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!