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The number  of inches, I, of water in  the pool  x minutes after the rain starts to fall is given by :

I  =  4 + 3x

BTW......there is no "inequality" here......it's just a linear equation modeling the situation

374.20833333333....pi

Hey guys! Thanks for using this thread. Just to speed things up, let's post another question. 

Mr. Osborne asks each student in her class to draw a rectangle with integer side lengths and a perimeter of 50 units. All of her students calculate the area of the rectangle they drew. What is the difference between the largest and smallest possible area?

sine  =  y / r  =   .642 / 1         

cosecant =   r / y  =   1 / .642

cosine =   x / r   

Note....  x = sqrt (1 - y^2 )  =    sqrt ( 1 - .642^2) ≈ .7667   

So.....x / r  =  .7667/ 1

secant  =  r / x   =   1 / .7667

tangent  =   y / x  =  .642 / .7667

cotangent  =  x / y  = .7667 / ,642

Terrific !! That is exactly the answer I have. Thank you very much.

143.47  =  100 * [ 1.01]^N / [ 1.01^N  - 1 ]      divide both sides by 100

1.4347  = 1.01^N / [ 1.01^N - 1]      note that we can write this as

1/ 1.4347  = 1 - 1/1.01^N     rearrange as

1/1.01^N  =  1 -   1/1.4347

1/1.01^N  = 4347 / 14347       and we can write this as

1.01^N  =   14347 / 4347        take the log of both sides

log 1.01^N  =  log [ 14347 / 4347 ]   and we can write

N* log 1.01  =  log [ 14347 / 4347]     divide both sides by log (1.01)

N  =  log [ 14347 / 4347]  / log (1.01)   ≈  120

Oh okay, but thanks so much!!!

CPhill can explain it much better than I can. He can show you how to calculate the coefficient of x^20 in the expansion of the above sequence. 

Once you know the sine of an angle, then you can get all the other functions using this famous identity:

Sin^2(x)  +  Cos^2(x) =1. To see how, go online to this link: https://en.wikipedia.org/wiki/Sine

Go down the page to "Other Trigonometric Functions" and look at the first column.

I'm not sure I understand the website. Can you rephrase it so it is simpler?

I found out that we must find how many ways are there to give out 20 dots to 10 dice. Try simplifying that and find a pattern... I'm working on that right now

There are 85,228 ways of getting 20 when rolling 10 dice. The probability of rolling a total of 20 is:

85,228 / (6^10) =85,228 / 60,466,176 =0.00140951 x 100=0.140951%.

The calculations for these odds are exactly the same as calculating the coefficient of x^20 in the expansion of this: (x+x^2+x^3+x^4+x^5+x^6)^10. So that x^20 =85,228x^20.

To read about this in detail, see this page of "Mathworld": http://mathworld.wolfram.com/Dice.html

We have always known that "you had gone bananas" !!!

Possibly to see how helpful you are???

https://www.khanacademy.org/math/algebra2/exponential-and-logarithmic-functions/introduction-to-logarithms/v/logarithms

Thanks everyone!!! Sorry for the late reply

I AM SO SORRY MELODY!!! I never meant to be rude!!! I just didn't check my problems because I figured out before you helped me figure it out!!! I am super duper sorry! Please don't be mad at me...

Here’s one for you.

If  f(x)  = f(-x)....the function is even

If  f (-x)   =  - f (x)   ....the function is odd

So  let   f(x)  = 7x^4   - x^2

Sub  -x  for x

 f(-x)   =  7(-x)^4  -  (-x)^2  =   7x^4  - x^2

So..... since   f(x)  = f(-x)......this function is even

Here's the third one :

Let's count the ways where the two C's can appear together

They can appear together in  any one of twelve positions

And the number of identifiable arrangements of the other letters  is

11 ! / [ 2! * 2! * 2! * 2! ]

So.....the total number of ways where they can occur together  is

12 * 11!  / [ 16]  = 29,937,600

So.....the number of ways in which they don't appear together is

194,594,400 - 29,937,600  =  164,656,800

g(x)   =  [ 4x^2 + 6 ]  /  [ x + 1]

Domain  =   all  reals except  for  x  = -1    [ this makes the denominator  = 0 ]

There will be something known as a "slant" asymptote and a vertical asymptote  at x = -1

See the graph, here :  https://www.desmos.com/calculator/orq4zkm2xz

h(x)  = [ 5x^2 + 2] / [ x^2  -  9 ]

Domain = all reals except x = -3   and x  = 3   [ these make the denominator  = 0 ]

Vertical asymptotes will occur at  x = - 3  and x  =3

See the graph, here : https://www.desmos.com/calculator/6flwyghtuw

The funny thing is, today's my lucky day. 

I believe GA has hit on the correct interpretation.....

0.84   rounds to  1

I'd like to take full credit for this.....but....I actually had to verify it with one of GA's trained chimps.....they're rarely wrong......particularly after a few banana daiquiris......

Here's the first one

C - O - M - M - U - N - I  - C - A -  T - I - O - N

The number of  "identifiable" arrangements is given by :

13!  /  [ 2! * 2!  * 2!  * 2! * 2!  ]  =

13!  [ 32]  =  194,594,400  "words"

This thread is a minor example of what a fifth-grader looks like when mommy uses him as a marionette.   Here, mommy manipulates his mouth and speaks in the dimwit dialect of stupid. This is a common language for many, but it’s very difficult to understand and translate into an educational language—such as Standard English.    The irony here is this is incomprehensible unless one grows up with it, and if one grows up with it, it’s very difficult to learn how to translate it.   

Using a Babble translator and my genetically enhanced Chimp brain—with mind reading skills, I have determined a probable translation:

How do you round off fractional numbers to the nearest whole number?

Specifically, how do you round off 0.84 to the nearest whole number?

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This is like “Finding Wally.”