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2x + 3y = 21 

is the same as    y = -2/3x + 7    slope , m = -2/3

Parallel slope is the same slope   -2/3

(-9- -17) / (2-j) = - 2/3     solve for 'j'

Yay. :))

Nice job.

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4cos(3x-20=1

cos(3x-20)=1/4

arccos(1/4)=3x-20

1.318116072 = 3x-20

1.318116072+20 = 3x

1.318116072+20/3 = x

21.31811607/3 = x

x = 7.106 

Did I do it right? 

The length of AD is 18.

$\frac{1^2 \pi}{(1 - (-1))(1-(-1))} = \frac{\pi}{4}$

https://web2.0calc.com/questions/help_42168

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4*cos(3x - 20) = 1

cos(3x - 20) = 1/4

arccos(1/4) = 3x - 20

Can you take it from here?

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There are 60 paths from A to B.

(a) $10 \cdot 9 \cdot 8 = \boxed{720}$

(b) $10^3 = \boxed{1000}$

Thanks :)

The smallest prime factor greater than 10 is 11. 

So our answer is 11^2 = 121

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"The proof is difficult to explain concisely and without a diagram."

This reminds me of the quote "I have discovered a truly remarkable proof of this theorem which this margin is too small to contain"

Your question is vague. What types of questions? Like, how to get started? How to use states? Complementary? etc.

Your question is like: "How do I be better at basketball?" A good question is something like: "How do I become better at 3 pointers and free throws?"

One possible improvement to your question is asking a particular aspect, or topic, of probability.

Let $p(x) = x^2, q(x) = 2x^3+1,$ and $r(x) = 7x^4 - 5x^3 - 6x - 2.$ Find $p(q(x)) + r(x).$

We have $(2x^3 + 1)^2 + (7x^4 - 5x^3 - 6x - 2) = 2x^6 + 4x^3 + 1 + 7x^4 - 5x^3 - 6x - 2 = \boxed{2x^6 + 7x^4 - x^3 -6x - 1}.$

Hello, welcome to web2.0calc. :))

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Thank you. :))

I learnt it from an amc problem. 

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Wow that's slick

We try a complementary approach

Multiples of 3 from 1 - 1200: $\left \lfloor{\frac{1200 - 1 + 1}{3}}\right \rfloor = \left \lfloor{\frac{1200}{3}} \right \rfloor = 400$

Multiples of 4 from 1 - 1200: $\left \lfloor{\frac{1200 - 1 + 1}{4}}\right \rfloor = \left \lfloor{\frac{1200}{4}} \right \rfloor = 300$

Multiples of $4 \cdot 3 = 12$ from 1 - 1200: $\left \lfloor{\frac{1200 - 1 + 1}{12}}\right \rfloor = \left \lfloor{\frac{1200}{12}} \right \rfloor = 100$

$1200 - (400 + 300 - 100) = 1200 - 600 = \boxed{600}$

\(4x^6+7x^4−x^3−6x−1\)

2/3 of the numbers will not be multiples of 3, and 3/4 of the numbers won't be multiples of 4. 

1200 * 2/3 * 3/4 = 600

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Probability is the chance that something will happen. 

The chance of me flipping a head is 1/2, 50% chance of happening. 

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The most fundamental definition of probability is \(\frac{cases that work}{total cases}\).  Keep this in mind while you work, it is the most important aspect of every probability question.