This linear model's rate of change is 0.7 minute per song. This may be computed by subtracting the y-values (166.6 - 96.6) from the x-values (238 - 138).
What is a linear model?A continual dependent variable is described as a function of one or more predictor variables in a linear model. They can assist you in comprehending and forecasting the behavior of complicated systems, as well as analysing scientific, economic, and medical data. Linear regression is a statistical technique for developing a linear equation. Linear functions have a straight line as their graph. There is one independent variable and one dependent variable in a linear function. x is the independent factor, while y is the dependent variable.
A linear equation is so named because plotting the graph of a given linear model yields a straight line.
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Find the area bounded by y=x-13/x^2-6x-27, x=2, x=7, and y=0
Answer
Step-by-step explanation:
How does the distance change during the last section of tom’s journey? What does this mean? Explain your reasoning
The distance is decreasing with time meaning that the object is going back to the starting point.
What does it mean when distance decreases with time?When distance decreases with time, it means that the object is moving towards its starting point or moving in the opposite direction from its initial position. In other words, the object is moving backwards or reversing its direction of motion.
Distance is a measure of the total amount of ground covered by an object in motion, while time is a measure of how long it takes the object to cover that distance. If the object is moving towards its starting point, it means that it is covering less and less distance over time, or the distance it covers is decreasing.
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can someone please help i don’t understand
Amy used her first 2 tokens at Glimmer Arcade to play a game of Roll-and-Score. Then she
played her favorite game, Balloon Bouncer, over and over until she ran out of tokens. Balloon
Bouncer costs 3 tokens per game, and Amy started with a bucket of 35 game tokens.
Which equation can Amy use to find how many games of Balloon Bouncer,
she played
Answer:
11
Step-by-step explanation:
Let's call the number of games of Balloon Bouncer that Amy played as "x".
Amy started with 35 tokens and used 2 for Roll-and-Score, so she had 35 - 2 = 33 tokens left.
Each game of Balloon Bouncer costs 3 tokens, so the total number of tokens used for Balloon Bouncer games is 3x.
Therefore, the equation to find the number of games Amy played is:
33 = 3x
Solving for x, we get:
x = 11
So Amy played 11 games of Balloon Bouncer.
Answer: 3g + 3 = 35
Step-by-step explanation:
What is the frequency of the function f(z)?
f(z)=-2 sin (2) +3
Express the answer in fraction form
Enter your answer in the box.
Work out 135% of 160
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{135\% of 160}}{\left( \cfrac{135}{100} \right)160}\implies \text{\LARGE 216}[/tex]
What is the area of this compound figure? PLEASE HELP
The area of the composite figure is equal to 254 m² square metres.
How to calculate for the area of the figureThe composite figure can be observed to be a vertical rectangle, a square and an horizontal rectangle, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:
area of the vertical rectangle = 19 m × 7 m
area of the vertical rectangle = 133 m²
area of the square = 5 m × 5 m
area of the square = 25 m²
area of the horizontal rectangle = 16 m × 6 m
area of the horizontal rectangle = 96 m²
total area of the composite figure = 133 m² + 25 m² + 96 m²
total area of the composite figure = 254 m²
Therefore, the area of the composite figure is equal to 254 m² square metres.
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a manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 420 gram setting. is there sufficient evidence at the 0.01 level that the bags are underfilled? based on a 37 bag sample, the manufacturer fails to reject the null hypothesis. what is the conclusion?
The conclusion is that the bag filling machine appears to be working correctly at this setting.
Based on the information provided, the manufacturer conducted a hypothesis test to determine if the bags are underfilled at the 420 gram setting. The null hypothesis (H0) is that the bags are not underfilled, while the alternative hypothesis (H1) is that the bags are underfilled.
Since the manufacturer failed to reject the null hypothesis at the 0.01 level of significance, this means that there is not enough evidence to support the claim that the bags are underfilled at the 420 gram setting. In other words, the bag filling machine appears to be working correctly at this setting.
It's important to note that the conclusion may change if the sample size or the level of significance is different. Additionally, other factors such as the accuracy of the measuring device used or the consistency of the banana chips themselves may also impact the results.
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HELP DUE TONIGHT!!!
Answer:
1. $1900
2. $9
Step-by-step explanation:
Part a:
‘If she doesn’t sell any copies of History is Fun’ means x = 0:
[tex]y = 1900 + 9(0)[/tex]
∴ y = Melissa’s total pay = $1900
Part b:
Rearranging the equation:
[tex]y = 9x + 1900[/tex]
∴m = slope of equation = positive 9
c = y-intercept = 1900
The shape of the graph would be increasing or ascending. And since the Number of copies (x) can never be negative, this means that the amount of pay CANNOT be less than $1900. The amount of $1900 is her minimum pay
The value of m for this equation indicates the change in Melissa’s total pay for every copy she sells.
∴Change in Melissa’s total pay = 9 dollars
Lena estimate is there a bottle contains 500 mm of water but actually contains 473 mm of water what is the percent error and Lena's estimate rounded to the nearest 10th of a percent HURRY FAST PLS!!!
5.4% is the percent error .
What is the formula for errors?
The difference between the estimated value and the actual value in relation to the actual value is given as a percentage and is known as the percent error.
The relative error is multiplied by 100 to calculate the % error, in other words. The absolute value of the difference between the measured value and the actual value is divided by the actual value, then multiplied by 100 to get the percent error.
= 500 - 473/500 * 100
= 27/500 * 100
= 5.4%
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What is the length of the radius of the above sphere if the volume is 14,130 in3?
Solve this equation and you will have the solution:
4 • 3.14 • r3 ÷ 3 = 14,130
Your last step when solving this equation is to find the cube root of a both sides!
The length of the radius of the sphere is 15 in.
What is a sphere?It is a three-dimensional figure and has a diameter and a radius and the volume of a sphere is 4/3πr³.
We have,
Volume of the sphere = 14130 in³
So,
4/3πr³ = 14130 _____(1)
Solve for r.
4/3 x 3.14 x r³ = 14130
keep r on one side and the rest on the other side.
r³ = 14130 x 3 / 4 x 3.14
Cube root on both sides.
r³ = 3375
∛r³ = ∛3375
[ 15 x 15 x 15 = 3375 ]
So,
r = 15
Thus,
The radius of the sphere is 15 in.
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Linette and Ruth breed poodles as a hobby. They sold half of the puppies and half a puppy from the latest litter to the local pet shop. Then they sold half of the puppies that were left in the litter and half a puppy to the poodle palace. Then they decided to give the one remaining puppy to their friend Grace. How many puppies were originally in the litter
There were originally 10 puppies in the litter, as of the given condition.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
We can represent the number of original puppies as "x", and the sequence of events can be represented as:
Sold half of the puppies, so they have x/2 left - 1 sold to the local pet shop.
Sold half of the remaining puppies, so they have (x/2 - 1)/2 left sold to poodle palace.
One puppy was given to Grace, so they have ((x/2 - 1)/2- 1 = x - 2 / 4 - 1 remaining.
Since they are left with x - 2 / 4 - 1 puppies in the end, we can set this equal to 1 (the remaining puppy given to Grace), and solve for x:
x - 2 / 4 - 1 = 1
x - 2 = {1 + 1} * 4
x = 8 + 2
x = 10
Therefore, there were originally 10 puppies in the litter.
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Gloria traveled a total of 888 miles to get from school to her apartment. Gloria took the bus from school and then walked the remaining 880880880 yards home.
Gloria walked 500500 Miles from nearest bus stop to home.
How to convert yards into miles ?
To convert a yard measurement to a mile measurement, divide the length by the conversion ratio.
Since one mile is equal to 1,760 yards, you can use this simple formula to convert:
miles = yards ÷ 1,760
The length in miles is equal to the yards divided by 1,760.
Given:
Gloria traveled : 888 miles
1 Mile = 1760 yards
880880880 yards = 500500 Miles
So she walked 500500 Miles from nearest bus stop to home.
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How so i graph this ans what is thr solution.
The system of equations has a unique solution. The solution of the system of equations is (-3,4).
What is the system of equations?
Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
Given equations are
y = x + 7 ......(i)
y = -7/3x - 3 ......(ii)
Putting x = 0 in equations (i) and (ii):
y = 0 + 7
y = 7
y = -7/3 × 0 - 3
y = -3
Putting x = 3 in equations (i) and (ii):
y = 3 + 7
y =10
y = -7/3 × 3 - 3
y = -10
Putting x = -3 in equations (i) and (ii):
y = -3 + 7
y = 4
y = -7/3 × (-3) - 3
y = 4
The points in equation (i) are (0,7), (3,10), (-3,4)
The points in equation (ii) are (0,-4), (3,-10), (-3,4)
Plot the points and join the points:
The intersection of the equation is (-3,4).
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there 10 cars in a race. in how many ways can three cars finish the race as the 1st, 2nd, and the 3rd places?
There are 10 cars in a race, in 720 ways can three cars finish the race as the 1st, 2nd, and the 3rd places.
An arrangement of particulars in a specific order is appertained to as a permutation. Then, the factors of sets are arranged in a direct or successional order. For case, the set A = ,6 has a permutation of 2, which is. There's no other way to organise the factors of set A, as you can see.
There are 10 cars in the race,
Three cars finish the race in the 1st ,2nd and 3rd order
1st finish the race have 10 chances
P(A) = 10
2nd finish the race have 9 chances
P(B) = 9
3rd finish the race have 8 chances
P(C) = 8
The number in which this can be put,
= P(A) x P(B) x P(C)
= 10*9*8
=720 ways
Therefore, in 720 ways can three cars finish the race as the 1st, 2nd, and the 3rd places.
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Find the mode of each group of numbers:
62,63,67,66,66,63,62,68,69,65,67,63,64,68,65,62,69,63,61,60,63,65
The mode of the data set given is 63.
What is the Mode of a dataset?Statistics uses the terms mean, median, and mode to describe central tendency. They each provide information about what value in a data set is conventional or representative of the data set in their own unique ways.
The number that appears the most frequently in a piece of data is the mode. Count the occurrences of each number in the data collection. The figure with the largest total is the mode. More than one mode is acceptable. Additionally, there is no mode if all numbers appear exactly once.
Given that:
62,63,67,66,66,63,62,68,69,65,67,63,64,
By rearrangement, we have:
62, 62, 63, 63, 63, 64, 65, 66, 66, 67, 67, 68, 69
Therefore, the highest occurring number(mode) is 63.
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Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis.
y = x^3/2
y = 27
x = 0
Volume of solid generated by revolving the plane region about the y-axis is [tex]\pi \left(\frac{1392}{7}\right)[/tex]
What do you understand by Shell method?The shell method formula is used to find the volume of a solid of revolution, formed by rotating a region about a line that is parallel to one of its sides.
The formula for the shell method is V = 2π* ∫r(x)h(x) dx where V is the volume of the solid, r(x) is the distance between the axis of revolution and the curve being rotated and h(x) is the height of the shell at x.
The shell method can be used when the region is more easily described by an equation in one variable. In contrast, the disk/washer method is used when the region is more easily described by an equation in two variables.
It is a powerful tool for solving many types of problems in calculus, physics and engineering. The shell method formula helps to determine the volume of a solid of revolution, which is an important concept in various fields of study.
Given:
y = [tex]x^\frac{3}{2}[/tex]
y = 27
x = 0
Shell method:
V = [tex]2\pi \int\limits_c^d p(y)h(y) dy[/tex]
Then the volume of a solid is
V = [tex]2\pi \int\limits_0^4x(27 - x^\frac{3}{2})dx[/tex]
= [tex]2\pi \left[ \int\limits_0^4 27x dx - \int\limits_0^4 x^\frac{5}{2}dx\right][/tex]
[tex]= 34\pi \left[\frac{x^2}{2} \right]_0^4 - \frac{4}{7} \pi \left[ x^\frac{7}{2} \right]_0^4[/tex]
[tex]= 34\pi \left(\frac{4^2}{2} \right) - \frac{4\pi}{7}(4)^\frac{7}{2}[/tex]
[tex]= 4\pi \left( \frac{68}{7} - \frac{2^7}{7} \right)[/tex]
[tex]= 4\pi \left( \frac{476 - 128}{7} \right)[/tex]
[tex]4\pi \left( \frac{348}{7} \right)[/tex]
[tex]= \pi \left( \frac{1392}{7} \right)[/tex]
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I don’t understand this can someone help
The ordered pair (2,10) means that the cost to feed 200 animals is of $10,000.
How to interpret the ordered pair?The general format of an ordered pair is given as follows:
(x,y).
The meaning of an ordered pair (x,y) is that y = f(x), meaning that the numeric value of the function at the value of x is of y.
The variables for this problem are given as follows:
x -> number of animals, in hundreds, hence x = 2 means that there are 200 animals.y -> cost to feed the animals, in thousands, hence y = 10 means that the cost is of $10,000.More can be learned about ordered pairs at brainly.com/question/1528681
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Which statements describe the graph of 2 8/9>x
There is an open circle on ²9.
21909.
The graph contains the point 0
,8
There is a closed circle on ²ğ.
The arrow points to the left.
The arrow points to the right.
2x on a number line? Select three options.
The inequality 26/9 > x represents a line with an open circle at 26/9 going toward positive infinity represented by an arrow.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, An inequality [tex]2\frac{8}{9} > x[/tex].
26/9 > x.
Now, As the inequality is strictly greater than 26/9 it would be represented by a line open circled at 26/9 and going towards +∞.
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A cylinder has a base diameter of 6m and a height of 12m what is the volume in cubic m, to the nearest tenths place
Answer:
339.3 cubic m
Step-by-step explanation:
r = Base radius
= [tex]\frac{Diameter}{2}[/tex]
= [tex]\frac{6}{2}[/tex] m
Base radius = 3 m
h = Perpendicular height
= 12 m
Volume of a cylinder: [tex]\pi r^{2} h[/tex]
= [tex]\pi (3 m)^{2} (12 m)[/tex]
= [tex]\pi (108)m^{3}[/tex]
= 339.3 cubic m (Rounded to the nearest tenths place)
can someone help please
Answer: x=3, y=-1
Step-by-step explanation:
2x+y=5
2y=2x-8
In equation 1, y=5-2x.
Substitute this value in equation 2.
2(5-2x)=2x-8
10-4x=2x-8
Thus,
4x+2x=10+8 (collecting terms)
6x=18
x=3
Now, we said earlier that y=5-2x.
Therefore, y=5-2(3) [because x=3]
y=5-6
y=-1
Hope this helps :]
what is the meaning of square?
Answer:
Step-by-step explanation:
A square is a 4 sided polygon in which all of its side lengths are equal and the diagonals are also be
pls help due now!!!!!!!!!!!!!!!
Answer: D. 6 cm
Step-by-step explanation:
V = 4/3πr^3
r = (3 V/4π)^1/3 = (3* 900/4*π)^1/3 = 5.98942
Consider the function f(x) = (x - 3)².
a. How could you restrict the domain of f(x) so that its inverse will be a function?
b. Graph f(x) with its restricted domain and then graph its inverse on the same set of axes.
c. Find the equation of the inverse of f(x) with its restricted domain.
The inverse of f(x) has no restriction on the domain.
The graph of the inverse function is given below.
The inverse equation is [tex]f^{-1}[/tex](x) = x² + 3.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = (x - 3)²
The inverse of f(x).
Step 1:
Make f(x) = y
y = (x - 3)²
Step 2:
Interchange x and y
x = (y - 3)²
Step 3:
Solve for y.
square root on both sides.
x² = y - 3
y = x² + 3
So,
[tex]f^{-1}[/tex](x) = x² + 3.
a)
[tex]f^{-1}[/tex](x) = x² + 3
we see that for any values of x, [tex]f^{-1}[/tex](x) is a function.
So,
There is no restriction on the domain.
b)
The graph is given below.
c)
The inverse equation is
[tex]f^{-1}[/tex](x) = x² + 3.
Thus,
The inverse of f(x) has no restriction on the domain.
The inverse equation is [tex]f^{-1}[/tex](x) = x² + 3.
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Yen takes her pomeranian kiwii to the dog park once inside the fence kiwii runs across the filed in 10 seconds his path is shown on the graph belowwhat is the average velocity 4 to 8 seconds
The average velocity from 4 to 8 seconds is given as follows:
v = [position at 8 seconds - position at 4 seconds]/4.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
The change in the distance from 4 to 8 seconds is given as follows:
position at 8 seconds - position at 4 seconds
The change in the time from 4 to 8 seconds is given as follows:
8 - 4 = 4 seconds.
Hence the velocity is of:
v = [position at 8 seconds - position at 4 seconds]/4.
Missing InformationThe problem is incomplete, hence the general procedure to obtain the average velocity was presented.
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Jonathan rides his bicycle at a velocity of 12 m/s East. He
comes to a hill and over the next 23 seconds, his velocity
decreases to 5 m/s East. What is Jonathan's acceleration?
Jonathan's acceleration is -0.3043 m/s² East, which means he is slowing down.
What is Acceleration?Acceleration is the rate of change of the velocity of an object with respect to time.
Jonathan's initial velocity, u = 12 m/s East
His final velocity, v = 5 m/s East
The time taken, t = 23 seconds
We can use the formula for acceleration:
a = (v - u) / t
Substituting the given values, we get:
a = (5 m/s - 12 m/s) / 23 s
a = -7 m/s / 23 s
a = -0.3043 m/s^2 East
Therefore, Jonathan's acceleration is -0.3043 m/s² East, which means he is slowing down.
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write the equations from word form.
The transformed functions is
a) The absolute value function reflected across the x axis and shifted up 2 units is y₁ = -| x₁ | + 2
b) The absolute value function that is shifted left 3 units and is compressed by a third is y₂ = ( 1/3 ) | x₂ + 3 |
c) The absolute value function reflected across the x axis stretched vertically by 5 units shifted left 4 units and up 6 units is y₃ = -5 | x₃ + 4 | + 6
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
a) The absolute value function reflected across the x axis and shifted up 2 units is y₁
The absolute value function is y₁ = | x₁ |
when reflected over x axis , the new function is
y₁ = - | x |
when shifted up 2 units ,
y₁ = -| x₁ | + 2
b)The absolute value function that is shifted left 3 units and is compressed by a third is y₂
The absolute value function is y₂ = | x₂ |
when shifted left 3 units ,
y₂ = | x₂ + 3 |
when compressed by a third , the new function is
y₂ = ( 1/3 ) | x₂ + 3 |
c)The absolute value function reflected across the x axis stretched vertically by 5 units shifted left 4 units and up 6 units is y₃
The absolute value function is y₃ = | x₃ |
when reflected across the x axis ,
y₃ = - | x₃ |
when stretched vertically by 5 units ,
y₃ = - 5 | x₃ |
when shifted 4 units left ,
y₃ = - 5 | x₃ + 4 |
when shifted 6 units up ,
y₃ = -5 | x₃ + 4 | + 6
Hence , the transformation of functions are solved
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In any set of positive integers the replacement of a set of three 2s with a set of two threes will not change the sum
The statement is incorrect. The replacement of three 2s with two threes will change the sum.
For example, consider the set {2, 2, 2}. The sum of this set is 6. However, if we replace three 2s with two threes, the new set becomes {3, 3}, and its sum is 6, which is different from the original sum. Hence, replacing a set of three 2s with a set of two threes does change the sum. An integer is a whole number that can be positive, negative, or zero. Integers are numbers that don't have any fractional or decimal component. Some examples of integers are: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, and so on. The set of integers is denoted by the symbol "Z", which stands for Zahlen, the German word for "numbers". Integers are an important mathematical concept used in many branches of mathematics and science, including algebra, number theory, and computer science.
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Complete Question
In any set of positive integers the replacement of a set of three 2s with a set of two threes will not change the sum" State whether the statement was correct or incorrect.
Please help (will mark as brainlest)
Answer:
TRIANGLE PROBLEM:
area : 6a^4
perimeter : 12a^2
SIMPLIFY problem:
-40c^2+26a^2+30ac
EVALUATE & FACTOR:
(q^2 - p) ( p^2 - q)
and the solved form is 240
hope it helps :)
Step-by-step explanation:
lol im an rsm kid too. but i hope these are right,
first i'm gonna start with 263 c.
AREA = 4a^2 * 3a^2 divided by 2.
12a^4 divided by 2 = 6a^4.
AREA = 6a^4
Perimeter you can find with the pythag. th.
(4a^2) ^2 + (3a^2 ) ^2 = c^2
16a^4 + 9a^4 = c^2
, the missing side is 5a^2
therefore the perimeter is 4a^2 + 3a^2 + 5a^2 = 12a^2
ok next, im gonna do 266
the answer is -40c^2+26a^2+30ac
make sure to check this w/ symbo or mthway
ok last one!!
factored form is (q^2 - p) ( p^2 - q)
and the solved form is 240
Two different investment companies offer college savings plans, one at 8. 4% compounded continuously and the other at 8. 6% compounded quarterly. Which is the better investment?
The 8.4% compounded quarterly is the better investment because it gives a good return.
Compound interest is “interest-on-interest”, or the ability of a financial instrument to generate earnings on its earnings. Compound interest, can be calculated using the formula :
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
where A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
(i)S = P
S = P(1.0854) (1.0854)
AP(1) = 1.0846 - 1
AP(1)= 0.08546 or 8.546%
(ii)r = 0.084/4
AP(2) = (1 + 0.084/4)⁴ -1
AP(2) = 1.08688 - 1
AP(2) = 8.668%
The 8.4% compounded quarterly investment is therefore preferable.
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