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3 years ago

Which is the better deal 0% interest on a $28,300 car or purchasing a $22,000 vehicle with a five-year 6% simple interest loan

Mathematics

1 answer:

ElenaW [278]3 years ago

3 0

Answer:

0% interest on a $28,300 car is a better deal.

Step-by-step explanation:

Compare the total amount to be paid for each option;

Option1 : 0% interest on a $28,300 car

You will pay a total of 28,300 since there is $0 payable on interest

Option 2: $22,000 vehicle with a five-year 6% simple interest loan

Find the Amount; A=Simple Interest + Principal

Simple Interest = Principal* rate * time = (22000* 0.06 *5) = 6600

Amount payable= 22,000+6,000= $28,600

Therefore,0% interest on a $28,300 car is a better deal.

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Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive

Elena L [17]

Answer:

Constructive Proof

Step-by-step explanation:

Let x be a positive integer

x must be equal to sum of all positive integers exceeding it

i.e.

x = x + (x - 1) + ( x - 2) + ......... + 2 + 1

Equivalently,

x = ∑i (where i = 1 to x)

The property finite sum;

∑i (i = 1 to x) = x(x + 1)/2

So,

x = x(x + 1)/2 ------- Multiply both sides by 2

2 * x = 2 * x(x + 1)/2

2x = x(x + 1)

2x = x² + x ------- subtract 2x from both sides

2x - 2x = x² + x - 2x

0 = x² + x - 2x ----- Rearrange

x² + x - 2x = 0

x² - x = 0 ------ Factorise

x(x - 1) = 0

So,

x = 0 or x - 1 = 0

x = 0 or x = 1 + 0

x = 0 or x = 1

But x ≠ 0

So, x = 1

The statement is only true for x = 1

This makes sense because 1 is the only positive integer not exceeding 1

1 = 1

It is a Constructive Proof

A proof is constructive when we find an element for which the statement is true.

8 0

3 years ago

In a recent survey, 80% of those surveyed indicated that they preferred swimming to biking. Part 1 : If 352 people preferred swi

sladkih [1.3K]

Answer: 88

Step-by-step explanation: The equation us .8x=352 and 352/.8 is 440, which is the total. Multiply 440 by .2 which gives you 88

4 0

3 years ago

Read 2 more answers

The couch in your living room is old. You decide to recover the couch cushions with new fabric instead of buying a new couch. Th

alexgriva [62]

Answer:

$36.25

Step-by-step explanation:

Surface area: 2*l*w+2*w*h+2*h*l

2*2*2.5+2*2.5*0.5+2*0.5*2

10+2.5+2

14.5 sq. ft.

14.5*2.50=36.25

6 0

3 years ago

What is the percentage of 18/20

labwork [276]

18/20 is 90%

You can use a calculator to divide 18 and 20 and you will get 0.9 which is 90%

Or. simplify by dividing the top and bottom by 2, to get 9/10 which is still 90%

:)

7 0

3 years ago

Read 2 more answers

For a certain bathtub, it takes the hot water faucet

Valentin [98]

So, we know both faucets open, can do the whole job in 6minutes

ok, how much has the faster cold water faucet done in 1minute then?

well, let's say the the rate of speed of the cold water faucet is "c", so in 1minute it has done 1/c of the whole work

now, we know the hot water faucet is slower, it takes it 3 times as long, that means is 1/3 the speed of the cold water faucet, so, how much does the hot water faucet do in 1min? well, we know is 1/3 fast as the cold one, the cold one is 1/c, what's 1/3 of 1/c? well, 1/3 * 1/c

now, we know they both added together, can do the whole job in 6 minutes, so in 1minute, they've done 1/6 of the job then

thus

$\bf \begin{array}{cccccclllllll}
\cfrac{1}{c}&+&\left( \cfrac{1}{3}\cdot \cfrac{1}{c} \right)&=&\cfrac{1}{6}\\\\
\cfrac{1}{c}&+&\cfrac{1}{3c}&=&\cfrac{1}{6}\\\\
\uparrow &&\uparrow &&\uparrow \\
\textit{cold water rate}&&\textit{hot water rate}&&\textit{total done by both}
\end{array}\\\\
-----------------------------\\\\$

$\bf \cfrac{3+1}{3c}=\cfrac{1}{6}\implies 24=3c\implies \cfrac{24}{3}=c\implies \boxed{8=c}
\\\\\\
\textit{now, if the cold water faucet can do it in 8 minutes by itself}\\\\
\textit{then the hot water faucet can do it in 3 times as long}
\\\\\\
3\cdot 8\implies \boxed{24}$

4 0

3 years ago