RiemannIntegralzzz

$1865593=0.39(x)$

$x=\frac{1865593}{0.39}$

$\boxed{x \approx 4783572}$

There were 14 total volunteers, with an average of $\frac{1306}{5*14}=\frac{1306}{70} \approx \boxed{19}$ per volunteer per day.

$P(1,2,3)=\frac{1}{2+3}=\frac{1}{5}$

$P(2,3,1)=\frac{2}{3+1}=\frac{2}{4}=\frac{1}{2}$

$P(3,1,2)=\frac{3}{1+2}=\frac{3}{3}=1$

$P(\frac{1}{5},\frac{1}{2},1)=\frac{\frac{1}{5}}{\frac{1}{2}+1}=\frac{1}{\frac{15}{2}}=\boxed{\frac{2}{15}}$

$2*4=2^4+4^2=16+16=\boxed{32}$

Plugging in, you get $\frac{2}{12}+\frac{12}{3}+\frac{3}{2}=\frac{1}{6}+4+\frac{3}{2}=4+\frac{1}{6}+\frac{9}{6}=4+\frac{10}{6}=4+\frac{5}{3}=\boxed{\frac{17}{3}}$

Great job @CPhill!

Hint: one way to define no solutions means that when you simplify everything(without possibly dividing by 0, such as 3x=5x, x=0 is a solution), you are left with two unequal numbers equaling each other, such as $3=5$.

Ummm... there are potentially an infinite number of slices of pizza, so you cannot possibly figure it out.

We have the sequence: triangle, square, circle, triangle, square, circle, triangle, square, circle...

The $50^{th}$ shape is the same as $50$(mod $3$)$=2$, because the shape repeats every $3$ items. So the $50^{th}$ shape equals the $2^{nd}$ shape equals a $\boxed{square}$

Looking at the function, you can see that $x$ can be all real numbers except for $-7$, as that would cause division by $0$.

So the domain would be $\boxed{(-\infty, -7)U(-7, \infty)}$

I will write everything in cents because I hate decimals more than anything :)).

Let $a$ denote the number of $50$ cent stamps he has, and let $b$ denote the number of $20$ cent stamps he has.

We have two equations: $a+b=30$ and $50a+20b=1200$.

Solving the first equation and substituting:

$a=30-b$

$50(30-b)+20b=1200$

$1500-50b+20b=1200$

$-30b=-300$

$30b=300$

$b=10$.

Now, we have $a+b=30$, so $a+10=30$, $a=20$.

So Clifford has $\boxed{20}$ 50 cent stamps and $\boxed{10}$ 20 cent stamps.

A simple check by multiplying them out:

$20*50+10*20=1200$

$1000+200=1200$

$1200=1200$(it works!)

$1/4x=3/4$

Multiply both sides by $4$

$1/4x*4=3/4*4$

$1*x=3$

$1x=3$

$\boxed{x=3}$