Answer: 0.24z
Step-by-step explanation: If you make 24% a decimal you will get 0.24. Then you make your equation 0.24z or 0.24 x z .
A study found that the mean amount of time cars spent in drive-throughs of a certain fast-food restaurant was 137.5 seconds. Assuming drive-through times are normally distributed with a standard deviation of 27 seconds, complete parts below:
The probability that a randomly selected car will get through the restaurant's drive-through in less than 101 seconds is -1.3
What is normal distribution ?
Normal distribution, also known as Gaussian distribution or bell curve, is a continuous probability distribution that is commonly used in statistical analysis to model real-world phenomena. A normal distribution is characterized by its mean (μ) and standard deviation (σ), and is symmetrical around its mean. The bell-shaped curve of a normal distribution is determined by the empirical rule, also known as the 68-95-99.7 rule, which states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Many natural phenomena, such as human height and weight, tend to follow a normal distribution, and this makes normal distribution a useful tool in statistical analysis and modeling.
According to the question:
(a) To find the probability that a randomly selected car will get through the restaurant's drive-through in less than 101 seconds, we need to standardize the value using the formula:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean drive-through time, σ is the standard deviation, and z is the corresponding z-score.
Plugging in the values given, we get:
z = (101 - 137.5) / 27 = -1.3
Using a standard normal distribution table or a calculator, we find that the probability of getting a z-score less than -1.35 is 0.0885. Therefore, the probability that a randomly selected car will get through the restaurant's drive-through in less than 101 seconds is:
P(X < 101) = P(Z < -1.35) = 0.0885 (rounded to four decimal places).
(b) To find the probability that a randomly selected car will spend more than 176 seconds in the restaurant's drive-through, we again need to standardize the value:
z = (176 - 137.5) / 27 = 1.42
Using a standard normal distribution table or a calculator, we find that the probability of getting a z-score greater than 1.42 is 0.0788. Therefore, the probability that a randomly selected car will spend more than 176 seconds in the restaurant's drive-through is:
P(X > 176) = P(Z > 1.42) = 0.0788 (rounded to four decimal places).
(c) To find the proportion of cars that spend between 2 and 3 minutes (120 and 180 seconds) in the restaurant's drive-through, we need to standardize the values of the lower and upper limits:
z1 = (120 - 137.5) / 27 = -0.65
z2 = (180 - 137.5) / 27 = 1.57
Using a standard normal distribution table or a calculator, we find the area between these two z-scores to be 0.6591. Therefore, the proportion of cars that spend between 2 and 3 minutes in the restaurant's drive-through is:
P(120 < X < 180) = P(-0.65 < Z < 1.57) = 0.6591 (rounded to four decimal places).
(d) To find the probability that a car spends more than 3 minutes (180 seconds) in the restaurant's drive-through, we standardize the value:
z = (180 - 137.5) / 27 = 1.57
Using a standard normal distribution table or a calculator, we find that the probability of getting a z-score greater than 1.57 is 0.0582. Since this probability is less than 0.05, it would be considered unusual for a car to spend more than 3 minutes in the restaurant's drive-through.
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Use mental math to assess reasonableness. Explain your thinking
Cameron spends $130 on a gaming system and $80 on video games. He
says he spends about $215. Is his statement reasonable? Explain your
thinking.
To assess the reasonableness of Cameron's statement that he spent about $215 on a gaming system and video games, we can use mental math to estimate the total cost.
We know that he spent $130 on a gaming system and $80 on video games. If we round $80 up to $100 and add it to $130, we get:
$130 + $100 = $230
So based on this estimate, it seems like Cameron's statement of spending about $215 is not entirely accurate. However, it is close to the actual total cost, which is within 10% of the estimated total.
Therefore, we can say that while Cameron's statement may not be entirely precise, it is reasonably close to the actual total cost and can be considered reasonable.
Halston takes two pieces of fruit for a snack. What is the probability that she chooses two pieces of fruit that are not bananas.
Fruit Amount
Pear 3
Orange 4
Banana 2
Answer:
The total number of fruits Halston can choose is 3 + 4 + 2 = 9.
The number of ways she can choose two fruits without restrictions is 9C2 = (98)/(21) = 36.
The number of ways she can choose two fruits where both are bananas is 2C2 = 1.
Therefore, the number of ways she can choose two fruits that are not bananas is 36 - 1 = 35.
So, the probability that Halston chooses two fruits that are not bananas is:
35/36
Therefore, the probability that Halston chooses two fruits that are not bananas is 35/36.
Is it possible to become smart without going to school?
Answer: it depends; if exam day, no
Step-by-step explanation:
help I don't understand
With the help of proportions in the given similar triangles we know that the value of x is 3.5 units.
What is triangle similarity?Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.
One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.
These three theorems—Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS)—are reliable techniques for figuring out how similar triangles are to one another.
So, in the given situation:
TR and WY are as follows:
TR/WU
24/2
2/1
Similarly,
TS/WV
2/1
7/x
7/3.5
Therefore, with the help of proportions in the given similar triangles we know that the value of x is 3.5 units.
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the sides of a triangle are in the ratio of 3:4:5 if its perimeter is 84 cm, then what is its area
Let's assume,
side a = 3x side b = 4x side c = 5xWe know that perimeter of triangle is sum of all the sides.
a + b + c = Perimeter
3x + 4x + 5x = 84
12x = 84
x = 84/12
x = 7
Hence,
side a = 3x = 3(7) = 21 cmside b = 4x =4(7) = 28 cmside c = 5x = 5(7) = 35 cmNow,
Semi-perimeter = Perimeter/2
= 84/2
= 42 cm
Using heron's formula,
Area = s√s - a)(s -b)(s -c)Where,
s is semi-perimetera, b and c are sides of triangle.= √42(42- 21)(42 ; 28)(42- 35)
= √42( 21 × 14 × 7)
= √42 × 2058
= √ 86,436
= 294 cm²
Therefore, Area of the triangle is 294 cm²
Somebody pls help meee!!
Anybody??
Answer:
85 degrees.
Step-by-step explanation:
These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.
Find the value of x.
13)
O
(2x+8)
62°
20 22 Kuta Software LLC.
14)
A
(x-4) (2x+1)
All rights reserve d-1-Made with Infinite Geometry.
Answer:
Without additional information or context, it is not possible to find the value of x for the given diagrams. Please provide more information or the full problem statement.
6. Cisterns are large tanks used to store water. The larger of the cisterns at the right is completely filled with water. If enough water is taken from the larger cistem to completely fill the smaller empty cistern, how many cubic feet of water will remain in the larger cistern? 3 ft. 2 ft. 2 ft. 3 ft. 1 ft.
Answer: 6
Step-by-step explanation: We are told that the large cistern is completely filled shown with the larger volume. To find volume, the formula is lxwxh and if you apply that to the model, the larger cistern has a volume of 24 ft cubed which means 24 is completely filled. If we calculate the volume of the smaller cistern, it is 6. The question asks us how many cubic feet will be left when the larger cistern pours enough water to completely fill up the smaller cistern (24). So we do subtraction, 24-6= 18 meaning 18 is the number that is going to get poured from the big to the small cistern to make it 24 or, completely filled. And when we subtract the 18 from 24 (because we poured 18 from the large one to the small one to make it full), we get 6. 6 is how much is left after the larger cistern poured 18 to fill up the smaller cistern.
If f(x) =X+2/x^2 -9
and g(x)=11/x^2+ 3x
(a) find f(x) + g(x)
(b) list all of the excluded values
(c) classify each type of discontinuity
The sum of the two functions f(x) + g(x) is (x+2)/(x^2 - 9) + 11/(x^2 + 3x)
Function calculation.
(a) To find f(x) + g(x), we simply add the two functions together:
f(x) + g(x) = (x+2)/(x^2 - 9) + 11/(x^2 + 3x)
(b) To determine the excluded values, we need to look for values of x that make the denominators of the two functions equal to zero. The denominators are:
x^2 - 9 and x^2 + 3x
Setting these equal to zero and solving for x, we get:
x^2 - 9 = 0 => x = ±3
x^2 + 3x = 0 => x(x+3) = 0 => x = 0 or x = -3
Therefore, the excluded values are x = ±3 and x = 0.
(c) To classify the type of discontinuity at each of the excluded values, we need to examine the behavior of the function as x approaches these values.
At x = ±3, the denominators of both functions become zero, which means that the function is undefined at these values. This creates a vertical asymptote, which is a type of infinite discontinuity.
At x = 0, the denominator of g(x) becomes zero, but the denominator of f(x) does not. This creates a removable discontinuity, because we can define f(0) separately to make the function continuous at this point. Specifically, we can set f(0) = 2/(-9) = -2/9 to remove the discontinuity.
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2×1+4×1/100 please help
Answer:2.04
Step-by-step explanation:
3. What is the angle of rotation of the following figure?
180°
60°
90°
45°
Answer:
180
Step-by-step explanation:
Finding the area and perimeter
Answer:
Lion area: 60
Lion Perimeter: 34
Tiger Area: 60
Tiger perimeter: 64
Step-by-step explanation:
DIRECTIONS: Use this information to answer Parts A, B, and C.
Each small square on this scale weighs 1 unit. Each larger square weighs 10 units. The weight of the triangle x is unknown. The scale is balanced. Look at the image.
A balanced scale. On one side there are four small squares and three large squares each labeled ten. On the other side there are two small squares, two large squares each labeled ten, and a triangle labeled x.
Question 1
Part A
Write an equation to represent relationship of the weights shown on the scale.
Enter the correct answer in the box.
An equation to represent relationship of the weights shown on the scale include the following: 22 + x = 34.
How to write an equation to represent relationship of the weights?Based on the information provided about the weights on this balanced scale, we can logically deduce the following parameters;
Each small square = 1 unit.
Each larger square = 10 units.
The variable x represent the weight of the triangle.
Since there are four small squares and three large squares each labeled ten on one side of this balanced scale, we have:
Total weight = 4(1) + 3(10)
Total weight = 34 units.
Similarly, there are two small squares, two large squares, and a triangle labeled x on the other side of this balanced scale, we have:
Total weight = 2(1) + 2(10) + x
Total weight = 22 + x
By equating the two equations, we have:
22 + x = 34
x = 34 - 22
x = 12
In conclusion, there are 34 units on each side of this balanced scale.
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The first detection of gravitational waves involved the merger of two black holes in a galaxy 1.3 billion light-years away. If the gravitational waves spread out from this event isotropically (the same in all directions) and just reached us, how large a volume have the gravitational waves traveled through? Give your answer in cubic light-years. Hint: -The volume of a sphere = 4/3πR3.
The gravitational waves would have traveled through a volume of approximately 3.244 x 10⁷⁴ cubic light-years.
What are gravitational waves?The space-time continuum is subject to gravitational waves, which move at the speed of light. They are caused by the acceleration of large objects that distort space-time around them, such as neutron stars or black holes.
The bending of space-time brought on by the existence of mass and energy is what Einstein's theory of general relativity refers to as gravity rather than a force.
The radius of the sphere can be determined using the formula:
R = Distance / Time
For 1.3 billion light years we have:
R = Distance / Time = 1.239 x 10²⁵ meters
Substituting the value in the volume:
V = (4/3) x π x R³ = 3.244 x 10⁷⁴ cubic light-years (approx)
Hence, the gravitational waves would have traveled through a volume of approximately 3.244 x 10⁷⁴ cubic light-years.
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Step-by-step explanation:
To solve the given equation, we can start by taking the square root of both sides of the equation:
(x – 7)^2 = 36
√((x – 7)^2) = ±√36
x – 7 = ±6
Now, we can solve for x by adding 7 to both sides of the equation for each case:
x – 7 = 6 or x – 7 = -6
x = 13 or x = 1
Therefore, the values of x that satisfy the equation are x = 13 and x = 1. The other values, x = -29 and x = 42, do not satisfy the equation.
factor 4t+2rt+8st completly
Given a right triangle with = 60° and the hypotenuse equal to 25 feet, which trigonometric
function would you use to solve for the opposite side?
cosine
secant
sine
tangent
We will use sine function, and length of the opposite side is [tex]\frac{25\sqrt{3}}{2}$[/tex] feet.
Explain about Sine function.To solve for the opposite side of the right triangle, we would use the sine function. In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.
In this problem, we are given that one angle of the right triangle is 60 degrees and the hypotenuse is 25 feet. Let's label the opposite side as x and the adjacent side as y. Then we can use the sine function:
[tex]$\sin 60^\circ = \frac{x}{25}$[/tex]
Simplifying the left side, we have:
[tex]$\frac{\sqrt{3}}{2} = \frac{x}{25}$[/tex]
Multiplying both sides by 25, we get:
[tex]$x = \frac{25\sqrt{3}}{2}$[/tex]
Therefore, the length of the opposite side is [tex]\frac{25\sqrt{3}}{2}$[/tex] feet.
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pls answer!!!!!!!!!!!!!!
The expressions in a single exponent are 9³/9⁹ = 9⁻⁶ and 14⁻³ * 14¹² = 14⁹
Diego's mistake is multiplying the expressions, wrongly
Rewriting the expressions in a single exponentExpression 1
Given that
9³/9⁹
To solve, we make use of the law of indices
So, we have
9³/9⁹ = 9⁻⁶
Expression 2
Here, we have
14⁻³ * 14¹²
Using the law of indices, we have
So, we have
14⁻³ * 14¹² = 14⁹
The mistake in Diego's expressionDiego's expression is given as
6⁴ * 8³ = 48⁷
The mistake in Diego's expression is that he multiplied 6 and 8, and then add the exponents
This is incorrect, and the actual solution is
6⁴ * 8³ = 1296* 512
6⁴ * 8³ = 2¹³ × 3⁴
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For a standard normal distribution, find:
P(z > -0.25)
Accοrding tο the standard nοrmal distributiοn, the prοbability that z is greater than -0.25 is 0.5987.
What is a standard nοrmal distributiοn?Nοrmal distributiοn, alsο knοwn as Gaussian distributiοn οr bell curve, is a prοbability distributiοn that describes the randοm variatiοn οf a cοntinuοus variable in a pοpulatiοn. In a standard nοrmal distributiοn, the mean is 0 and the standard deviatiοn is 1, and the curve is fully described by the parameters οf mean and standard deviatiοn. The nοrmal distributiοn is used in many statistical applicatiοns tο mοdel and analyze cοntinuοus data.
Using a standard nοrmal distributiοn table οr a calculatοr, we can find that the area tο the right οf z=-0.25 is apprοximately 0.5987.
Therefοre,
[tex]$$P(z > -0.25) = 1 - P(z \leq -0.25) = 1 - 0.4013 = 0.5987$$[/tex]
Sο the prοbability that z is greater than -0.25 is 0.5987.
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Complete Question
Find P(Z > 0.25), using the standard normal distribution. The average number of calories in a 1.5-ounce chocolate bar is 250. Suppose that the distribution of calories is approximately normal with standard deviation 10. Find the probability that a randomly selected chocolate bar will have between 230 and 260 calories. A single die is rolled 5 times. Find the probability of getting at least one number which is greater than 4. Given data values: 11, 3, 5, 12, 17, 13, 10, 6, 8, 21, 14, 20, 9, 15, 7. (a) Find the percentile rank for 10. (b) What value corresponds to the 70th percentile? A survey found that the American family rates an average of 25 pounds of glass garbage each year. Assume the standard deviation of the distribution is 7pounds. Find the probability that the mean of a sample of 49 families will be between 19 and 26 pounds.
To find my equation, shift f(x) = x^2 + 5 left 3
PLEASEEEE
Answer:
f(x) = (x+3)^2 + 5
Step-by-step explanation:
Hope this is right :)
Write numbers to make an expression equivalent to 5x - 4
Expression equivalent to 5x - 4 are 5(x - 4/5), 5x - 20/5, 10x/2 - 8/2 and 3(5x/3) - 4
How numbers to make an expression equivalent to 5x - 4To create an expression equivalent to 5x - 4, we need to use arithmetic operations such as addition, subtraction, multiplication, and division, along with numbers and variables. The goal is to manipulate the numbers and variables in a way that results in the same value as 5x - 4.
Here are some examples of how we can do this:
5(x - 4/5)
In this expression, we start with x and subtract 4/5 from it. Then we multiply the result by 5. This is equivalent to distributing the 5 to x and -4/5, which gives us 5x - 4.
5x - 20/5
Here, we simply subtract 20/5 (which simplifies to 4) from 5x. This gives us 5x - 4.
(25x - 20)/5
In this expression, we start with 25x and subtract 20 from it. Then we divide the result by 5. This is equivalent to simplifying the expression to 5x - 4.
10x/2 - 8/2
This expression might look a bit different, but it's still equivalent to 5x - 4. Here, we start with 10x and divide it by 2, which gives us 5x. Then we subtract 8/2 (which simplifies to 4) from it, giving us 5x - 4.
3(5x/3) - 4
In this expression, we start with 5x and divide it by 3. Then we multiply the result by 3, which gives us 5x. Finally, we subtract 4 from it, giving us 5x - 4.
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If the radius of a circle is 4, what is the circumference? Use pi
as 3.14.
please help<33
HELP PLEASE 7TH GRADE MATH MULTIPLE OPTION
What is the surface area of the cylinder represented by the net? Give your answers in terms of π.
Complete each sentence.
A net of a cylinder showing two circles, each touching one side of a rectangle between them. The radius of each circle is 3.2 centimeters. The side length of the rectangle that does not touch the circles is 8.7 centimeters.
The area of one circular base is
Choose...
π
cm2.
The perimeter of the circular base is
Choose...
π
cm.
The height of the cylinder is
cm.
The total surface area of the cylinder is
Choose...
π
cm2.
Answer:
Step-by-step explanation:
Area of one base:
[tex]A=\pi r^2=\pi (3.2)^2 =10.24\pi cm^2[/tex]
Perimeter of circle base:
[tex]P=2\pi r=2\times \pi \times 3.2 =6.4 \pi cm[/tex]
Height of cylinder:
[tex]h=8.7cm[/tex] (given in question)
Total surface area:
[tex]SA=[/tex] area 2 circles + area rectangle
[tex]=(2\times 10.24 \pi) +(6.4\pi\times 8.7)[/tex] (Area rectangle = cylinder height x
circle perimeter)
[tex]=239.26cm^2[/tex]
2. Match the quadratic equation to it's answer. Round to the nearest tenth if necessary.
1. 8x²+9-313
2. 32-25x²-4
3 -1-5x^2= -321
4. 3x²-75
5. 2x²-3=29
a. x=5,-5
b. x=8,-8
c. X=1.2=-1.2
d. x=6.2,-62
E. X=4,-4
Answer:
1-d
2-c
3-b
4-a
5-e
To match the quadratic equations to their answers, we need to solve each equation and compare the solutions with the given options. After solving each equation, the answers can be identified as a. x=5,-5; b. x=8,-8; c. x=1.2,-1.2; a. x=5,-5; e. x=4,-4.
Explanation:To match the quadratic equations to their answers, we need to solve each equation and compare the solutions with the given options. Let's go through each equation:
Solving 8x²+9-313=0 gives x = 5 or x = -5. So, the answer is a. x=5,-5.Solving 32-25x²-4=0 gives x = 8 or x = -8. So, the answer is b. x=8,-8.Solving -1-5x^2=-321 gives x = 1.2 or x = -1.2. So, the answer is c. x=1.2,-1.2.Solving 3x²-75=0 gives x = 5 or x = -5. So, the answer is a. x=5,-5.Solving 2x²-3=29 gives x = 4 or x = -4. So, the answer is e. x=4,-4.Learn more about Quadratic Equations here:https://brainly.com/question/34196754
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Elisabeth invests $2, 926 in an account earning 0.64% simple interest. How much money will she have earned in interest after 19 years? (Round it to two decimal places)
Answer:
Step-by-step explanation:
The simple interest formula is:
I = Prt
where I is the interest earned, P is the principal or initial investment, r is the annual interest rate as a decimal, and t is the time in years.
Substituting the given values:
P = $2,926
r = 0.64% = 0.0064 (as a decimal)
t = 19 years
I = 2,926 * 0.0064 * 19
I = $353.21
Therefore, Elisabeth will have earned $353.21 in interest after 19 years.
Find the probability of rolling an even number on a single die
The probability of rolling an even number on a single die is 1/2, or 50%. This can be calculated by considering the possible outcomes of rolling the die.
There are six possible outcomes, and three of these are even numbers (2, 4, and 6). Therefore, there is a 3/6, or 1/2, chance of rolling an even number. In terms of probability, this can be expressed as a fraction, percentage, or decimal. As a fraction, the probability of rolling an even number on a single die is 3/6, or 1/2. As a percentage, the probability of rolling an even number on a single die is 50%. As a decimal, the probability of rolling an even number on a single die is 0.5. No matter how it is expressed, the probability of rolling an even number on a single die is 1/2, or 50%. This can be easily remembered by considering that there are six possible outcomes, and three of them are even numbers.
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Given g(x) = 8x2 − x + 2, find the following.
1) g(0)
2) g(−1)
3) g(r)
4) g(x + h)
Answer:
Step-by-step explanation:
Given g(x) = 8x2 − x + 5, find the following.
(a). g(0) = 5
(b). g(−1) = 14
(c). g(r) = ?
(d). g(x + h) = ?
Birthday Party!
Sandy and her twin brother Jason are having a birthday party, but... they haven't yet decided how many candy bars to buy.
and they haven't yet decided how many people to invite!
They made a chart to
write down all the
possible combinations
of people and candy
bars so they could
figure out how many people to invite
and how many candy bars to buy.
Across the top is the number of
people they are thinking about
inviting. On the left is the number of
candy bars they are thinking about
buying.
Help them fill out the chart!
Put the number of candy bars that
each person will get in the cell. Look
for patterns as you work to help you
fill the chart out more quickly!
What patterns do you see in the
chart?
How many candy bars will they buy?
1
2
3
4
5
6
7
8
9
10
1
How many people will they invite?
3
5 6
7
8
2
4
5.7 Apprentice Birthday Party Student
Unless otherwise noted, SFUSD Math Core Curriculum is licensed under the Creative Commons Attribution 40 International License
9 10
Based on the information we can infer that the number of candy bars they buy depends on the number of guests you have.
How to find the number of candy bars they are going to buy?To find the number of candy bars they are going to buy we need to look at the graph. In this case, if the maximum number of bars they are going to buy is 10 and the maximum number of people they are going to invite is 10, we can infer that 1 bar would correspond to each person.
Based on the above, we can infer that the relationship is directly proportional between the candy bars and the guests. In accordance with the above, the number of sweets depends on the number of guests.
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The Hillmans have $12,000 in a savings account. The bank pays 1.25% interest on the savings account, compounded continuously. Find the total balance after four years.
The total balance after four years when compounded continuously is $12,615.24.
What is continuous compounding?A technique of calculating interest on a loan or investment where interest is compounded an endless number of times annually is called continuous compounding. Continuous compounding is a method of growing an investment or debt over time by continually adding interest earned over a relatively brief period of time to the principal. In financial computations where interest is earned or charged continuously, such in the bond or mortgage markets, continuous compounding is frequently utilised.
The compound interest is given as:
[tex]A = Pe^{(rt)}[/tex]
Substituting the values:
[tex]A = 12000 * e^{(0.0125 * 4)}\\A = 12000 * e^{(0.05)}[/tex]
A = 12000 * 1.05127
A = 12615.24
Therefore, the total balance after four years is $12,615.24.
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