A ratio can be expressed as a fraction.

Using 'g' to represent the number of girls and 'b' to represent the number of boys, the ration of boys to girls is b / g.

The ratio of boys to girls is 2:7 becomes:     b / g = 2 / 7

Since there are 250 more girls than boys:     g = 250 + b

Substituting the second equation into the first:     b / (250 + b) = 2 / 7

Cross multiply:      b · 7 = 2 · (250 + b)

Multiply out:          7b = 500 + 2b

Subtract:              5b = 500

Divide:                   b = 100             --->    g = 250 + b     --> g = 250 + 100     --->   g = 350

Check:      b / g = 2 / 7     --->     100 / 350  does reduce to 2 / 7.

You can calculate how much money the car lot took in ($31,137 + $10,507). 

However, how much it "made", after deducting what it originally paid for the cars plus all the other expenses can't be calculated from the problem.

Multiplying by 10^8 results in moving the decimal point 8 places to the right.

Since you already have 3 decimal places, you will need to add another 5 places, thus append 5 zeroes.

Therefore, the answer is 149600000.

So we have

√(x²) + x² / [x² +1]    and we just want to simplifiy this

First of all,we need to be careful with the first term.....many people simplify this as just "x", but that's not correct. To see why, what if x = -3 ??? If we wrote "x," we would be claiming that we could get a negative answer from a positive square root, which is impossible. The correct answer is that √(x²) = lxl  ... (this is the definition of absolute value anyway....)

So we have

lxl +  x² / [x² +1]    and getting a common denominator, we have

[ lxl* (x² +1) +  x²  ] / [x² +1]

Counting from the left side, the first 4 digits are 1265.

Check to see if the last digit should be a 5 or a 6.

Since the next digit is a 5, round the previous 5 up to 6.

The correct answer is 12.66.

Very nice, Alan !!!!!

Very interesting, Melody !!!

Thx for the reply geno3141 :)

I knew someone would get the answer :)

There are 10! (10 factorial which is 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) ways to choose ten items.

Only one of these ways is alphabetical, all the others aren't, so there are 10! - 1 ways that are not alphabetical.

(OK, one of these ways is reverse alphabetical, so do you want to count that as alphabetical also? )

This answer assumes that no names are duplicated.

First, collect all the variables to one side; since the right side has only one term, which is the variable, get rid of the 3y from the left side by subtracting 3y from both sides:

3y + 6 - 3y < 2y - 3y

Simplify:

6 < -1y

Remove the -1 by dividing both sides by -1; however if you multiply or divide an inequality by a negative number you must change the direction of the inequality (you don't change the direction if you add or subtract a negative -- only if you multiply or divide):

6 / -1 > -1y / -1

-6 > y     --->   y < -6

To solve an equation do the opposite to the number that you want to remove.

You want to remove the 2; since it represents division, multiply both sides by 2:

2 · 24 = 2 · -r / 2

48 = - r

Now, to remove the negative sign, which represents multiplying by -1, divide by -1:

48 / -1 = -r / -1

-48 = r 

That distance/displacement question does looks interesting. 

I understand the steps to solve and the other numbers, but where do you get 0.5 from?

11 = 10 + 1 = 10^1 + 1

101 = 10^2 + 1

11 x 101 = (10^1 + 1)(10^2 + 1)= 10^3 + 10^2 + 10^1 + 1

(The problem starts with 11 -- which is 10^1 + 1 -- Now mutiplying by 10^2 results in new terms -- 10^3 + 10^2 -- which are just larger than the old terms (which are saved by multiplying by 1) )

10001 = 10^4 + 1

11 x 101 x 1001 = (10^3 + 10^2 + 10^1 + 1) x (10^4 + 1) = 10^7 + 10^6 + 10^5 + 10^4 + 10^3 + 10^2 + 10^1 + 1

(The old answer was 1111 = 10^3 + 10^2 + 10^1 + 1 -- Now multiplying by 10^4 results in the new terms -- 10^7 + 10^6 + 10^5 + 10^4 -- which are just larger than the old terms 10^3 + 10^2 + 10^1 + 1 (which are saved by multiplying by 1) )

So, if we multiply by a number -- a power of ten that results in sufficiently new terms -- we will get an answer that begins with only 1s and if we then append to that the old terms by multiplying the old terms by 1, we will get an answer that has only 1s.

The necessary power of ten in the new factor is detemined by your requirement for the number of zeroes.

Realised I was doing a strange combination of adding and multiplying at the same time.

It makes sense now.

Thanks

Thx for the answer. I guess there are two of us now :)

Yes, the product will always be repuit; I don't know the answer, but there must be one because anomalies do not occur very often in science/math. I am curious what the answer is now.

Thanks for your reply, was begining to think the way I had written it in words rather than numbers was scaring people off. Since found out how to write with superscript - Format then superscript to turn on or off. Was just about to repost correctly written but you beat me to it.

I'm still a bit confused.

When I got to 1/a²a²b² as you did, I combined a²a²b² thinking this basically meant a2*a2*b² which I worked out to 2a⁴b².

I'm not suggesting you are wrong as you have the same answer as my book says but I can't understand how a²*a² is a⁴, not 2a⁴ as I have put.

Sorry to question it but I can't understand it as it is, am I looking at it incorrectly?

a^-2 = 1 / a²

( 1 / a² ) / ( a² b² )

    = ( 1 / a² )  · ( 1 / ( a² b² ) )

    = (1  ·  1  ) / ( a² · a² b² )

    = 1 / (a^4 b²)

In other words, with an "a to the power of minus 2" move the factor to the denominator and make the exponent positive two.

Then combine that with what is already in the denominator (another a² and a b²) to end with an a^4 b² in the denominator.

(51-[3+4]squared) to the power of 5

So you mean:

[ 51 - (3+4)^2 ]^5

Fist add the numbers in the round paranthesis (actually called addends). We know that the sum is 7, so we get:

( 51-7^2 )^5

Seven squared equals 49, we get:

(51-49)^5

51-49=2, we get:

2^5

2^5 = 2*2*2*2*2, we get:

32

3+4=7

7^2=49

51-49=2

2^5=32

I also did some research on that Infinite Loop road sign.

If you hover the cursor over the log key you will see ln, e^x, lg2 and 2^x pop up.  lg2 is log to the base 2.

Alternatively, you can type log(x,2) where x is the number of which you want to find log to the base 2.

to solve a basic algebraic equation you must seperate like terms, putting all knowns on one side and all unknowns on the other. Once you have done this you can solve x

x+5=6

x=6-5

x=1

Chris's infinite loop got me thinking.    .....    Thanks Chris.

There is a place in Western Australia called Useless Loop!

I've been there, or at least I have been to Monkey Mia which is nearby.

Monkey Mia is famous for its very tame wild dolphins.  

They come right into shore and can be feed and petted by well, anyone. (Except they are not very hungry)

I think that is my shoulder in the photo. This really is a wild dolphin. 

@@ End of Day Wrap        Sat 27/9/14        Sydney, Australia      Time 8:25 pm      ♬  

Hi all,

Great answers today from DragonSlayer554, Geno3141, GoldenLeaf, Coolkille98, CPhill, Rosala, Chilledz3non, AlexM, Alan and NuclearGearhead.  Thanks everyone.     

Thanks for giving my wraps thumbs up Dragon, I really appreciate that.    

Now for a few interest posts:

1) Rosala's funnies   (Thanks Rosala)