BlackjackEd

Gang they asked for hints XD

Greetings Answerscorrectly, 

I assume you have at least been learning something from your course/Alcumus, so I'll keep the hints short.

To start, we want to create a fraction something like this:
 

$\frac{\textbf{Number of Targeted Results}}{\textbf{Number of All Results}}$

To find the numerator, we want to find the probability for getting the desired card for each of the 5 moves.

If you don't know how to do that, here are instructions for each card draft.

1. Pick a random card regardless of colour and number

2. Pick a randomly coloured card that has the same number as 1.

3. Pick a randomly coloured card that is not the same number as 1. or 2.

4. Pick a randomly coloured card that is not the same number as 1., 2., or 3.

5. Pick a randomly coloured card that is not the same number as 1., 2., 3., or 4.

As for the denominator, I think you can figure that out yourself. 

Don't forget that cards are NOT put back into the pool after taken out!

If you need any more help or have found something wrong with my answer (hint?), say the word.

I hope this helps you answer correctly, Answerscorrectly! (heh, I've been waiting to say that for a while..)

Ooh are you doing the intro to C&P course?

Lol I did it a while ago and remember being stuck on these card questions... I'll try to see if I can help...

Thank you so much CPhill!!!!

(that took you like no time at all )

Let $a$ and $b$ be the roots of the quadratic $2x^2 - 8x + 7 = x^2 + 15x + 23.$  Compute $a^4 + b^4$.

We can first calculate the roots of the quadratic.

They are: 

$\frac{23+\sqrt{593}}{2}$ and $\frac{23-\sqrt{593}}{2}$.

Now we can calculate the $a^4 + b^4$ part.

$(\frac{23+\sqrt{593}}{2})^4+(\frac{23-\sqrt{593}}{2})^4$

$=\frac{314209+12903\sqrt{593}}{2}+\frac{314209-12903\sqrt{593}}{2}$

$=\boxed{314209}$

Our final answer is $\boxed{314209}.$

*There is probably a much faster and more efficient way to solve this that someone more educated than I am will be able to teach you clearly 

That was so fast... they're both correct, thanks so much!!!

Now the harder ones 

$\textbf{Fill in the blank: 3*___ = 81*5}$

Let us fill in the blank with a variable, namely $x$.

$3\times{x}=81\times5$

Simplify to:

$3x=405$

$\boxed{\textbf{x=135.}}$

In the high school band, there are 2 percussionists on the sideline for every 13 marching instruments If the high school band has 150 total members how many percussionists are on the sideline?  

The ratio of percussionists to total band members is 2:(2+13), or 2:15.

As ratios are equal to fractions, we can put this in an equation:

${2\over15}={x\over150}$.

Cross-multiply to solve:

$300=15x$

$20=x$.

$\boxed{\textbf{There are 20 percussionists on the sideline.}}$

Hope this helped,

(LaTeX version)

$\textbf{Compute}$

$\binom{5}{3} - \binom{6}{3} + \binom{7}{3} - \dots - \binom{22}{3} + \binom{23}{3} - \binom{24}{3}$

(LaTeX version)

$\textbf{Fill in the blanks to make the equation true. (Each blank should contain a 2-digit number.) }$

$18\times18 + 19\times18 + 20\times18 + \dots+ 45\times18 =\boxed{\phantom{X}} \times \boxed{\phantom{X}}$

Does that include the 4-digit integers, 6-digit etc.?

You're both wrong, but thanks for trying! 

The answer was $9$ .

Excellent job guys...