The number 12 can be broken up to \(x^2*y^2\), since the number of factors is \((2+1)(2+1)=3\cdot3=9.\) The three numbers do not work here since there are no possible outcomes.

Thus, we can have: \(2^2*3^2=36.\)

\(2^2*5^2=100.\)

\(2^2*7^2=196.\)

I do not think any more possible outcomes are there, and you can still check my work.

Thus, the answer is \(36+100+196=\boxed{332}.\)

\(8=2^3.\)

Thus, we have \(\left \lfloor \frac{100}{2} \right \rfloor+\left \lfloor \frac{100}{4} \right \rfloor+...+\left \lfloor \frac{100}{32} \right \rfloor+\left \lfloor \frac{100}{64} \right \rfloor=97\). Since \(97=32*3+1\), \(\boxed{32}\) is our searched answer.

-azsun

We can also represent these using combinations.

We have to find the value of \(\binom{10}{8}.\)

A quicker way is to recognize Pascal's triangle, and this is the tenth row, and the sum is \(2^{10}=1024.\) Thus, the answer is, \(\frac{\binom{10}{8}}{1024}=\boxed{\frac{45}{1024}}.\)

I think it's x=-4, y=1.

Try to rewrite the expression as the sum of squares plus a number.

Is the answer -11? Inspiration: https://www.quora.com/If-x-and-y-are-real-numbers-then-what-is-the-minimum-value-of-x-2-+4xy+6y-2-4y+4

Don't take my word for it, though.

Solving these equations gives us: x=y*tan(29), and x=(y+100)(tan25).

Use a unit circle to find the appropriate values. y should be approximately 529.9. Then, solve for x by plugging the value of y back in.

\(2.8-6=\boxed{-3.2}\).

We first go by the exterior angle measure: \(\frac{360}{n}\).

Now, \(n\) has to be a factor of \(360\) , so we count how many factors this number has.

Since \(360=2^3*3^2*5\)\(\) , we add one to each power, resulting in \(4*3*2=24\) factors.

Finally, a polygon cannot have one or two sides; thus the answer is \(24-2=\boxed{22}\) regular polygons.

Since they are walking in opposite directions, we add their rates. 3+4=7mph. Now, we divide from 14 to get an answer of 2.

Good solution, but it's \(5*5, \) not \(5.5\) .

Hey, Manuel! What's up?

Thank you, everyone!

Wow! I wasn't active in such a long time, I'm so sorry. Finally, I saw this post! Happy birthday CPhill, hope you have a blast!

Enjoy my recipe:

Oreo flavor!

That seems better! Thank you, CPhill!

Translating this, we get \(\ln \left(10^{z+2}\right)=\ln \left(27\right).\) Now, we just apply the log rule(\(\log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\)) , and get \(\left(z+2\right)\ln \left(10\right)=\ln \left(27\right).\)

Then, we can simplify this to be \(\left(z+2\right)\ln \left(10\right)=3\ln \left(3\right).\)So, we solve it, and our final answer is \(z=\frac{3\ln \left(3\right)}{\ln \left(10\right)}-2.\)

Continuing on, we have \(\frac{24}{2}, \frac{-20}{2}\). Thus, our answer is \((12,-10)\).

I hope Rom will give you a detailed answer, but there are 10 possible choices out of 90 values, so 10/90=1/9.

For Question 3, I'm getting two different answers. 9, is my first take.

Hint: Difference of Squares! a^2+b^2=c^2, c^2-b^2=a^2, (c+b)(c-b)=36.

You also know the perimeter is 18, so 6+b+c=18, b+c=12.

So, (12)(c-b)=36, c-b=3..

Now, we have two equations, and if we subtract, we will get: c=7.5