## I feel naked and stupid without a calculator?

Because I was born into a generation who depends upon graphing calculators I have used and abused them while I was learning math. In the past, I never really cared for understanding math. I hated it and viewed it as a necessary evil for graduating high school. Then, things changed. As a senior this year things finally clicked; mathematics seemed to make sense. Its elegant, beautiful, logical, and simple.

Now, I am even considering majoring or doing a minor in mathematics once I get to university.However I am faced with a problem if I choose to go down that path. I lack an appreciation and a sense for numbers and their operations that is innate to many mathematicians. Even though I have no problem understanding the work, I often ponder the question „Why does this work?“. Sadly, relying on a graphing calculator doesn’t help the situation. For example if I am faced with the task of graphing an equation to the nth degree, I can’t really graph it. I don’t know the direction of the curves, or even a rudimentary visualization of the graph. I just plug the equation into the calculator and copy the graph. Neither do I know how to find the numerical approximation of a square root or third root of a number. I can’t solve logarithms without plugging them into the calculator. The calculator does all the work for me.

If I seek mathematical intuition, I need to understand why things work. Simply, I feel naked without a graphing calculator. So, how can I fix that? What is the best way to teach myself arthimetic (such as finding the nth root of a number), or learning how to graph without a calculator as an aid?

Thanks.

Nearly everybody relies on the calculator. If you understand something, why should you ask the question „why does this work“? If you understood it, you would already know the answer to why it works.

For the equation xʰ or , look at it this way.
What happens when 0 < x < 1? ƒ(x) will be very small (positive).
What happens when −1 < x 1? ƒ(x) will be very large (positive).
What happens when x < −1? ƒ(x) will be very large (positive/negative dep. On whether n is odd or even).

So if n is odd, the graph will look like a cubic, but very steep for x 1.
If n is even, the graph will look like a parabola, but very steep for x 1.

For large numbers, it is hard for everyone to approximate the root of that number.
Again, almost everyone uses the calculator to solve logarithms. How do you approximate the power of a base?

I guess you’re confused with numbers that have powers. It’s okay, you’re on the same boat with everyone else.

I want to see how many ratties I can have in our new, big cage. =)
Oh wow! I can properly accomodate seventeen rats! I would need 12 more! lol

Here’s one: http://www.rattycorner.com/odds/calc.shtml
🙂

## Would you agree that the odds on you, in particular, being born, are astronomical?

500 years ago, the claim that you, particularly, would have been born, would have been seen to have been so improbable as to be impossible.

Indeed, if any one of a billion billion things had gone differently, you would not have been here now.

If your great great great + grandfather had tripped over a rock, which delayed him from getting to the market, he may have never met your great great great + grandmother.

If during WW2, a German pilot had overslept by five minutes one day, his bomber may have dropped a bomb which killed your grandfather, instead of someone else’s grandfather.

While YOU may not have been born, others would have been.

Just like in evolution, one cannot look at what is the end result and state „this is what was PLANNED“.

Isn’t the end result only what one sees because, out of the infinite number of all the other possibilities, that is the one which happened?

Thus, isn’t the end result NOT impossible or improbably, but actually assured, just not predictable?

1) Would you agree that the odds on you, in particular, being born, are astronomical?

No – the odds are 100%. Same with you.

2) 500 years ago, the claim that you, particularly, would have been born, would have been seen to have been so improbable as to be impossible.

First: I doubt that’s true.

Second: if true, it’s only because such a probability as you are describing is based on limited available knowledge. That is: if the probability-calculator knew more, his probability would be more exact and precise. If the probability-calculator was omniscient, he would be able to calculate the probability of my being born 500 years in his future as 100%.

3) Just like in evolution, one cannot look at what is the end result and state „this is what was PLANNED“.

Of course I can. Why would you think I can’t? Reasonably (that is, logically) I can. Legally I can. You have drawn a conclusion that the premises simply do not support logically.

4) Isn’t the end result only what one sees because, out of the infinite number of all the other possibilities, that is the one which happened?

Obviously that is a correct statement.

5) Thus, isn’t the end result NOT impossible or improbably, but actually assured, just not predictable?

It’s predictable.

It’s not predictable with 100% confidence if less than all of the relevant factors are taken into account or if less than all of the relevant factors are known. If even one relevant factor is not taken into account or is not precisely and accurately known, the confidence of the prediction is less than 100%. The more you know relative to a prediction, the more confident your prediction can be. If you know everything relevant to the prediction (like with a die that has the number „1“ on all six sides), then you can predict the outcome with 100% accuracy.

– Jim, Bach Sci Physics 1989

## Odds of winning a hand of Blackjack at a casino?

Heres the thing. Im broke at the moment having only 360 in the bank, and i have rent due on Monday. Rent is 350. I was thinking about going. Playing 2 (\$10 hands) then whether win or lose that \$20, bet a \$100 hand. And if i win, ill be in about a hundred dollars, then go home an be abe to pay my rent AND be able to eat til payday.. But if i lose, i starve an wont make rent. I understand the risk, but im willing to take the gamble so dont try and scold me, i dont wanna hear it.
So you black jack players. What do you think my odds are at winning that \$100 hand?

I’ll let pdq explain why you’re making the worst decision of your life but anyways, if you must go through with this mistake, I’ll tell you how to go through it properly. But first, let me just tell you this, Blackjack is a very very bad game in the short term (but one of they best Casino game in the long run, though that house still has the edge – except against card counters which I can tell you’ll never become). Players only win about 43% of hands – that right there should tell you not to play.

Now, with basic strategy, even though they (the players) still loose the vast majority of their hands, they only loose about 61 cents for every \$100 they bet. This is because of all the options you have in Blackjack (such as Split, Double Down, ect) that allow you to win big on good hands (like 11s – which should always be doubled down) and that one option (surrender) which allows you to loose small on bad hands (16s).

Basic strategy is the best stagnant strategy (unchanging, the only profitable strategies require you change your decisions and bets according to card previously dealt.. I’m not talking about betting systems!). If you must play, play with perfect basic strategy and MAKE SURE the table pays 3:2 on Blackjacks, NOT 6:5. Also, if you can, play at a table with a continuous card shuffling machine (see my answer here if you want to know why: http://answers.yahoo.com/question/index;_ylt=Av_Si0IJL4pAhtw750U_iy3ty6IX;_ylv=3?qid=20120611183819AALlyU8 ). Make sure you can double on any two cards, can surrender against any dealer up card, and can split and re-split any two cards. If you can find it, play at a table where the dealer stands on soft 17s. Avoid single deck tables, yes it is true that less decks are better but they alter the game in various ways that cancel out the advantage of having less cards (such as 6:5 payoffs on Blackjacks). If you see multiple tables that look like they offer good rules, you can use this http://wizardofodds.com/games/blackjack/calculator/ to see which one’s mathematically better.

Now, how well do you know basic strategy? Did you know that you should stand a 12 against a 14? That you should surrender a 15 against a 10? That you should split 6s against a 12? Just print a chart here http://www.blackjackinfo.com/bjbse.php or here http://wizardofodds.com/games/blackjack/strategy/calculator/ and bring it to the casino (make sure you set it up with the rules of the table you will be playing at). Making the wrong decisions will make your already horrendously terrible mistake even worse. If you can’t read charts well, I have all the basic strategy moves written out at my answer here: http://answers.yahoo.com/question/index;_ylt=Am3gk8hoMStVexetrNEZvrvty6IX;_ylv=3?qid=20120528102414AAEuvGM (and yes, it is correct!)

Now, back to the question, what are the odds of winning that \$100 hand? For every card dealt, the odds of winning the next hand in Blackjack change. This makes calculating that impossible without knowing what cards have already been dealt. Generally though, as I said, the player will win 43% of their hands.

However, playing 2 hands and then betting \$100 gives you the same odds of winning as betting that \$100 on the 1st hand or the 946th hand, so I don’t know why you plan to bet \$10, then \$10, then \$100. Why not bet \$10, \$10, \$10, \$10, \$10, \$10, \$10, \$10, \$10, \$10, \$10, \$10? (Then quit and quit for real) This is actually probably better because the variance won’t instantly destroy you.

## is -9x^5 -8 Even, odd or neither?

You can check if its even odd or neither by doing the following

if its even, plug in (-x) for x and if the new equation turns outs equal to the old one than it is even

if it is odd, plug in (-x) for x and (-y) for y and if the new eq turns out equal to the old one its odd

if both tests dont work its neither

or you can check it on a graphing calculator…
Even: symmetrical over the y axis
odd: symmetrical over the origin
neither: not even or odd