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The equation you would use is I= P( Money started with) * r(Percent in decimal form) * t(Time in years) for the intrest questions

The equations you would use for the sale questions is (money * percent in decimal=x) then do (money-x)  for sale or (money+x) for markup

1.) 65*.2= 13, then do 65-13= $52

2.)1200*.03*4= 144$

3.)4.50*.40 then do 4.50+1.80= $6.30

4.)150*.55*4=$330 earned

I might be wrong with these so other people reply to correct me please so I can correct it!

That is right! This is called "continued fraction" as the questioner rightly says so:

We can represent it as follows: x = 1; 1, 2, 1, 2, 1, 2.......etc., which,in turn, can be written as:

1+ 2 / {1+x} = x, solve for x

2/(x + 1) + 1 = x

Bring 2/(x + 1) + 1 together using the common denominator x + 1:
(x + 3)/(x + 1) = x

Multiply both sides by x + 1:
x + 3 = x (x + 1)

Expand out terms of the right hand side:
x + 3 = x^2 + x

Subtract x^2 + x from both sides:
3 - x^2 = 0

Subtract 3 from both sides:
-x^2 = -3

Multiply both sides by -1:
x^2 = 3

Take the square root of both sides:
 x = sqrt(3) or x = -sqrt(3). Since the continued fraction has all positive signs, then the correct is: sqrt(3).

@Guest yeah that is a faster way I should've done that

No, it is called "continued fraction" of a well-known number: It means:

1 + 1/(1 + 1/(2 + 1/(1 + 1/2 +.......etc.)))

((4+i)/(3-i))+((5-2i)/(4+2i))-((3+7i)/(1-2i)) 

Thank you so much!

Thank you so much!

The equation you would use is I= P * r * t

P is the begining amount, or $225,000 in your case

r is the intrest rate or 13%, which converted to a decimal is .13

t is the amount of time in years so in your case, it is 5

225000 × 0.13 x 5 = $146250

The difference between two numbers is 9. Three times the smaller is equal to twice the larger.  What are the numbers? 

Let the smaller number = S

Let the larger number =L

L - S = 9 ...........(1)

3S =2L..............(2)

From (1) we have:

L = 9 + S     sub into (2)

3S = 2(9 + S)

3S = 18 + 2S

3S - 2S = 18

S = 18 the smaller number.

L - 18 = 9

L = 9 + 18

L = 27 the larger number.

Can you please rephrase that? I'm not sure what {1; 1, 2, 1, 2, 1, 2, 1, 2.........etc.}. Also, I think the mathy term you are trying to say is "repeating decimal", or "continued decimal".

We make 2 equations(x is the smaller number; y is the bigger number):

y-x=9

3x=2y

y-x=9

y=(3x)/2

(3x)/2-x=9 => (3x)/2-(2x)/2=9 => x/2=9 => x=18

y=(3*18)/2 => y=54/2 => y=27

Therefore, x and y are 18 and 27 respectively.

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depends on the brand

actually @CPhill thats wrong

you have 1 mode so you have 3 61s and 178, 179

12 

16+(-4)=16-4=12

Mean  =   [ Sum of the Values ] /  [ Number of Values ]  =

[ −54 + (−32) + (−70) + (−25) + (−65) + (−42)  ]  / 6  =

[ -288 ]  / 6  =

-48

Yay!! Thanks!

It does seem like there would be a more elegant way to do it.... 

GOOD JOB , hectictar....that's exactly the correct answer  !!!

BTW  - I solved this several years ago  [ after thinking about it for a LONG time] and used an algebraic approach like you did.....I remember that  Lloyd's solution was rather elegant - no algebra involved - , but I can't remember how he did it.....!!!!!

Ah ha!!! I think I found a way  (Though maybe not the best way)

Let's call the width of the river = w ,

the rate of the "first" boat = r₁  , the rate of the second boat = r₂  ,

and the time it takes for the boats to meet the first time = t₁

time = distance / rate

Let's say the first boat is the one that goes  w - 720 yards. So...

t₁  =  (w - 720) / r₁

And the second boat goes  720 yards.

t₁  =  720 / r₂

(w - 720) / r₁  =  720 / r₂   →   r₁  =  (w - 720) / (720 / r₂)

Then,  t₂  is the time it takes the boats to meet again. So the first boat must travel the remaining 720 yards and then it must go  w - 400  yards to be 400 from the other side.

t₂  =  (720 + w - 400) / r₁  =  (w + 320) / r₁

And the second boat must go the remaining  w - 720 yards and then it must go 400 yards.

t₂  =  (w - 720 + 400) / r₂  =  (w - 320) / r₂

(w + 320) / r₁  =  (w - 320) / r₂   →   r₁  =  (w + 320) / ( (w - 320) / r₂ )

(w - 720) / (720 / r₂)  =  (w + 320) / ( (w - 320) / r₂ )

(w - 720) * (r₂ / 720)  =  (w + 320) * (r₂ / (w - 320) )       Divide both sides by  r₂ .

(w - 720) / 720  =  (w + 320) / (w - 320)

 -7x+3 = 14   subtract 3 from both sides

-7x  = 11       divide both sides by -7

x  =  -11/ 7

Should be next to the = button or under the numbers

Thank you so so much!!! 

It is actually for a fraction sign.

Mass  = Density  x Volume

The Volume is     [1.00 * 4.00 * 2.50] cm^3 =  10 cm^3

So...we have that

Mass =  [22.57gm / cm^3]  *  [10 cm^3]  =   225.7 gm