 0.8438.
Explain about the independent samples?Randomly chosen samples are known as independent samples since their results are independent of other observations' values. The premise that sampling are independent underlies many statistical analysis.When each trial possesses the same probability of achieving a given value, the number of trials or observations is represented using the binomial distribution.In the following 18 samples to be evaluated,
Let X = the number of samples that now the pollutant is present in.
Thus, with p = 0.10 and n = 18, X is a binomial random variable.
Using the binomial theorem:
[tex](^{n} _{r} ) p^{x} q^{n-x}[/tex]
p = 0.10
q = 1 - 0.10 = 0.9
n = 18
The likelihood that only two samples out of 18 obtained in different ways from the same river were polluted
P(x = 2) = [tex](^{18} _{2} ) (0.1)^{2} (0.9)^{18-2}[/tex]
= [tex](^{18} _{2} ) (0.1)^{2} (0.9)^{16}[/tex]
= 153 x 0.01 x 0.1853
= 0.8438
Thus, the probability that, out of 18 separate samples received from one river, just two were contaminated is 0.8438.
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Amadou is going to invest $16,000 and leave it in an account for 20 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest tenth of a percent, would be required in order for Amadou to end up with $44,000?
Jonathan says that the function represented by the graph is always decreasing. Is he correct? fI not, where is the function decreasing?
Explain your reasoning.
If the slope of the graph is increasing from positive x-axis to negative x-axis, then the function is not that decreasing. Therefore, Jonathan's statement is incorrect.
What is the graph function about?The function is decreasing on intervals where the slope is negative. In this case, since the slope is increasing from positive x-axis to negative x-axis, the function is decreasing on the interval where x is negative.
To determine this interval more precisely, we would need to find the x-value(s) where the slope changes sign from positive to negative. These x-values correspond to critical points, such as local maximums or minimums. The function is decreasing before a local maximum and after a local minimum.
Therefore, Jonathan's statement is not correct, and the function represented by the graph is decreasing on the interval where x is negative.
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which of the following code segments assigns bonus correctly for all possible integer values of score ?
The code segment that assigns bonus correctly for all possible integer values of score is D, which uses nested if statements to implement the game's rules for assigning a value to bonus based on the value of score.
The code segment that assigns bonus correctly for all possible integer values of score is D:
IF(score < 50)
{
bonus ← Ø
}
ELSE
{
IF (score > 100)
{
bonus ← score (10)
}
ELSE
{
bonus ← score
}
}
This code segment correctly implements the rules for assigning a value to bonus based on the value of score. It first checks if score is less than 50, and if so, it assigns 0 to bonus. If score is greater than or equal to 50, it checks if score is greater than 100, and if so, it assigns 10 times score to bonus. Otherwise, it assigns score to bonus. This covers all possible integer values of score and ensures that bonus is assigned correctly according to the game's rules.
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Complete question is in the image attached below
T/F. Star clusters with lots of bright, blue stars of spectral type O and B are generally younger than clusters that don't have any such stars.
The given statement "Star clusters with lots of bright, blue stars of spectral type O and B are generally younger than clusters that don't have any such stars." is True. The reason for this is that O and B stars are short-lived and burn through their fuel quickly.
The reason for this is that O and B stars burn through their fuel quickly, causing them to exhaust their nuclear fuel and end their lives in a relatively short period, typically within a few tens of millions of years.
On the other hand, stars of lower mass and cooler temperatures, like G and K type stars like our sun, have longer lifetimes and take billions of years to exhaust their nuclear fuel.
Therefore, clusters without any bright, blue stars are likely to have evolved for longer periods, allowing these short-lived stars to have already expired.
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A normal distribution is informally described as a probability distribution that is "bell-shaped" when graphed. Draw a rough sketch of a curve having the bell shape that is characteristic of a normal distribution.
Choose the correct answer below.
A.
A symmetric curve is plotted over a horizontal scale. From left to right, the curve starts on the horizontal scale and rises at a decreasing rate to a central peak before falling at an increasing rate to the horizontal scale.
B.
A symmetric curve is plotted over a horizontal scale. From left to right, the curve starts above the horizontal scale, falls from the horizontal at an increasing rate, then falls at a decreasing rate to a central minimum before rising at an increasing rate, then rising at a decreasing rate, and finally becoming nearly horizontal.
C.
A symmetric curve is plotted over a horizontal scale. From left to right, the curve starts on the horizontal scale, rises from horizontal at an increasing rate, then rises at a decreasing rate to a central peak before falling at an increasing rate, then falling at a decreasing rate, and finally approaches the horizontal scale.
The correct answer is C. A normal distribution is a symmetric probability distribution that is bell-shaped when graphed. When plotted on a horizontal scale, the curve starts on the horizontal axis, rises to a central peak, and then falls back to the horizontal axis.
The curve is symmetric, meaning that the left and right halves of the curve are mirror images of each other. The curve approaches the horizontal axis but never touches it, which indicates that there is a non-zero probability of observing values at any distance from the mean, although the probability decreases as the distance from the mean increases.
Normal distribution is a type of probability distribution that is commonly found in natural and social phenomena, where the majority of the observations tend to cluster around the mean, with fewer observations further away from the mean.
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what is 7 in x 3 in x 6 in x 4 in x 15 in=
Answer:
7,560 inches.
Step-by-step explanation:
Given: 7 in x 3 in x 6 in x 4 in x 15 in = ?
First, multiply 7 and 3:
21 in x 6 in x 4 in x 15 in
Then multiply 21 and 6:
126 in x 4 in x 15 in
Then multiply 4 and 15:
126 in x 60 in
Finally, multiply 126 and 60:
= 7,560 inches.
How this app works? Why I can’t find any answers? I need pay for points when I ask questions? I subscribe this app and when I’m lucky to the answers almost the answers are wrong
6x+16=8x-18 i need x
Answer:
x = 17
Step-by-step explanation:
Subtract 6x from both sides:
2x - 18 = 16
Add 18 on both sides to isolate the variable:
2x = 18 + 16
2x = 34
Divide by 2: x = 17
Prove the following using a direct proof:
The sum of the squares of 4 consecutive integers is an even integer
It ahs been proved by mathematical induction that the sum of the squares of 4 consecutive integers is an even integer.
How to solve Mathematical Induction?To prove that the sum of the squares of 4 consecutive integers is an even integer.
Let x, (x + 1), (x + 2), (x + 3) be the four consecutive integers.
The sum of the squares of these integers are:
S = x² + (x + 1)² + (x + 2)² + (x + 3)²
Expanding this gives us:
S = 4x² + 12x + 14
Simplifying this gives:
S = 2(2x² + 6x + 7)
The number 2x² + 6x + 7 is either even number or odd number.
However, since it is multiplied by 2x² + 6x + 7, the sum will always be an even number.
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olivia and kieran share money in the ratio 2:5. Olivia gets £42. how much did kieran get?
[tex] \huge \: \tt \green{Answer} [/tex]
Olivia and kieran share ratio 2 : 5
[tex] \texttt{olivia's share \: of \: money = £42 }= \frac{2}{7} \\ [/tex]
Total Amount of Money = Olivia's share of money × Reciprocal of olivia's share
[tex] \tt \: = > 42 \times \frac{7}{2} \\ \\ = > 147[/tex]
Kieran's share of Money =
[tex] = > 147 \times \frac{5}{7} \\ \\ = > \sf{ \pink{£105}}[/tex]
10 points!!! ASAP PLEASE HELP FIND THE AREA AND THE PERIMETER!!
Answer:
Area = 559.17 square feet
Perimeter = 94.26 ft
Step-by-step explanation:
Make sure all the units are the same and consistent.
r = radius of semi-circle
= [tex]\frac{Diameter}{2}[/tex]
= [tex]\frac{18}{2}[/tex] ft
= 9 ft
Area of composite figure = Area of rectangle + Area of semi-circle:
= [Length × Breadth] + [[tex]\frac{1}{2}[/tex] × (Area of circle)]
= [24 ft × 18 ft] + [[tex]\frac{1}{2}[/tex] × ([tex]\pi r^{2}[/tex])]
= 432 [tex]ft^{2}[/tex] + [[tex]\frac{1}{2}[/tex] × ([tex]\pi 9^{2}[/tex])] [tex]ft^{2}[/tex]
= 432 + [[tex]\frac{1}{2}[/tex] × (3.14) ×(81)]
= 559.17[tex]ft^{2}[/tex]
Perimeter of composite figure =
Circumference of semi-circle + 3 outer sides of rectangle:
= [[tex]\frac{1}{2}[/tex] × [tex]2\pi r[/tex]] + [24 + 18 + 24]
= ( [tex]\pi r[/tex] + 66) ft
= [(3.14)(9) + 66] ft
= 94.26 ft
I need help with this
Answer:
Angle AIC is vertical.
Step-by-step explanation:
Defn of vertical angles
This year, the ratio of Alan's age to Bernice's age is 1:2. Four years ago, the total age of Alan and Bernice was 55 years. How old is Alan this year?
Answer:
21 years old
Step-by-step explanation:
Set Alan's age as x, Bernice's age as y
2x=y
x-4+y-4=55
x+y=63
3y=63
x=21
y=42
Sharon used 8 roses and 6 tulips to make a bouquet. The tape diagram below shows the relationship between the number of roses and the number of tulips in the bouquet.
Answer:
Step-by-step explanation:
its C
Using the data table, what is the probability that Baxter’s Shelties will NOT have a Tri-Color puppy this year? Justify your decision.
can’t seem to get this any help
A. 27.4
B. 37.3
C. 40.0
D. 42.0
Answer:
Step-by-step explanation:
In the boys triangle:
[tex]tanx=\frac{56}{48}[/tex]
[tex]x=tan^{-1}(\frac{56}{48} )=49.4\textdegree[/tex]
Because triangles are similar:
[tex]tan 49.8=\frac{h}{32}[/tex]
[tex]h=32tan49.8 = 37.3[/tex]
I need your help to buy a door for my house. I have a scale drawing for the door I want but I am not sure of the true size. In the scale drawing the length is 4 in and the width as 7in. The scale for the door is 1 in = 1.5 ft. What are the actual measurements of the door?
Answer:
According to the scale, 1 inch on the drawing represents 1.5 feet in real life. So, to find the actual length of the door, we need to multiply the length on the drawing by the scale factor:
4 inches x 1.5 feet/inch = 6 feet
Similarly, to find the actual width of the door, we need to multiply the width on the drawing by the scale factor:
7 inches x 1.5 feet/inch = 10.5 feet
Therefore, the actual measurements of the door are 6 feet by 10.5 feet.
which of the following correctly relates the measures of the diameter (d) and radius (r) of a circle
The equation which correctly relates the measure of diameter and radius of a circle is (c) r = d/2.
The Diameter (d) of a circle is defined as the distance across the circle through its center. The radius (r) of a circle is defined as the distance from the center of the circle to any point on the circle.
We know that the radius of the circle is half of diameter, because it extends from the center to the edge of the circle, while the diameter extends all the way across the circle.
So, we can express the relationship between d and r as:
⇒ d = 2r
To solve for r, we can divide both sides by 2:
We get,
⇒ r = d/2
Therefore, The correct equation is Option (c) r = d/2.
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The given question is incomplete, the complete question is
Which of the following correctly relates the measures of the diameter (d) and radius (r) of a circle?
(a) d = r/2
(b) r = 2d
(c) r = d/2
(d) d = 2/r
100 POINTS + BRAINLIEST PLS BE FAST!!
i) Find the mean, median, and mode of the frequency table as follows:
Mean = 6.6Median = 8Mode = 3.ii) The average that justifies the teacher's statement congratulating the class that 'over three quarters were above average' is the average mark of 10, which is 5.
What are the mean, median, and mode?The mean refers to the average or the quotient of the total values divided by the number of items.
The median is the middle value in the data, which occurs with marks 8 for the 13th and 14th students.
The mode is the value that occurs most frequently, which is 3 which occurs 6 times.
Frequency Table:
Mark Frequency Cumulative Frequency
3 6 18 (0 + 3 x 6)
4 3 30 (18 + 4 x 3)
5 1 35 (30 + 5 x 1)
6 2 47 (35 + 6 x 2)
7 0 47 (47 + 7 x 0)
8 5 87 (47 + 8 x 5)
9 5 132 (87 + 9 x 5)
10 4 172 (132 + 10 x 4)
Mean = 6.6 (172/26)
Median = 8
Mode = 3
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find the value of the derivative (if it exists) at
each indicated extremum
Answer:
The value of the derivative at (-2/3, 2√3/3) is zero.
Step-by-step explanation:
Given function:
[tex]f(x)=-3x\sqrt{x+1}[/tex]
To differentiate the given function, use the product rule and the chain rule of differentiation.
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Product Rule of Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{7 cm}\underline{Differentiating $[f(x)]^n$}\\\\If $y=[f(x)]^n$, then $\dfrac{\text{d}y}{\text{d}x}=n[f(x)]^{n-1} f'(x)$\\\end{minipage}}[/tex]
[tex]\begin{aligned}\textsf{Let}\;u &= -3x& \implies \dfrac{\text{d}u}{\text{d}{x}} &= -3\\\\\textsf{Let}\;v &= \sqrt{x+1}& \implies \dfrac{\text{d}v}{\text{d}{x}} &=\dfrac{1}{2} \cdot (x+1)^{-\frac{1}{2}}\cdot 1=\dfrac{1}{2\sqrt{x+1}}\end{aligned}[/tex]
Apply the product rule:
[tex]\implies f'(x) =u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}[/tex]
[tex]\implies f'(x)=-3x \cdot \dfrac{1}{2\sqrt{x+1}}+\sqrt{x+1}\cdot -3[/tex]
[tex]\implies f'(x)=- \dfrac{3x}{2\sqrt{x+1}}-3\sqrt{x+1}[/tex]
Simplify:
[tex]\implies f'(x)=- \dfrac{3x}{2\sqrt{x+1}}-\dfrac{3\sqrt{x+1} \cdot 2\sqrt{x+1}}{2\sqrt{x+1}}[/tex]
[tex]\implies f'(x)=- \dfrac{3x}{2\sqrt{x+1}}-\dfrac{6(x+1)}{2\sqrt{x+1}}[/tex]
[tex]\implies f'(x)=- \dfrac{3x+6(x+1)}{2\sqrt{x+1}}[/tex]
[tex]\implies f'(x)=- \dfrac{9x+6}{2\sqrt{x+1}}[/tex]
An extremum is a point where a function has a maximum or minimum value.
From inspection of the given graph, the maximum point of the function is (-2/3, 2√3/3).
To determine the value of the derivative at the maximum point, substitute x = -2/3 into the differentiated function.
[tex]\begin{aligned}\implies f'\left(-\dfrac{2}{3}\right)&=- \dfrac{9\left(-\dfrac{2}{3}\right)+6}{2\sqrt{\left(-\dfrac{2}{3}\right)+1}}\\\\&=-\dfrac{0}{2\sqrt{\dfrac{1}{3}}}\\\\&=0 \end{aligned}[/tex]
Therefore, the value of the derivative at (-2/3, 2√3/3) is zero.
Consider the function f (x) = -2/3x + 5.
What is f(-1/2)?
Enter your answer, as a simplified fraction, in the box.
f(-1/2) =
Answer: f(-1/2) = 16/3
Step-by-step explanation:
Substituting -1/2 for x in the given function:
f(-1/2) = (-2/3)(-1/2) + 5
f(-1/2) = 1/3 + 5
f(-1/2) = 16/3
Therefore, f(-1/2) = 16/3.
Karina is making a quilt and she has determined she needs 420 square inches of green fabric and 688 square
inches of burgundy. How many square yards of each material will she need? Round your answers up to the
nearest quarter yard.
The green fabric:
square yards
The burgundy fabric:
How many total yards of fabric will she have to buy?
square yards
square yards
1. The total yards of each fabric that Karina will buy to make a quilt is as follows:
a) Green Fabric = 12 square yards
b) Burgundy Fabric = 19 square yards
2. The total yards of fabric she will buy is 31 square yards.
How are the total determined?The total yards of fabric can be determined by unit conversion using division operation.
Given that 36 inches = 1 yard, the square inches of fabric are converted to square yards by dividing the total by 36.
The total number of green fabric Karina requires = 420 square inches
= 12 square yards (420/36)
The total number of burgundy fabric Karina requires = 688 square inches
= 19 square yards (688/36)
The total number of fabric (green and burgundy) = 1,108 square inches (420 + 688)
36 inches = 1 yard
1,108 inches = 30.78 square yards (1,108/36)
= 31 square yards or (12 + 19)
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If A = [ 1 2 4 0 5 6 ] and B= [ 7 3 2 5 1 9] find C= A+B and D=A-B
Step 1: Arrange the arrays so that A and B are in the same order: A = [ 1 2 4 0 5 6 ], B = [ 7 3 2 5 1 9]
Step 2: To find C = A+B, add each element of A and B together.
C = [1+7, 2+3, 4+2, 0+5, 5+1, 6+9]
C = [8, 5, 6, 5, 6, 15]
Step 3: To find D = A-B, subtract each element of B from A.
D = [1-7, 2-3, 4-2, 0-5, 5-1, 6-9]
D = [-6, -1, 2, -5, 4, -3]
According to a poll, about % of adults in a country bet on professional sports. Data indicates that % of the adult population in this country is male. Complete parts (a) through (e).
(b) Assuming that betting is independent of gender, compute the probability that an adult from this country selected at random is a male and bets on professional sports.
P(male and bets on professional sports)
0.0568
(c) Using the result in part (b), compute the probability that an adult from this country selected at random is male or bets on professional sports.
P(male or bets on professional sports)
0.5362
(d) The poll data indicated that 7.3% of adults in this country are males and bet on professional sports. What does this indicate about the assumption in part (b)?
A.
The assumption was incorrect and the events are not independent.
Part 5
(e) How will the information in part (d) affect the probability you computed in part (c)? Select the correct choice below and fill in any answer boxes within your choice.
A.
P(males or bets on professional sports) = ?
a) D. No. A person can be both male and bet on professional sports at the same time
How to solveb) If the events A and B are independent, P(A&B) = P(A) x P(B)
P(male and also bets on professional sports) = 0.484x0.13 = 0.0629
c) P(male or bets in professional sports) = P(male) + P(bets in professional sports) - P(male and also bets on professional sports)
= 0.484 + 0.13 - 0.0629
= 0.5511
d) A. The assumption was incorrect and the events are not independent
(if the were independent, the percentage would have been 6.29)
e) A. P(male or bets on professional sports = 0.484 + 0.13 - 0.081
= 0.5330
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Graph the linear equation.
42 + 6y = -12
Plot two points on the line to graph the line.
The graph of the linear function 4x + 6y = -12 is given by the image presented at the end of the answer.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The function for this problem is given as follows:
4x + 6y = -12.
In slope-intercept form, the function is given as follows:
6y = -4x - 12.
y = -2x/3 - 2.
The slope and the intercept are given as follows:
Intercept of b = -2, meaning that when x = 0, y = -2.Slope of -2/3, meaning that when x decays by 3, y increases by two, hence the graph also passes through point (-3,0).More can be learned about linear functions at https://brainly.com/question/24808124
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The roots of a quadratic equation a x +b x +c =0 are (2+i √2)/3 and (2−i √2)/3 . Find the values of b and c if a = −1.
[tex]\begin{cases} x=\frac{2+i\sqrt{2}}{3}\implies 3x=2+i\sqrt{2}\implies 3x-2-i\sqrt{2}=0\\\\ x=\frac{2-i\sqrt{2}}{3}\implies 3x=2-i\sqrt{2}\implies 3x-2+i\sqrt{2}=0 \end{cases} \\\\\\ \stackrel{ \textit{original polynomial} }{a(3x-2-i\sqrt{2})(3x-2+i\sqrt{2})=\stackrel{ 0 }{y}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{ \textit{difference of squares} }{[(3x-2)-(i\sqrt{2})][(3x-2)+(i\sqrt{2})]}\implies (3x-2)^2-(i\sqrt{2})^2 \\\\\\ (9x^2-12x+4)-(2i^2)\implies 9x^2-12x+4-(2(-1)) \\\\\\ 9x^2-12x+4+2\implies 9x^2-12x+6 \\\\[-0.35em] ~\dotfill\\\\ a(9x^2-12x+6)=y\hspace{5em}\stackrel{\textit{now let's make}}{a=-\frac{1}{9}} \\\\\\ -\cfrac{1}{9}(9x^2-12x+6)=y\implies \boxed{-x^2+\cfrac{4}{3}x-\cfrac{2}{3}=y}[/tex]
I will mark you brainiest!
In a triangle, the interior angles add up to 180º.
True
False
Answer:
it should be true because sum of 3 interior angle of a triangle is 180 degree
Answer:
True.
Step-by-step explanation:
A triangle's angles add up to 180 degrees because one exterior angle is equal to the sum of the other two angles in the triangle. In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the third angle to make a 180 angle.
Use the equation f=d–5 to find the value of f when d=7.
Answer:
2
Step-by-step explanation:
since d=7 and the equation is d-5 in the place of d we'll put 7 therefore 7-5=2
Se depositan $ 8.000 en un banco que reconoce una tasa de interés del 36% anual, capitalizable mensualmente. ¿Cuál será el monto acumulado en cuatro años?
Answer:
Se depositan $ 8.000 en un banco que reconoce una tasa de interés del 36% anual, capitalizable mensualmente. ¿Cuál será el monto acumulado en cuatro años?
Step-by-step explanation:
Para resolver este problema, podemos utilizar la fórmula del interés compuesto:
A = P*(1 + r/n)^(n*t)
Donde:
A: el monto acumulado después de t años
P: el capital inicial
r: la tasa de interés anual
n: el número de veces que se capitaliza el interés por año
t: el tiempo en años
En este caso, tenemos:
P = $8.000
r = 36% = 0.36
n = 12 (ya que la tasa de interés se capitaliza mensualmente)
t = 4 años
Sustituyendo estos valores en la fórmula, obtenemos:
A = $8.000*(1 + 0.36/12)^(124)
A = $8.000(1 + 0.03)^48
A = $8.000*(1.03)^48
A = $16.751,83
Por lo tanto, el monto acumulado en cuatro años será de $16.751,83.
