Answers
The relation is:
(1, 2), (-3, 5), (6, 6), (-2, 0), (1, 2)
Is a function, because each element in the domain is mapped to a single element in the range.
Do the ordered pairs represent a function?A relation maps elements from one set, called the domain, into another set, called the range.
For example, the element x mapped into element y is written as (x, y).
Particularly, a relation is a function if each element from the domain is mapped into only one element of the range.
So, if we had two points like (2, 4) and (2, 5), then the relation is not a function (because the element 2 is mapped into two different elements of the range).
Here the relation is:
(1, 2), (-3, 5), (6, 6), (-2, 0), (1, 2)
So the input x = 1 appears twice, but both times is mapped to the same element, so this relation is a function.
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Related Questions
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.
y = x5, y =
square root of x
; about the x-axis
Answers
Rotating the area bounded by the given curves around the designated line yields the solid's volume as [tex]V = \frac{9}{22}\pi[/tex]
The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Different forms have various volumes.
The amount
of space that a solid occupies is measured by its volume. The amount of unit cubes required to completely fill the solid serves as the measurement. The capacity of an object to hold matter is generally thought of as its volume in three dimensions.
The functions provided are,
[tex]`y = f(x) = \sqrt{x}``y = g(x) = x^5`[/tex]
By rotating the area around the x-axis, the solid's volume is given by (using washer method)
[tex]V = \pi int_a^b [f^2(x)-g^2(x)]dx[/tex]
evaluate the integral, limit the plugins, and
[tex]V = \pi int_0^1 [(\sqrt{x})^2-(x^5)^2]dx\\\\V= \pi int_0^1 [x-x^10]dx V = \pi [\frac{x^2}{2}-\frac{x^11}{11}]_0^1 V = \pi [\frac{1^2}{2}-\frac{1^11}{11}]. V = \pi [\frac{1}{2}-\frac{1}{11}] = \frac{9}{22}\pi[/tex]
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what is 1/2 times 3
Answers
Answer:
1.5
Step-by-step explanation:
Answer:
1.5
Step-by-step explanation:
3 times 1/2=1/5
The graph shows the proportional relationship between the number of gems collected and the number of levels that h been completed in a video game.
Determine the constant of proportionality for the relationship.
Answers
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The constant of proportionality for the relationship is 70.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 6 is an equation.
We have,
The number of gems collected at different levels is:
At 2 levels, 140 gems are collected.
At 4 levels, 280 gems are collected.
At 6 levels, 420 gems are collected.
This means.
y ∝ x
y is the number of gems collected.
x is the level.
Now,
y = kx
140 = k x 2
k = 140/2
k = 70
Thus,
The constant of proportionality for the relationship is 70.
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The price of a cake plus 11% delivery charge comes to a total cost of $19.98. What was the price of the cake?
Step 1 of 2 : Describe the above situation as a linear equation, using "x" or "y" as variable names to describe the unknown quantity. Enter the equation in the box below:
Answers
Answer:
x + 0.11x = 19.98
Step 2 of 2 : Solve the equation for the unknown quantity.
x = 18.18
Find the value of Za:
Z 0.47=
Round to 2 decimals
Answers
The value of za is 80.47.
What is value?Value is the regard that something is held to deserve,the important, worth or usefullness of something.
let us find the value of zero Alpha, Given that alpha is .32. So the value of Z the it is 0.32. Well, we need to begin to considering that we need to the find actually the differentiate one minus alpha. Thus it is going to be in this case one of the (-) 10.32. This is going to be the 0.68. So actually Z of .32, we're going to need to find 0.68 inside the Z table. So let's look at it at it. Look at that at 0.68 oh eight.Let give us the Z score of 80.47. So we can tell that the Z score of zero of alpha, given that the Alpha is 00.32 is going to be 0.47.
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In 52.38, which is in the tens place
Answers
Answer:5
Step-by-step explanation:
5 2 . 3 8
5= tens
2= ones
3= tenths
8= hundreths
5 is in the tens place
help simplify this 3^1-1
Answers
3-1
Solution
2
May I have Brainly
Answer: 2 or 1?
Step-by-step explanation:
3^1 = 3 then 3 - 1 = 2
or 3^(1 - 1) then 3^0 = 1
Use the formula A=P (1+ r/n)ⁿ⁺ to solve the compound interest problem.
Find how long it takes a $ 1700 investment to earn $ 500 interest if it is invested at 2 % interest compounded quarterly.
$ 500 interest will be earned in approximately ___ years. (Round to the nearest tenth.)
Answers
The answer to the given problem can be stated as, "$ 500 interest will be earned in approximately 0.14 years."
What is compound interest?The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.
The formula to calculate the amount is as follows,
A = P(1 + r)^(nt)
The, the interest is given as P[(1 + r)^(nt) - 1]
Substitute all the corresponding values in the above expression to obtain,
500 = 1700[(1 + 2/100)^(nt) - 1]
=> 500 + 1700 = 1700(1 + 2/100)^(nt)
=> (1 + 2/100)^(nt) = 2200/1700
=> 1.02^(nt) = 22/17
Since, there are 4 quarters in one year, n = 4.
1.02^(4t) = 1.294
=> 4t = log(1.294) ÷ log(1.02)
=> 4t = 0.562
=> t = 0.14
Hence, it will take 0.14 years to earn the interest of $500.
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PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 50 POINTS
Answers
Answer:
Step-by-step explanation:
Its A
Answer:A
Step-by-step explanation:A cylinder with 8 units.
Kayla is marking down slippers so that they sell. She advertises that they are now $37, down from $74. What percentage of discount is that
Answers
What’s the answer please thank u
Answers
Answer: 1/2
Step-by-step explanation:
slope is rise over run (up and down over left to right)
help meeeeeeeeeee pleaseee
Answers
The number of acres owned for which the average intake is 2200 calories per day is 2 acres obtained by the algebraic expression that relates the acres of land and the calories per day.
What is an algebraic expression?An algebraic expression is formed by variables, constants, and arithmetic operations. An algebraic expression provides the relation between the input and output variables i.e., x and f(x) respectively.Calculation:It is given that, the number of calories consumed daily by a person owing x acres of land is given by the algebraic expression,
C(x) = 270 ln(x+1) + 1900
The average intake of calories consumed per day is given by C(x) = 2200
Here x is the number of acres of land. Then, the required number of acres of land is
C(x) = 270 ln(x+1) + 1900
⇒ 2200 = 270 ln(x+1) + 1900
⇒ 270 ln(x+1) = 2200 - 1900
⇒ 270 ln(x+1) = 300
⇒ ln(x+1) = 300/270 = 10/9
Applying base 'e' on both sides, we get
⇒ (x+1) = [tex]e^\frac{10}{9}[/tex]
⇒ x+1 = 3.0377
⇒ x = 3.0377 - 1 = 2.0377
When rounding the final answer to the nearest tenths, we get x = 2 acres.
When rounding the final answer to the nearest thousand, we get x = 2.038 acres.
Thus, for an average intake of 2200 calories per day, the number of acres of land owned is approximately 2 acres.
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Takeuru only uses eggs for souffles in his restaurant. He uses 3 eggs per souffle. Last week he bought 4 times as many eggs as he baked souffles. Takeuru has 18 eggs left over.
How many eggs did Takeuru buy and how many souffles did he bake?
Answers
Takeuru made 18 souffles with the 72 eggs he purchased.
What is meant by ratio?A ratio in mathematics demonstrates how many times one number is contained in another. For instance, the ratio of oranges to lemons in a dish of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of oranges to the total amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8 (or 3:4). (or 4:7).
The quantities in a ratio can be of any kind, such as counts of people or things, measures of lengths, weights, or times, etc. Both numbers must be positive in the majority of situations.
Let e = the quantity of eggs Takeuru purchased.
Takeuru purchased s souffles total.
Then, as Takeuru purchased 4 times as many eggs as he used to make soufflés, e=4s.
Since Takeuru uses 3 eggs for each souffle he bakes and has 18 eggs remaining after backing, the equation is: e-3s=18.
This states that after Takeuru utilized three eggs for each souffle, there are still 18 eggs available.
There are now two equations:
e=4s
e-3s=18
When we solve for s using equation (2) and the value of e from equation (1), we get the following results: s=18
e=4s
e=4×18
e=72
Therefore, Takeuru purchased 72 eggs.
There were 18 soufflés that Takeuru purchased.
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The formula A=23.1 e^{0.0152t} models the population of a US state, A, in millions, t years after 2000.
a. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was ? million.
Answers
The population of the city in 2000 = 23.1 million
In 2006 the population will be equal to 28.3 million
Applications of Compound interest:Compound interest may be used in a variety of situations, including increasing or decreasing population, Increasing the count of bacteria increasing an item's value, and a decrease in an item's worth.
The formula for Compound interest is given by
A = Pe^rtWhere P = Principal amount or Initial value
r = rate of interest or increase
t = time period
Here we have
The formula [tex]A = 23.1 e^{(0.0152t)}[/tex] represents the population of a US state, A, in millions, 't' years after 2000.
Here we need to solve the following questions
a. What was the population of the state in 2000
Compare the given formula with A = Pe^rt
=> [tex]23.1 e^{0.0152t} = Pe^{rt}[/tex]
=> Initial value or initial population, P = 23.1 and
rate of increase r = 0.0152
Therefore,
The population of the city in 2000 = 23.1 million
b. When will the population of the state reach 28.3 million?
As we know in 2002 the population = 23.1 million
Let's assume that after 'n' year the population will become 28.3 million
As we know Rate of increase = 0.0152
From the given formula
Population of the city after n, A = 23.1 e^(0.0152n)
As we assumed the population after n years = 28.3
=> 23.1 e^(0.0152n) = 28.3
=> e^(0.0152n) = 28.3/23.1
=> e^(0.0152n) = 1.225
Apply log on both sides
=> log e^(0.0152n) = log 1.225
=> 0.0152n log e = log 1.225
=> 0.0152n (1) = 0.0881
=> n = 0.0881/0.0152
=> n = 5.8 ≅ 6
After 6 years the population will be 28.3 million
After 6 years i.e 2000 + 6 = 2006
Therefore,
In 2006 the population will be equal to 28.3 million
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Consider the following solid s. The base of S is a circular disk with radius r. Parallel cross-sections perpendicular to the base are squares. Set up an integral that can be used to determine the volume V of the solid. V = dx LIO 26TO = 2 dx Find the volume V of the solid. V=
Answers
The volume of the described solid is V = 16r³/3
Given,
A solid line S should be drawn between z=a and z=b. If S has a cross-sectional area of Px through x and is perpendicular to the x-axis, then A (x)
Volume of S = limₙ→∝ ∑i=₁ⁿ A(xi) Δx = [tex]\int\limits^b_a {A(x)} \, dx[/tex]
The equation of circle x² + y² = r² where r is the radius of the circle.
Equation of upper semicircle yu= √(r²-x²) and
Equation of lower semicircle yl = -√(r²-x²)
Area of cross-section A(x) = (yu² - yl²)
Substitute yu and yl values
A(x) = [√(r²-x²) - (-√(r²-x²) )]² = 4(r² -x²) (1)
The limit for volume v varies from -r to r
Thus Volume v = ₋[tex]\int\limits^r_r {A(x)} \, dx[/tex]
Substitute A(x) from (1)
V = ₋[tex]\int\limits^r_r {4(r^{2}-x^{2} ) } \, dx[/tex]
⇒V = 4[r²x - x³/3 ]
⇒V = 4(r³ - r³/3) - 4(-r³ + r³/3) = 4[2 (r³ - r³/3)] = 16r³/3
The volume of the described solid S where the base is a circular disk or radius r and parallel cross sections perpendicular to the base are squares is V = 16r³/3
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Suppose that balloon owners get to pay lower costs for insurance next year. How would this affect the demand curve for balloon rides? How would this affect the supply curve for balloon rides?
Answers
A balloon payment is a one-time, large-scale principal payment made near the end of the loan term.
What impact would this have on the demand curve for hot air balloon rides?Total revenue is the amount of money made from the sale of a specific number of items at a specific price.A demand curve is a graph that shows the amounts of stores consumers want at different prices and contains the demand for that product on the y-axis and the price on the x-axis.If a product's price decreases, consumers are more likely to choose it over alternatives that are suddenly more expensive or to simply purchase more quantities of the product, which raises demand from customers.In a similar vein, demand will decline if price rises, all else being equal.To learn more about demand curve demonstrate refer to:
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Mrs tucker writes the fraction 11/4
Answers
Answer: 4 2/3
Step-by-step explanation:
the perimeter of the rectangle is 26inches and the length is 8 inches what is the width?
Answers
Answer:
5 inches
Step-by-step explanation:
P=2(l+w)
Solving for w
w = p / 2 - l = 26 /2 - 8 = 5
You are buying 3 shirts and 2 pairs of pants. You spend $300. Let x represent the price of the shirt and y represent the price of the pants. Write an equation that can be used to find the price of the shirts and pants. Directions: Write the equation in both slope-intercept and standard form for each of the scenarios below. a. Standard Form: b. Slope-Intercept Form: c. If the shirts cost $20 each how much were each of the pants? d. Using the Standard Form, identify the x-intercept of the graph and explain how the x-intercept relates to the price of the pants and shirts. e. Using the Standard Form, identify the y-intercept of the graph and explain how the y-intercept relates to the price of the pants and shirts
Answers
Answer:
see the explanation
Step-by-step explanation:
Let
x ----> the price of the shirt
y ---> he price of the pants
we have that
The price of three shirts plus the price of two paints must be equal to $300
so
This is the equation of the line in standard form
Convert to slope intercept form
Isolate the variable y
subtract 3x both sides
Divide by 2 both sides
----> equation of the line in slope intercept form
Find out the x-intercept
Remember that the x-intercept is the value of x when the value of y is equal to zero
In this problem, the x-intercept is the price of the shirt when the price of the paints is equal to zero
Using the Standard Form, identify the x-intercept of the graph
The standard form is
The x-intercept is C/A
we have
so
The x-intercept is the point (100,0)
That means---> The price of the shirt is $100 when the price of the paints is equal to $0
Alternative method to find out the x-intercept (equation in slope intercept form)
For y=0
solve for x
The x-intercept is the point (100,0)
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Simplify the Linear Expression 6(y + 2) + 9 Responses
Answers
The linear expression 6(y + 2) + 9 in the simplified form will be 6y + 27.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear expression is given as,
⇒ 6(y + 2) + 9
Simplify the expression, then we have
⇒ 6(y + 2) + 9
⇒ 6y + 18 + 9
⇒ 6y + 27
The linear expression 6(y + 2) + 9 in the simplified form will be 6y + 27.
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The formula A=18.5 e⁰.¹⁷⁰⁸⁺ models the population of a US state, A, in millions,
a. What was the population of the state in 2000 ?
b. When will the population of the state reach 26.6 million?
Answers
The population of the state 2,000 is 18.5 Million. And the time at which the population of the state reaches 26.6 million will be 2.126 years.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The equation is given below.
[tex]\rm A = 18.5 \times e^{0.1708\times t}[/tex]
The population of the state in 2,000 is calculated as,
[tex]\rm A = 18.5 \times e^{0.1708\times 0}[/tex]
A = 18.5 × e⁰
A = 18.5 Million
The time at which the population of the state reaches 26.6 million will be given as,
[tex]\rm 26.6 = 18.5 \times e^{0.1708\times t}\\\\1.4378 = e^{0.1708\times t}[/tex]
Take natural log on both sides, then we have
0.1708 × t = ln 1.4378
t = 2.126 years
The population of the state 2,000 is 18.5 Million. And the time at which the population of the state reaches 26.6 million will be 2.126 years.
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Taylor earns $10.35 per hour and is paid double-time for each hour that she works over 40 hours in a week. Determine Taylor's gross pay if she worked 48 hours last week.
$248.40
$579.60
$596.80
$414.00
Answers
Find the requested value.
f(4) for f(x) =
(7x+7, if x ≤0
2-3x, if 0
X, if x ≥ 3
A)4
B)3
C)35
D)-10
Answers
The requested value of f(4) is -10.
What is an expression?
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
Here, we have
Given: f(x) =(7x+7, if x ≤ 0
2-3x, if 0 =X, if x ≥ 3
f(4) means the value of f(x) when x = 4.
Which expression on the right applies when x = 4?
The first one because it applies only when x ≤ 0 and
The last one because it applies when x ≥ 3 and 4 is greater than 3. The answer is the last expression.
since 4 lies between 0 and greater than
f(4) = 2 - 3(4)
f(4) = -10
Hence, the requested value of f(4) is -10.
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Consider the algebraic expression
32pq2−4p2q+12pq−7
Find terms that are not constants.
a) 32p2q,−4p2q,12pq, 7
b) 32, -4, 12, 7
c) 32pq2,4pq2,12pq
d) 32pq2, −4p2q, 12pq
Answers
The term which are not constant are;
⇒ 32pq², - 4p²q, 12 pq
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
⇒ 32pq² - 4p²q + 12pq - 7
Now,
We know that;
In the algebraic expression the constant term has no variables.
Thus, The term which are not constant are;
⇒ 32pq², - 4p²q, 12 pq
Therefore, The term which are not constant are;
⇒ 32pq², - 4p²q, 12 pq
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PLEASE ANSWER ASAP!!
It's two sections and my answers are included but please correct them if I'm wrong
Answers
Some answers are correct, but not all. These are ones that need fixing.
2a.
[tex]\lim_{x\rightarrow-2^-}f(x) = 0[/tex] because as you come towards x = –2 from the left, your y-values are getting closer to 0.
2b.
[tex]\lim_{x\rightarrow-2^+}f(x) = 1[/tex] because as you come towards x = –2 from the right, your y-values are getting closer to 1.
2e.
[tex]\lim_{x\rightarrow5}f(x) = -1[/tex] because as you come towards x = 5 from both sides, your y-values are getting closer to -1.
3a.
[tex]\lim_{x\rightarrow3^-}f(x) = -1[/tex] because as you come towards x = 3 from the left, your y-values are -1.
[tex]\lim_{x\rightarrow3^+}f(x) = 1[/tex] because as you come towards x = 3 from the right, your y-values are 1.
[tex]\lim_{x\rightarrow3}f(x)[/tex] does not exist, since those two one-sided limits aren't don't agree.
3b.
[tex]\lim_{x\rightarrow0^-}f(x) = -\infty[/tex] because as you come towards x = 0 from the left, your y-values are getting huge in a negative way.
[tex]\lim_{x\rightarrow0^+}f(x) = \infty[/tex] because as you come towards x = 0 from the right, your y-values are getting huge in a positive way.
20 point question! Please help!
Answers
With 13 you will have 169pi
So 169/9 so 18,8
past records show that the average number of accidents drowning at a beach resort is 3 per year for every 100000 of tourists visiting the resort. if in a year 200000 tourists visited this resort, find the probability that;
a. there will be no drowning this year
b. there will be at least 6 accidents this year
Answers
The probability that there will be no drowning this year is 0%
and the probability that there will be at least 6 accidents this year is 0.003%
What is the probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
We have,
3 per year for every 100000 of tourists
if in a year 200000 tourists visited this resort,
Probability formula:
P(A) = f / N
P(A) = Probability of an event (event A) occurring.
f = Number of ways an event can occur (frequency)
N = Total number of outcomes possible.
so f = 3,
N = 100000
P(A) = f / N = 3/100000 = 0.00003 = 0.003%
so, the probability of the previous year is 0.003%.
0.003% = f / 200000
f = 200000 * 0.003% = 6
a) The probability that there will be no drowning this year:
P(A) = 0 / 200000 = 0
b) The probability that there will be at least 6 accidents this year:
P(A) = 6 / 200000
P(A) = 0.003%
Hence, the probability that there will be no drowning this year is 0%
and the probability that there will be at least 6 accidents this year is 0.003%
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Mrs. Perky bought 2 3/4 gallons of blue paint. Each gallon of blue paint cost $19.50. Mrs. Perky also bought 1 1/3 gallons of orange paint. Each gallon of orange paint cost $16
Answers
Answer:
$74.96 if rounding to hundredths place.
Step-by-step explanation:
If you are looking for the total amount spent, first we will convert 2 3/4 into a decimal, which is 2.75. 2.75 X 19.50 = 53.625. She bought 53.525 dollars worth of blue paint, now we solve for orange. 1 1/3 X 16 = 64/3, which is simplified to 21 1/3. If we add the two togetherwe get 74.9583, but the 3 is repeated. If you are asked to rount to the 100th place, the asnwer is $74.96. If you are rounding to nearest dollar, it is about $75.
Hope this helped :)
Let A={9,8,3,0,5} and B={8,4,7,5,0}. Select from the following choices the one that represents the intersection of A and B?
Answers
The required intersection of the two sets A and B is given as A∩B = [8, 5, 0].
Given that,
Let A={9,8,3,0,5} and B={8,4,7,5,0}. The intersection of A and B is to be determined.
Sets are an orderly collection of items in mathematics that can be expressed in set-builder or roster form.
here,
P[PUB] = {9,8,3,4,0,5,7} = 7
P[A∩B] = P[A] + p[B] - P[AUB]
P[A∩B] = 5 + 5 - 10
= 3
From accumulating the common elements between the sets,
A∩B = [8, 5, 0]
Thus, the required intersection of the two sets A and B is given as A∩B = [8, 5, 0].
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To help open up a jewelry store, Ann borrowed money from a bank.
She took out a personal, amortized loan for , at an interest rate of , with monthly payments for a term of years.
For each part, do not round any intermediate computations and round your final answers to the nearest cent.
If necessary, refer to the list of financial formulas.
(a) Find Ann's monthly payment.
(b) If Ann pays the monthly payment each month for the full term, find her total amount to repay the loan.
(c) If Ann pays the monthly payment each month for the full term, find the total amount of interest she will pay.
Answers
(a) Ann's monthly payment: $133.33
(b) Ann's total amount to repay the loan:$8000
(c) The total amount of interest Ann will pay:-$12000
What is amortized loan?
A loan that has planned, monthly payments that are applied to both the principle and interest accrued is known as an amortized loan.
To solve this problem, we need to use the following formula for an amortized loan:
[tex]Monthly\ payment = (Interest rate / 12) * Loan\ amount / (1 - (1 + (Interest \ rate / 12))^(-Term * 12))[/tex]
(a) Find Ann's monthly payment:
Substituting the given values into the formula, we get:
[tex]Monthly\ payment = (0.08 / 12) * 20000 / (1 - (1 + (0.08 / 12))^(-5 * 12))\\\\Monthly\ payment = 133.33[/tex]
Therefore, Ann's monthly payment is $133.33.
(b) Find Ann's total amount to repay the loan:
The total amount to repay the loan is equal to the sum of the monthly payments over the term of the loan. Since Ann's monthly payment is $133.33 and the term of the loan is 5 years, the total amount to repay the loan is equal to $133.33 * 5 * 12 = $8000.
(c) Find the total amount of interest Ann will pay:
The total amount of interest Ann will pay is equal to the total amount to repay the loan minus the loan amount. Since Ann's total amount to repay the loan is $8000 and the loan amount is $20000, the total amount of interest Ann will pay is equal to $8000 - $20000 = -$12000.
Note that the total amount of interest Ann will pay is a negative number because the loan amount is greater than the total amount to repay the loan. This means that Ann will end up paying less than the loan amount due to the amortization of the loan.
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