All Answers 358087 Answers

We can choose any 5 of the 7 seats for them to sit in. And for each of these choices, there are 5! ways to arrange the children.

So we have...

C(7,5) * 5!  = 2520 ways......

ln(a) = b  means that a = e^b, so ln(x+9) = 1 means x+9 = e¹ so x = e - 9 or in approximate decimal form:

$${\mathtt{x}} = {\mathtt{e}}{\mathtt{\,-\,}}{\mathtt{9}} \Rightarrow {\mathtt{x}} = -{\mathtt{6.281\: \!718\: \!171\: \!540\: \!954\: \!8}}$$

A logistic curve (function f(x) below) seems to fit reasonably well.

However, there is no such thing as the equation, in general, when creating curves that are a best-fit to a few data points.  You can fit lots of curves to this data; some will fit better than others.  Did you have a particular type of curve in mind?  Your title suggests you want a logarithmic fit of some sort, but straight line fits to ln(y) vs x; y vs ln(x) or ln(y) vs ln(x) all give very poor fits! 

Pi is an irrational number......thus it never terminates.........

-7(-a^2)(-b^3)

Simply multiply out all the terms and note that we have 3 negatives [since 2 negatives make a positive or plus, we are left with +*- which means we end up with a negative, -].

So, our answer is: -7a^2b^3.

The graph looks like this: 

Notes:

*When x = 0 --> y = |0-1| + 2|0-3| = |-1| + 2|-3| = 1 + 6 = 7 --> (0,7).

*When x = 1 --> we notice that we are left with 2|x-3| since |1-1| = |0|. The graph also becomes steeper when x = 1 until x = 3.

2^(0.2976) = 1.2290980416714191.

Note: Since 0.2976 is ~0.3 --> 3/10, we can also write it as 2^(3/10) = the 10th root of 2^3 = the 10th root of 8 --> 1.2311444133449163.

The two answers are very similar.

What is the "a" in between the numbers? 

If it stands for "and" then 18200 + 10 = 18210.

It is similar to 12 in. = 1 foot, so 12 inch pounds = 1 foot pound.

examples:

101     103     107     109
113     127     131     137     139     149     151     157     163     167
173     179     181     191     193     197     199     211     223     227
229     233     239     241     251     257     263     269     271     277
281     283     293     307     311     313     317     331     337     347
349     353     359     367     373     379     383     389     397     401
409     419     421     431     433     439     443     449     457     461
463     467     479     487     491     499     503     509     521     523
541     547     557     563     569     571     577     587     593     599
601     607     613     617     619     631     641     643     647     653
659     661     673     677     683     691     701     709     719     727
733     739     743     751     757     761     769     773     787     797
809     811     821     823     827     829     839     853     857     859
863     877     881     883     887     907     911     919     929     937
941     947     953     967     971     977     983     991     997    

Look at it this way.....if I gave you "2 less than 5"...isn't that just 5 - 2??

Then, "twice x "  is just 2x

And three less than "twice x" is just....... 2x - 3

Does that make sense??

We don't have to look very far for the first 3 digit number that "works"....doesn't 101 fit the bill??

It's not divisable by any even number nor by 3 or 5, either....

There are many numbers that "work'   (103 would be the next one.)

Did I misread this question??

Now my problem is to understand the expressions 3 less than twice x  You know that English is not my mother language =D  .. What is less than mean ! 

I just solved this by trial-and-error.

I'm sure there's a formula to this, but here's my reasoning:

If it is not divisiable by 2, 3, 4 ,5 ,6 ,or 10, it really has to be divisiable by 7, because 7 is a prime number.

So I tried 777, but that is divisiable by 3. 

Next I tried 707, and when divided by 2, 3 ,4 ,5 ,6, and 10 it did not come out as a whole number.

So I got 707. Hope this helps.

My answer is the same as Ninja's and Ninja is very good at explaining things but maybe a different presentation will help.  

3 less than twice x is (2x-3)  I just put it in brackets to make it clear

and

2 more than the quatity 3 times x is (3x+2)

and product means multiply

so the product of these is 

(2x-3)*(3x+2) = (2x-3)(3x+2)

and when you expand that out you get

$$(2x-3)(3x+2)\\
=2x(3x+2)-3(3x+2)\\
=6x^2+4x-9x-6\\
=6x^2-5x-6$$

Is that any clearer??  If not let us know and we will explain some more. 

I want to stress Alan's first answer.

With real numbers you cannot have the logarithm of a negative number.

I don't think that is so unusual - we are always guessing what the askers want. lol

How about 

2.37465892

or

2.365

or

2.365190352

or

3.370499999

If the number in the 3rd decimal places is 4 or less then the one in the 2nd place stays the same,

If the number in the 3rd decimal places is 5 or more then the one in the 2nd place goes up by one!

I hope that helps, 

Thanks, Melody.....now that I look at it, I think this is probably what the questioner meant, too. However, we both provided him/her with answers to two different things....that's unusual...!!!

Do you mean inverse trig?

inverse sin is the same as arc sin. so you'd press 2nd function then asin

It is the same idea for inverse cos and inverse tan.  

There's actually an option to switch the calculator to "fractions."

Assuming that we have some "one-to-one function" of x = f(x) = "y"

(Note that we might have to "restrict" the domain of the original function in order to produce an "inverse.")

1st, isolate x on one side of the equation

2nd, "switch" (exchange) x and y

3rd, for "y," write f^-1(x)  ...the " f^-1(x)" indicates the inverse function....

That's it, in a nutshell !!

2a+4-7a+a

So we have

2a + 4 - 6a =

-4a + 4

Thankns Ninja,

OR you could just copy it into the site calculator!

$${\frac{{\left({\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{-{\mathtt{5}}}\right)}^{{\mathtt{2}}}{\mathtt{\,\times\,}}\left({\mathtt{2.63}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{17}}}\right)}{{\mathtt{6.7}}}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{3}}} = {\mathtt{62\,805\,970\,149.253\: \!731\: \!343\: \!283\: \!582\: \!1}}$$

If I was going to do it more by hand.  I'm sure this is the same as Ninja, just presented a little differently.

$$\\\frac{(4 \times 10^{-5})^2(2.63 \times 10^{17})}{6.7} \times 10^3\\\\
\frac{16 \times 10^{-10}\times 2.63 \times 10^{17}}{6.7}\times 10^3 \\\\
\frac{16 \times 2.63}{6.7}\times 10^{
(3-10+17)} \\\\
6.28060\times 10^{
10} \qquad \mbox{Correct to 6 significant figures}\\\\$$

One of us has made a mistake Ninja.  Can you find it?

I found it  - you put 10^3 on the bottom and I put it one the top.

Both interpretations are valid.  That is why people need to use brackets (properly)!

That is an interesting explanation Sasini. I will give you thumbs up too.