All Answers 357328 Answers

I am with Rom, I think that + is meant to be a comma.  

Once you respond to our query we might be able to answer you.

$\text{The point }p \text{ is described by a 2D joint uniform distribution}\\ p(x,y) = \dfrac{1}{18},~0\leq x \leq 3,~0\leq y\leq 6\\ P[x+y \leq 4] = P[y\leq 4-x] = \\ \displaystyle \int_0^3 \int_0^{4-x}~\dfrac{1}{18}~dy~dx = \\ \displaystyle \int_0^3 \dfrac{4-x}{18}~dx = \\ \left. \dfrac{4x-\frac{x^2}{2}}{18}\right |_0^3 = \dfrac{12-\frac 9 2}{18} = \dfrac{5}{12}$

in (b) is it really supposed to be $\dfrac 1 \alpha + \dfrac 1 \beta$

or does it mean that $\dfrac 1 \alpha, ~\dfrac 1 \beta,~\dfrac 1 \gamma$ are all roots?

wow!

14 days (im guessing fortnite)

0/0 is undefined. x/0 = undefined for whatever x is 

Just ask Siri what 0/0 is...she'll say you are a cookie monster with no friends and no cookies!

The answer is complete

Did you attempt the problem before and get it wrong? if you did, (I know the website you are on ) then even if you get it right the next time, it will only give 5/7, not 7/7. If you attempt two times and get those attempts wrong, but get the third attempt correct, then you score 3/7 points. This process continues al the way until 1/7. 

 - PM

Google translate helped me a little here...

ok, how 'bout you?

True.

The scale factor of the smaller triangle to the larger is   12/16 = 3/4

The area of the smaller   =

Area of larger x ( scale factor of smaller to larger)^2   =

105 *  (3/4)^2   =

105 *  9/16  ≈   59 ft^2

$\text{The way to look at this semi formally is to consider the different cases}\\ \text{There can be 0-2 pairs of letters chosen}\\ \text{with 0 pairs there are }\dbinom{7}{4}4! =840 \text{ unique 4 letter words}\\ \text{with 1 pair there are }3\dbinom{4}{2}\dbinom{6}{2}2!=540 \text{ unique 4 letter words}\\ \text{This last bit deserves some discussion}\\ \text{The 3 comes from the fact that 3 of the letters can be chosen as a pair, I, N, V}\\ \text{The }\dbinom{4}{2} \text{ comes from the fact that we select two slots from the 4 to place this pair}\\ \text{The }\dbinom{6}{2} \text{ comes from the fact that we can select 2 letters from 6 to complete the word}\\ \text{The 6 comes from removing the numbers that are the pair, and the }\\ \text{2nd copies of the two other numbers}\\ \text{Finally the }2! \text{ comes from the fact the these last two letters are distinct and their order matters}$

$\text{Finally with 2 pairs there are }\dbinom{3}{2}\dbinom{4}{2} =18 \\ \text{This is choosing two pairs from the 3 available and choosing 2 slots from the 4}\\ \text{adding all these up we get}\\ 840+540+18 = 1398$

Good job, PM !!!!!

Here's how PM arrived at his answer.....

                b^2   + 4b    -   2

4b - 6   [  4b^3 +  10b^2 - 32b + 15 ]

               4b^3 -     6b^2

              ______________________

                            16b^2  - 32b

                            16b^2 -  24b

                            ________________

                                       -8b  + 15

                                       -8b +  12

                                       _________

                                                   3

Maybe in some money-efficient video game. 

16 + 16 + 2 sqr(12^2 + 9^2) = 62     Using pythagorean theorem to find the missing side(s)....

OK, the correct answer is $b^2 +4b - 2 + \dfrac{3}{4b-6}$. 

Note that when you subtract a multiple of 4b-6, you must change all of the terms. For 4b-6 to have a b^3, you should multiply 4b-6 by b^2 to get 4b^3 - 6b^2. You cannot directly change it to $-4b^3 +4$ like you did in the image. 

Knowing this, you should be able to determine the answer. 

- PM

TRUEEE

CPhill, even for a person who is the "best" in many people's eyes, you still remain humble. I greatly admire that characterisitc. 

- PM

Excellent, PM!!!

Thanks....but....not the "Best".....only one of a lot of very dedicated people....!!!!