Doggo

I tried that but it was wrong. Please help!

 The 5th term is $\frac{5}{9}$ . Here's my methodology:

To find the 5th term, we have to first find the difference between each of the terms. Since adding the difference 8 times to the 1st term gives us the 9th term, we can set up the equation $\frac{4}{9}-\frac{2}{3}=8x$.

We can then solve for x to get $x=-\frac{1}{36}$. 

Then, all we have to do is add $4x$  to the 1st term to get $\frac{2}{3}-\frac{5}{36}=\frac{24}{36}-\frac{4}{36}=\frac{20}{36}=\boxed{\frac{5}{9}}$.

I hope this helps!

–Doggo

To solve this problem, you actually don't need to know the cone formula! This is simply the Pythagorean Theorem. 

Using the theorem, which is  $a^2+b^2=c^2$ , we can insert our variables into the equation. Since $c^2$ is the hypotenuse of the triangle, 12 will be our $c$. 

$h^2+6^2=12^2$

$h^2+36=144$

$144-36=h^2$

$h^2=108$

$h=\sqrt108=6\sqrt3$

So, the height of the cone is $6\sqrt3$ cm. 

Hope this helps!

Doggo

Hint: Use complementary counting! What is the total number of possibilities – the ones that have two consecutive digits of one?

Hint 2: There are $3^6=729$ total possibilities. What do you need to subtract?

Hope this helps!

Your methodology is correct, but you've made an arithmetic mistake:

$3x+6=282$

$3x=282-6=276$

$x=92$

Hope this helps!