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I figured it out using my graph !!!!! 

Melody I tried graphing it on desmos, if you would like to play around with it

60 seconds in a minute, so you get 60/3=20 dollars each minute, and the answer is \(19\cdot20=\boxed{380}\)

Hope this helped :)

a. We see that 4=2+2, 6=4+2, 10=8+2, 18=16+2, etc. This means if the Nth term in this sequence is \(a_n\), then \(\boxed{a_n=2^n+2}\)

b. We see that 2=1x2, 6=3x2, 12=6x2, and 20=10x2.

Now if you are familiar with numbers, you may recognize immediately that 1 is the sum of the first positive integer, 3 is the sum of the first 2 positive integers, 6 is the sum of the first 3, and 10 is the sum of the first four, so the answer is the formula for this multiplied by 2, which is \(\boxed{b_n=n(n+1)}\)

If you are not familiar with numbers, thats ok! We can look at the sequence 1,3,6,10, and see that 3-1=2, 6-3=3, and 10-6=4. This makes us think, the next one will be 15, then 21, etc. We now know that this sequence is twice the sum of the first n positive integers, and we can find the formula as follows:

Pair up 1 and n, 2 and (n-1), 3 and (n-2), etc. You will get \(\frac{n}{2}\) pairs if n is even, and \(\frac{n-1}{2}\) pairs if n is odd, with \(\frac{n+1}{2}\) being left out. Either way, the sum is then \(\frac{n(n+1)}{2}\), and so 2 times that is \(\boxed{n(n+1)}\)

Hope this helped

If it's wrong please tell me how so I can learn :)

I'm sorry, but this is wrong

If a number is congruent to n modulo n, then it is congruent to (n-n) modulo n, which means it is divisible by n.

Now, (using a calculator because I'm lazy) adding all of these numbers up, we get 

1 + 12 + 123 + 1234 + 12345 + 123456 + 1234567 + 12345678 + 123456789 + 1234567890 + 12345678901 + 123456789012 = 137174210008. 

Now n must be a factor of 137174210008, and n must be less than 9, so testing, we get that only 2,4, and 8 divide 137174210008 and are less than 9, so \(\boxed{n=\{2,4, or \space 8\}}\)

Hope this was helpful :)

Alternative solution:

Pair the numbers up as follows

We can see that there are 2010/2=1005 rows, and the sum of each row is 2011, which is equal to 1 modulo 2010, thus the answer is

1005*1 = 1005

Hope this helped :)

We can first factor the denominator as \(\frac{1}{(x)(x+2)}\). In order for this to be a terminating decimal, both \(x\) and \(x+2\) have to only have factors of 2 and/or 5. Testing small values of x, we find that \(x = \{2,8, etc.\}\). Looking at this, we can see that the second smallest integer value of x is \(\boxed{8}\)

Each ball can go in 2 boxes, so the answer would be 2^5=32

Set the length of the second peice to be \(x\), then the first piece would have a length of \(3x\), and the third piece would have a length of \(x-30\). Then we obtain the equation \(x+3x+x-30=100\) , or \(5x-30=100\). Solving, we get that x = 26, but this makes the third piece have negative length, so this is impossible.