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there are 22, $1 bills since we get the equation x+2(x+11)+3(x-18)=100 where x=22 there so there are 22, $1 bills

It is generally much easier to compute the "combinations" first and then convert the combination into permutations. With a very short computer code, each of these combinations is converted to permutations and then summed up. I wrote such a short computer code just for the pupose of converting these 71 combinations into permutations and the result is: 2,111 permutations.

12233 , 12234 , 12235 , 12244 , 12245 , 12255 , 12333 , 12334 , 12335 , 12344 , 12345 , 12355 , 12444 , 12445 , 12455 , 12555 , 13334 , 13335 , 13344 , 13345 , 13355 , 13444 , 13445 , 13455 , 13555 , 14444 , 14445 , 14455 , 14555 , 15555 , 22333 , 22334 , 22335 , 22344 , 22345 , 22355 , 22444 , 22445 , 22455 , 22555 , 23334 , 23335 , 23344 , 23345 , 23355 , 23444 , 23445 , 23455 , 23555 , 24444 , 24445 , 24455 , 24555 , 25555 , 33344 , 33345 , 33355 , 33444 , 33445 , 33455 , 33555 , 34444 , 34445 , 34455 , 34555 , 35555 , 44445 , 44455 , 44555 , 45555 , 55555 , Total = 71 combinations.

We're going to turn each sentence into an equation.

a = number of $1, b= number of $2, c= number of $3

b=a+11

c=a-18

a+2a+3b=100

Substituting the first two equations into the third equation,

a+2a+22+3a-54=100

Simplifying, we get 6a=132, a=22

So there are 22 one-dollar bills.

s\o we have 65-60=5 and 60*10=600 then we do 600/5=120 which means 2 hours later at 5:10

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.

For example, 10^3 = 1,000; therefore, log10 1,000 = 3.

1/2 base * hieght is the formula we use to solve th area

my username on aops is amazingxin777 (same as this one)

Hint

we get 180-3angle A=AngleB

and 

AB=BC-2

Just continue on the sequence

\(1\text {st} \space \text {term}\)      \(2\text {nd} \space \text {term}\)       \(3\text{rd}\space\text{term}\)       \(4\text{th} \space \text{term}\)        \(5\text{th} \space \text{term}\)        \(6\text{th} \space\text{term}\)        \(7\text{th} \space \text {term}\)      \(8\text {th} \space \text{term}\)      \(9\text{th} \space \text{term}\)      

20 (even)      10 (even)          5 (odd)            16 (even)           8 (even)           4 (even)           2 (even)         1 (odd)           4 (even)

\(10\text{th} \space\text{term}\)

         2 

So the answer is \(\boxed {2}\)

hint: \(\text {distance} =\) \(\text {speed} \times \text {time}\)

Alright, let's write a couple of equations.

First, let x equal the speed at which she went to the other town (what we're trying to find) and let y equal the time it takes her.

Then, because distance=speed*time, 150=xy

Our second equation is going to be on her way back. 150=(x+15)(y+\(\frac{1}{2}\)). We put \(\frac{1}{2}\)hr instead of 30 minutes because our speeds are given in km/hrs. 

Now we expand: 150=xy+\(\frac{1}{2}\)x+15y+\(\frac{15}{2}\)

Substitute 150=xy (our first equation). 150=150+\(\frac{1}{2}\)x+15y+\(\frac{15}{2}\)

This simplifies to \(\frac{1}{2}\)x+15y+\(\frac{15}{2}\)= 0

Multiply by two: x+30y+15=0

From our first equation, y=(150/x), and substituting this into our above equation:

x+30(150/x)+15= x+(4500/x)+15=0

Multiply by x: x²+15x+4500=0

Factorize to get (x+60)(x−75)=0

We get either -60 or 75. Speed must be positive, so the answer is 75. 

3 .

6

4.

216+72sqrt3

Maybe it is \(2^6\) but you probably have to minus the repeats.

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I sometimes ask alcumus problems

I do (I am rabbit317)