You are planning to buy one of two brands of sofas, which you hope to use over the next twenty years. Brand J costs $975 and lasts for about twenty years. Brand K costs $265 and lasts for about five years, so you will need to buy four Brand K sofas to equal one Brand J sofa. In either case, you plan to pay for your sofa using your credit card, which has an interest rate of 14.55%, compounded monthly. You can pay off a Brand J sofa with eight years of monthly payments, and you can pay off a Brand K sofa with three years of monthly payments. Assuming that you make no other purchases on your credit card, over twenty years, which brand will be cheaper, and how much cheaper will it be? (Round all dollar values to the nearest cent.) a. Brand J will be $591.36 cheaper than Brand K. b. Brand J will be $85.00 cheaper than Brand K. c. Brand K will be $1,132.23 cheaper than Brand J. d. Brand K will be $340.32 cheaper than Brand J.

Answers

Answer 1

The loan amount is calculated by amortization and Brand K will be $340.32 cheaper than Brand J

What is Amortization?

Loan amortisation is the practise of making recurrent payments over time to completely pay off the principal and interest on a loan.

Mortgage amortisation is a word used in finance to describe the process of paying down your mortgage. The mortgage lender establishes a payment plan for you when you take out a mortgage. This uncomplicated plan, which includes equal payments over the course of your loan if you have a fixed-rate mortgage, is easy to understand.

The amount is calculated using the amortization formula:

P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}

where:

P is monthly payment

a is credit amount

r is the interest rate

t is the time in years

n is number of times the interest is compounded

Given data ,

Let the total loan amount for the brand J be represented as J

a = $975

r = 14.55% = 0.1455

t = 8 years

n = 12

Now , the amortization formula is

P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}

P = 975 ÷ {{[(1 + 0.1455/12)^12×8] - 1} ÷ [0.1455/12(1 + 0.1455/12)^12×8]}

P = $17.24

Total amount paid J = $17.24 × 96 = $1655.04

Let the total loan amount for the brand K be represented as K

a = $265

r = 14.55% = 0.1455

t = 3 years

n = 12

Now , the amortization formula is

P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}

P = 265 ÷ {{[(1 + 0.1455/12)^12×3] - 1} ÷ [0.1455/12(1 + 0.1455/12)^12×3]}

P = $9.13

Total amount paid K = $9.13 × 12 × 3 × 4 = $1314.72

The difference of amount of sofa j and sofa k = D

D = J - K

D = $1 655.04 - $ 1314.72 = $ 340.32

Hence , Brand K will be cheaper than Brand J by $340.32

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Related Questions

The Clemson Tiger Football team won the 2016 College Football National Championship. During the regular season, they won 11 games and lost 1. The data set below is the number of points by which they won (positive values) or lost (negative value) each game.

{6,6,59,19,6,46,7,3,54,−1,22,49} = {-1,3,6,6,6,7,19,22,46,49,54,59}

What is the median? ________
What is the mode? _________
What is the mean? _________
What is the 5% trimmed mean? (Round to the nearest whole number when determining the number of values to trim).
Are these averages parameters or statistics?

Answers

median  is the middle value, since there is an even number, add the 2 middle numbers and divide by 2

median = 9 +17 = 26/2 = 13

mode is the number that is repeated most often

mode = 6

mean is the average of all the numbers, when added they equal 276

276/12 = 23

mean = 23

5% trimmed mean = 218 /10 = 21.8

 the averages are statistics since the points of a football game can vary

For the initial value problem y' −xy = x, y(0) = 1. write down the first four nonzero terms of the series

Answers

Not clear if you're supposed to find a series solution to the ODE, or solve exactly then give the requested terms of the series expansion of the that solution...

The exact solution is easy enough to find. We can separate the variables:

[tex]y'-xy=x\iff \dfrac{\mathrm dy}{\mathrm dx}=x(1+y)\implies \dfrac{\mathrm dy}{1+y}=x\,\mathrm dx[/tex]
[tex]\implies\ln(1+y)=\dfrac{x^2}2+C[/tex]
[tex]\implies y=Ce^{x^2/2}-1[/tex]

Given that [tex]y(0)=1[/tex], we have

[tex]1=C-1\implies C=2[/tex]

Then recall that

[tex]e^x=\displaystyle\sum_{n\ge0}\frac{x^n}{n!}[/tex]

to write the solution as

[tex]y=2\displaystyle\sum_{n\ge0}\frac{\left(\frac{x^2}2\right)^n}{n!}-1[/tex]
[tex]y=1+2\displaystyle\sum_{n\ge1}\frac{\left(\frac{x^2}2\right)^n}{n!}[/tex]

so the first four terms of the series are

[tex]1+x^2+\dfrac{x^4}4+\dfrac{x^6}{24}[/tex]

Let a and b be events in a sample space s such that p(a) = 0.41, p(b) = 0.46 and p(a ∩
b.= 0.14. find p(a | b).

Answers

B the answer to the problem
Final answer:

The conditional probability that event a will occur given that event b has occurred, denoted as p(a | b), is approximately 0.3 or 30%.

Explanation:

The question is asking for the conditional probability of the event a given that event b has occurred, written as p(a | b). In probability theory, the formula for conditional probability is p(a | b) = p(a ∩ b) / p(b). Here, we already know that p(a ∩ b) = 0.14 and p(b) = 0.46. Substituting these values into the formula gives us:

p(a | b) = 0.14 / 0.46 = 0.304347826.

So, the probability of event a occurring given that event b has occurred is approximately 0.3 or 30%.

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6x+24/x^2+7x+12 simplify

Answers

Please enclose the denominator in parentheses to reduce ambiquity.

6x+24/x^2+7x+12

becomes

6(x+4)                  6(x+4)
------------------ = ----------------   Cancel the factors (x+4)
(x^2+7x+12)        (x+4)(x+3)

                               6
                      = -------------
                              x+3

rewrite y^2(9y^2+4y-9) in standard form

Answers

y²(9y² + 4y - 9)

Simplify.

(y² · 9y²) + (y² · 4y) + (y² · -9)

Simplify.

9y⁴ + 4y³ - 9y²

~Hope I helped!~


if f'(2) = 3.1 and g'(2)=7.3 then the graph of f(x)+g(x) has slope 10.4 at x=2.True or false

Answers

For functions, its derivative on a certain variable is its slope. This means that the slope of f(2) is 3.1 and that of g(2) is equal to 7.3. 

To determine the slope of the f(x) + g(x) in terms of x is equal to,
             f'(x) + g'(x) 
Then, substitute x with 2,
            f'(2) + g'(2)
Substituting the known values,
           3.1 + 7.3 = 10.4

Hence, the answer is TRUE. 

Final answer:

The statement is true, as the slope of the graph of f(x)+g(x) at x=2 is the sum of the slopes of f and g at that point, which equals 10.4.

Explanation:

The statement is true.

In calculus, the derivative of a function at a particular point measures the rate at which the function is changing at that point. It is analogous to the slope of the tangent line to the graph of the function at that point.

When we are given that f'(2) = 3.1 and g'(2) = 7.3, these values represent the slopes of the functions f and g at x = 2, respectively.

To find the slope of f(x) + g(x) at x = 2, we simply add the slopes of f and g at that point. This is based on the rule that the derivative of the sum of two functions is the sum of their derivatives, or symbolically, (f+g)' = f' + g'.

Therefore, the slope of the graph of f(x)+g(x) at x=2 is indeed 10.4 (3.1 + 7.3).

A store had 888 sodas, both diet and regular. The ratio of diet sodas to regular sodas was 8:4. How many diet sodas were there?

Answers

so you need to divide 888 by 12 to find how much much is 1 in the ratio, 888/12=74 
so, diet sodas,

74*8=592

there were 592 diet sodas.

Hope this helps.


Answer:no. I don’t understand. Where did the 12 come from

Step-by-step explanation:

What does it mean to say that lim n → ∞ an = ∞? the terms an become small as n becomes large. the terms an approach zero as n becomes large. the terms an become large as n becomes large. the terms an become small as n becomes small. the terms an become large as n becomes small?

Answers

The limit [tex]\lim_{n \to \infty} a_n = \infty[/tex] means that the term  [tex]a_n[/tex] becomes large as n becomes large

The limit of a function describes the behavior of such function as the independent variable approaches a certain value

Infinity [tex]\infty[/tex] represents a very large number

In the limit, both n and [tex]a_n[/tex] tend to infinity

The given limit is:

[tex]\lim_{n \to \infty} a_n = \infty[/tex]

The limit above describes the behavior of [tex]a_n[/tex] as n approaches infinity

As n approaches infinity [tex]a_n[/tex]  also approaches infinity

Therefore, the description of the limit [tex]\lim_{n \to \infty} a_n = \infty[/tex] is that the term  [tex]a_n[/tex] becomes large as n becomes large

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Final answer:

The statement 'lim n → ∞ an = ∞' means that the terms an become large as n becomes large.

Explanation:

The statement lim n → ∞ an = ∞ means that the terms an become large as n becomes large.

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By decreasing each dimension by 1 unit​, the area of a rectangle decreased from 40 square feet​ (on the​ left) to 28 square feet​ (on the​ right). Find the percent decrease in area.

Answers

Attached a pic of the solution (s).
Final answer:

The percent decrease in the area of a rectangle from 40 square feet to 28 square feet is calculated by dividing the difference in areas (12 sq ft) by the original area (40 sq ft) and multiplying by 100%. The result is a 30% decrease in area.

Explanation:

The percent decrease in the area of a rectangle can be found by first calculating the difference in the areas and then dividing that difference by the original area. In this case, the original area of the rectangle was 40 square feet and it decreased to 28 square feet, a difference of 12 square feet.

We use the formula for percentage change which is:

(change in value) / (original value) × 100%

Here, the change in value is the difference in areas (12 square feet) and the original value is the original area of the rectangle (40 square feet). Thus we calculate:

(12 sq ft/ 40 sq ft) * 100% = 30%

So, the percent decrease in the area of the rectangle is 30%.

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The height of Niagara falls is 182.How many yards high is Niagara falls

Answers

i believe the answer is 60.6
Final answer:

To convert the height of Niagara Falls from meters to yards, we multiply the given height of 182 meters by the conversion factor of 1.09361 yards per meter, which gives us approximately 199.18 yards.

Explanation:

The height of Niagara Falls is provided in this question as 182. However, no units are given so let's assume this is in meters as that's a common unit for height. The conversion factor from meters to yards is approximately 1 meter = 1.09361 yards. Therefore, we multiply the given height in meters by this conversion factor to get the height in yards.

First, identify the height given in the question- here it is 182.Next, apply the conversion factor: 182 meters * 1.09361 yards/meter.Doing this multiplication gives us approximately 199.18 yards.

So, Niagara Falls is approximately 199.18 yards high when converted from meters.

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The length of a ribbon is 3/4 meter. Sun Yi needs pieces measuring 1/3 meter for an art project. What is the greatest number of pieces measuring 1/3 meter that can be cut from the ribbon? How much ribbon will be left after Sun Yi cuts the ribbon?

Answers

the greatest number of pieces is 2 pieces. There will be 1/12 remaining

a consumer purchased a computer after a 15% price reduction. if x represents the computer's original price, the reduced price can be represented by

Answers

The answer represented by x X .15

Makayla's local movie theater has a moviegoer club that charges an annual registration fee of 25 dollars.However, movie tickets are discounted for members at 6 dollars per ticket, instead of 9 dollars per ticket.Let m equal the number of movie tickets Makayla purchases in a year. Write a function to model the amount of money Makayla spent going too the movies during the year she joined the club. C(m)=6x+25 The domain is best represented by: A)integers B)whole numbers C)rational numbers D)real numbers Algebra chestercat

Answers

domain is the value of x, in this case, the number of tickets. you cannot cut a whole ticket into fractions of pieces, it cannot be negative wither, so the number of tickets has to be a whole number.

Jana is doing an experiment. She is on a dock that is 10 feet above the surface of the water. Jana drops the weighed end of a fishing line 35 feet below the surface of the water. She reels out the line 29 feet, and then reels it back in 7 feet. What is the final distance between Jana and the end of the finishing line?

Answers

To solve we have the following equation below,

Assumption: Line of reference is the surface of the water.

Final distance between Jana & fishing line = (dock height) +(reels out) -(reels back)  


Final distance between Jana & fishing line = 10 + 35+ 29 - 7 = 67 feet

 ANSWER: 67 feet

Check the answer that best describes the relationship between f(x) and x. (for example if f(x) is θ(x)θ(x) check that as your answer and not o(x)o(x) or ω(x)ω(x) even though these are true also in this case.)

Answers

Which course is this for? I feel like I may need a little more information, but the simplest explanation I can give given the question is:

f(x) is the value of a function f evaluated at the value x. The formal definition of a function is a particular set of rules that associates a particular value with another. For an analogy: you can think of as a machine that takes in an input, transforms it according to a certain set of rules, and produces an output. In this analogy, x would be the input and f(x) would be the output.

Prove or disprove that the product of two irrational numbers is irrational

Answers

Hi. The statement you gave is somewhat true, but not always. I disprove this and there are tons of websites that can help you with more in depth explanation. Have a good day.

The product of two irrational numbers can be either rational or irrational.

The product of two irrational numbers is not always irrational. To understand this, let's consider an example and a counterexample.

Example of an Irrational Product

Take the square root of 2 (\/(2)) and the square root of 3 (\/(3)). Both of these numbers are irrational. Their product is:

\/2 × \/3 = \/6

Since \/6 cannot be expressed as a fraction of two integers (making it irrational), this is an example where the product of two irrational numbers is irrational.

Counterexample of a Rational Product

Now, consider another example with \/(2) and \/(2). Since both are irrational, their product is:

\/2 × \/2 = 2

Here, 2 is a rational number because it can be written as a fraction (2/1). Therefore, this is a counterexample where the product of two irrational numbers is rational.

In summary, the product of two irrational numbers can be either rational or irrational depending on the specific numbers involved.

I REALLY NEED HELP WITH MY CALC CORRECTIONS. THIS IS THE THIRD TIME IVE POSTED THIS. I NEED HELP ASAP PLS!! I HATE CALC 1

Answers

1. As x approaches 1,  f(x) approaches  3-1,  that is 2.

If a = 2 and b = 3,   f(1) = 2(1)^2 + 3(1)  = 5

So there is a 'jump' in values of x at x = 1.  So its not continuous at x=1.

2.  For continuity  at x = 1, ax^2  + bx must = 2  that is when a + b = 2.

3. for continuity at x = 2 , ax^2 + bx  must be = 0 that is when a*2^2 + 2b = 0

- that is 4a + 2b = 0.

4. we have system of equations:-

a + b = 2
4a + 2b = 0 

this gives a = -2 and b = 4   So  f(x) is continuous when a = -2 and b = 4.

Only the Fahrenheit one plz

Answers

The formula given is:
F = 1.8C + 32
The temperature C is given as -20
So, all you have to do is plug the given C temperature in the formula to get the corresponding F temperature as follows:
F = 1.8(-20) + 32 = -36 + 32 = -4 degrees Fahrenheit

Jane saved $ 800. Her sister has 10 times as much money. How much money does Jane's sister have? Use number or words to explain your answer.

Answers

10 times ad much money means to multiply. so 800 times 10 is 8,000

on Monday 2/3 of the team practiced Tuesday 7/8 Wednesday 1/2 and Thursday 3/4 on which date were the most team members present at practice

Answers

On Wednesday because half of the team was there
Find common denominator to compare fractions. Use 24
Monday =2/3 (8/8)=16/24 16 out of 24 showed
Tuesday=7/8 (3/3)=21/24 21 out of 24 showed
Wednesday=1/2 (12/12)=12/24 12 out of 24 showed
Thursday =3/4 (6/6)=18/24 18 out 24 showed

On Tuesday, 21 out of 24 players showed up and that is the most team members showed up.

2+1.25f=10−2.75f solve for f

Answers

Hey there!

2 + 1.25f = 10 - 2.75f
Add 2.75f to both sides.

1.25f + 2.75f = 4f

4f + 2 = 10
Subtract 2 from both sides.

4f = 8
Divide both sides by 4 to solve for f.

f = 2

I hope this helps!

The value of f is 0.02.

What is an expression ?

Expression is a formation of numbers and variables with mathematical operations.

According to the given question we have to solve for f or we can say we have to find the value of f for the given expression which is

2+1.25f=10−2.75f                (lets multiply each term by 100 to remove

                                                                                              decimals )  

∴ 200 + 125f = 1000 - 275f

125f + 275f = 1000 - 200

400f = 800

      f = 800/400

      f = 2.

As we have multiplied by 100 we have to divide by 100 we obtain the exact result.

So, 2/100 is = 0.02

f = 0.02.

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What is the distance between 0.5 to -1.5

Answers

7.07 is the distance between the two points
the difference is one

A suit is on sale for $154. If the original price of the suit was $440, what percent was discounted for the sale?

Answers

so, we know the original price is 440, but it got dropped to 154, for a difference of 286.

so, if we take 440 to be the 100%, what is 286 off of it in percentage anyway?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 440&100\\ 286&p \end{array}\implies \cfrac{440}{286}=\cfrac{100}{p}\implies p=\cfrac{286\cdot 100}{440}[/tex]

A data set a has a mean of 7,a median 5,and a mode of 8.wich of the the numbers 7,5,and 8 must be in the data set?

Answers

If the mode is 8, then 8 actually shows up in the data set.  This is not true of 7 or 5.

PLZ HELP IM FAILING!!!!!! The linear equation y−3=4(x+5)y−3=4(x+5) y minus 3 equals . 4 open x plus 5 close is in what form.

Answers

Here, as in your previous post, you present the same equation several times in different forms.  Don't do that.  Present the equation once, exactly once.  What you have input contains considerable unnecessary duplication which confuses you as well as me (at first).

y-3 = 4(x+5) is "the equation of a straight line in point-slope form."  That's it.


How can you check to see if this equation is correct? 12+39=49

Answers

Use the equation 49 - 39 = ___ and see if you get 12. You can also flip it and use 49 - 12 = ___ and see if you get 39.

Answer:

By solving it.

Step-by-step explanation:

In order to see if the equation is correct, you just have to perform the operations in both sides of the inequality and then check if those are equal, that means that the equation is correct, for example if both sides of the equation give as a result 10 then the equation is correct, now let´s do it with the problem:

12+39=49

51=39

Since 51 is not equal to 39 that means that the equation is not correct.

A lawn is in the shape of a trapezoid with a height of 40 feet and bases of 60 feet and 140 feet. How many bags of fertilizer must be purchased to cover the lawn if each bag covers 1800 square​ feet?

Answers

2.2222 bags are needed to cover the land

The weight of 1000 identical samples of a substance is 10 pounds. What is the weight of 10 samples?

Answers

Help?? I need that question to but just that the weight instead of being 1000 is 2000
First find the weight of 1 sample. 10/1000= 0.01 so each sample weights .01 pound. So what is the weight of 10 samples. Well we multiply 10 * .01 = .1 pounds

A video editor takes 15 hours to add a

Answers

so the Level III editor does it in 15 hours, the Level II(slower) does it in 25 hours and the Level I(even slower), does it in 34 hours.

now, since the Level III one does it in 15 hours, in 1 hour alone, how much has it done?  well, it only has done 1/15 of the whole work.

the Level II has 1 hour done only 1/25 of the whole work then, and the Level I has only done 1/34 of the whole work.

now, say they all do it in "t" hours, so how much have they edited in 1 hour altogether then?  well, they have only done 1/t.

[tex]\bf \stackrel{\textit{Level III rate}}{\cfrac{1}{15}}+\stackrel{\textit{Level II rate}}{\cfrac{1}{25}}+\stackrel{\textit{Level I rate}}{\cfrac{1}{34}}~~=~~\stackrel{\textit{total work done}}{\cfrac{1}{t}} \\\\\\ \textit{doing a quick prime factoring, we end up with an LCD of }\underline{2550}~thus[/tex]

[tex]\bf \cfrac{1}{15}+\cfrac{1}{25}+\cfrac{1}{34}=\cfrac{1}{t}\implies \cfrac{170~+~102~+~75}{2550}=\cfrac{1}{t}\implies \cfrac{247}{2550}=\cfrac{1}{t} \\\\\\ 247t=2550\implies t=\cfrac{2550}{247}\implies t=10\frac{80}{247}\implies t\approx 10hrs,~19min[/tex]

Find f`(x) for the following function. Then find f(5),f(0),f(-9).
f(x)=2x+1 (simplify)

Answers

If f`(x) means the derivative, or gradient, of f, then the answer is 2.
f(5)=11, f(0)=1 and f(-9)=-17.
We can calculate the gradient using these values:

Gradient=(11-1)/(5-0)=(-17-1)/(-9-0)=(-17-11)/(-9-5)=2.
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