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If a 1.25L bottle costs $0.75 how much does 125ml cost?

1 Liter =1,000 milliliters

1.25L x 1,000 =1,250 ml. So,

[125 / 1,250] x $.75 =$07.50 or 7.5 cents, or about ~8 cents.

Just divide:

15 / 474 =0.0316 x 100 =3.16%

Something seems to be wrong with your input :/

2 x (1999 x 1/24 + ?) 1 3/5 - 3 5/11 x 3 2/3 = 127 

\(2 \times (1999 \times \frac{ 1}{24} + ?) \text{ [something seems to be missing here] } 1 \frac{3}{5} - 3 \frac{5}{11} \times 3\frac{ 2}{3} = 127 \)

If by "numbers,' you mean consecutive positive integers, this isn't possible...to see why.....

Let the  "numbers"  be  x, x + 1  x + 2, x + 3, x + 4, x + 5

Adding these together  we get     6x + 15

So

6x + 15  =  150       subtract 15 from both sides

6x  =  135              divide both sides by 6

x  =  22.5      so.....the first number isn't an integer and neither are the other five

But.......the average of these "consecutive" numbers is 25  as follows

[ 22.5  +  23.5 + 24.5 + 25.5 + 26.5 + 27.5 ]  / 6  =

[ 22.5 + 27.5 + 23.5 + 26.5 + 24.5 + 25.5 ] / 6  =

[50 + 50 + 50 ] / 6   =

150 / 6    =

25

sin2x  / [ 1 - cos 2x ]  =   cot x

[2 sinx cos x ] / [ 1 - (1 - 2sin^2x) ]

[ 2 sinx cosx ]  /  [ 2sin^2 x]

{2 cos x ]  /  [ 2 sin x ]

cos x  / sin x              =       cot x

thank you 

sin ( x + y)   =   sinx cos y  +  sin y cos x

cos x  =   sqrt  ( 1 - sin^2 x)   =   sqrt [ 1 - (1/2)2 ]  = sqrt  ( 1 - 1/4)   =  sqrt (3/4)   = sqrt (3)/2

cos y  =  sqrt  ( 1 - sin^2 y )   =  sqrt [ 1 - (1/4)^2  ]  =    sqrt [ 1 - 1/16]  =   sqrt (15/16)  = sqrt (15) /4

So

sin ( x + y)   =  

sinx cos y  +  sin y cos x    = 

( 1/2) * sqrt(15)  /  4      +    (1/4) * sqrt (3) / 2    =

sqrt (15) / 8   +   sqrt (3) / 8  =

[ sqrt (15) + sqrt (3) ]   / 8

Correct.....!!!

if there's 474 boys, 15 of them would be 474/15 or about 32%

Number 1:5

Number 2:8

In this problem, "one number" and "another number" are simply referring to variables like x and y. "Is" means equal to. Therefore, twice one number is simply 2 multiplied by a variable. For my variables, I'll simply use x and y.

\(2x+y=18\)

\(4x-y=12\)

This is a system of equations. Normally, I gravitate toward substitution, but I'll actually use elimination to solve this. Notice how there is a y-term and a negative y-term. I can add the equations together to get this:

\(6x=30\)

Divide by 6 on both sides:

\(x=5\)

Okay, our first number is equal to five. To find the next number, y, substitute 5 into one of the equations. It doesn't matter which one; you'll get the same answer:

\(2(5)+y=18\)

Simplify 2*5:

\(10+y=18\)

Subtract 10 on both sides to isolate y, our second number:

\(y=8\)

Let the original tire be 100cm circumference and the new one be 120cm circumference

(that is 20% =bigger)

Say you want to go 1200cm

that would be 120  rotations for the original one and 100 rotations for the new one.

\(\frac{120-100}{120}*100\% =\frac{200}{12} \%=16.\dot6\%\)

The number of tire rotations needed has decreased by  16 and 2/3 %

------------------

Explaining it a different way :)

If the circumference has increased by 20% i.e. it is now 120% of the original

then

the gound covered by the tire will be  120%

so the rtations needed will be 100%/120% = 10/12 = 83.3% of the original.

which is 100-83.3 = 16.6% less than the original.   (that is .6repeater)

I've resolved it now, thank you

And

\(3 \times n^{-8}\\ =3 \times \frac{1}{n^{+8}}\\ =\frac{3}{n^8}\)

sin(70)/sin(39) = 0.8029615959688345     if the angles are in  radians

sin(70)/sin(39) = 1.4931863549155849   If the angles are in degrees

The answer is not an angle so I do not know what you mean

Sorry I didn't realise that the forum calc was set, by default)  to radians.

Thanks for pointing this out to me Hectictar ;)

If you have 5 potato chips, and I give you negative one potato chip, how many potato chips do you have? I know that it is impossible in real life, but just imagine how many potato chips you would have if I gave you negative one? That would make you have 4 potato chips.

5 potato chips plus negative 1 potato chips = 4 potato chips

5 + - 1

= 5 - 1

= 4

So...

   70 + - 60

= 70 - 60

= 10

\(3\cdot m^2\cdot n^{-5}\cdot m^{-2}\cdot n^{-3} \\~\\ =3\cdot m^2 \cdot m^{-2} \cdot n^{-5}\cdot n^{-3} \\~\\ =3\cdot m^{2+-2}\cdot n^{-5 + -3} \\~\\ =3\cdot m^0\cdot n^{-8} \\~\\ =3\cdot n^{-8}\)

Thanks, I have used paint very little.  :/

I usually use geogebra but maybe paint would be better  for pics like this.

 I should experiment with paint I guess.

If you haven't used it yet you may like to play with geogebra, it is very good.

Thank you Melody !! 

I just used " paint " to make the picture. :)

mutiply 0.5*(BxH)=A

the slope of this line  =  \(\frac{2-1}{3--2}\,=\,\frac{1}{5}\)

and the line passes through (-2, 1) so..

(y - 1) = \(\frac15\)(x - -2)

y - 1 = \( \frac15 \) x + \(\frac25\)

y = \( \frac15 \) x + \(\frac75\)

Multiply through by -5.

-5y = -x - 7

Add x to both sides.

x - 5y = -7

What a pretty pic Hectictar!

What program do you draw your pictues in?

This is how I would do it.

let acos(u) = alpha  

Draw a right angled triangle and let alpha be an acute angle.

since  cos( alpha) = u/1

let  the adjacent side by u and the hypotenuse be 1

using pythagoras's theorem you get  

 \(\text{opposite side=}\sqrt{1-u^2}\)

\(cosec(\alpha)=\frac{hyp}{adj}=\frac{1}{\sqrt{1-u^2}}\)

but you do not know which quadrant alpha is in so

\(cosec(\alpha)=\pm\frac{1}{\sqrt{1-u^2}}\)