A bat and a ball cost £1.10 in total. The bat costs £1 more than the ball. How much does the ball cost?  The answer to this question is somehow 5p. How?!! Should it not be 10p?
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A bat and ball cost \$1.10.  The bat costs a dollar more then the ball.  How much does the ball cost?  If this is not the correct place to ask a question like this please tell me and I will remove it :)     The ball costs \$0.05, not \$0.10
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Could someone please provide an explanation for the origin of ? (Ideally someone who I have been speaking with on the h-bar)  Any advanced maths beyond basic calculus will most probably leave me at a loss, though I do not mind a challenge! Please assume little prior knowledge, as over the past few days I have discovered that much of my understanding surrounding the process as virtual particle pairs is completely wrong.
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I was thinking of this problem.  I believe the solution and I think I understand it, but if I take the following approach I'm completely confused. Problem 1:  I will offer you the following game. You pay me \$10 and I will flip a fair coin. Heads I give you \$5 and Tails I give you \$20. The expectation is \$12.5 so you will always play the game.  Problem 2:  I will give you an envelope with \$10, the envelope is open and you can check. I then show you another envelope, closed this time and tell you: This envelope either has \$5 or $20 in it with equal probability. Do you want to swap? I feel this is exactly the same as problem 1, you forgo \$10 for a \$5 or a \$20, so again you will always switch.  Problem 3:  I do the same as above but close the envelopes. So you don't know there are $10 but some amount X. I tell you the other envelope has double or half. Now if you follow the same logic you want  to switch. This is the envelope paradox.  What changed when I closed the envelope?? EDIT: Some have argued that problem 3 is not the envelope problem and I'm going to try and provide below why I think it is by analysing how each views the game. Also, it gives a better set up for the game. Providing some clarification for Problem 3: From the perspective of the person organising the game:  I hold 2 envelopes. In one I put \$10 close it and give it to the player. I then tell him, I have one more envelope that has either double or half the amount of the envelope I just gave you. Do you want to switch? I then proceed to flip a fair coin and Heads I put \$5 in and Tails I put \$20. And hand him the envelope. I then ask him. The envelope you just gave me has twice or half the amount of the envelope you are holding. Do you want to switch?  From the perspective of the player:  I am given an envelope and told there is another envelope that has double or half the amount with equal probability. Do I want to switch. I think sure I have $X$, hence $\frac{1}{2}(\frac{1}{2}X + 2X) &gt; X$ so I want to switch. I get the envelope and all of a sudden I am facing the exact same situation. I want to switch again as the other envelope has either double or half the amount.
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Is momentum conserved when an object bounces back against a wall? The wall doesn’t move, but the object moves in the opposite direction. Assume this is an ideal, elastic collision.  If, initially, the momentum of the system came from the ball, and after the collision, the momentum of the system was also from the ball, but in opposite directions, then momentum would not have been conserved?   I have a feeling this is wrong, so anybody clarify this for me?
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It's a wide-spread marketing technique that seems to have been around forever- selling products for £1.99, £9.99, £19.99, instead of £2, £10 and £20.  Presumably the pyschology is that submliminally £99.99 seems disproportionately closer to £99 (or £90) than £100 does.  But surely the technique is so utterly transparent and consumers so wary of marketing techniques nowadays that it is completely ineffective. And worse, by doing it, you risk detering potential customers by coming across as deceptive or dishonest.
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The question I'm asking is pretty much:  How do you convert PSI to Velocity?  Everywhere I look it says You can't, but can you?  And what would you need to know to do so if there is no direct way to convert?  My homework is to convert 0.14 PSI into m/s.  EDIT Sorry guys my teacher does like being tricky, no clue why. Sorry for any inconvenience this may have caused.
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Possible Duplicate:          We usually say "10 pounds", but for a single bill we say "10 Pound note" and not "10 pound(s) note". And when we have a lot of notes we say again "10 Pound notes". Why this disparity?
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I have been wondering what a gold piece is worth, due to the fact there are many things that cost the same, but in reality, are probably worth radically different prices, such as a Goat and a Whip, which both cost 1 gp.  What is a gold piece really supposed to be worth? Like, how would things be priced if they were in familiar modern monetary units instead of "gp"? That would give me something to base my adjustments to abnormal prices on, such as items not listed in the PHB.
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What happens if I have only the 8 (black) ball left to pot and my opponent who has a colored ball scratches the cue ball? Do I get a ball in hand or do I have to try potting the black ball from behind 'the line'?
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The questions are: a) There are $5$ comic books, $3$ cooking books, $2$ grammar books. In how many ways can these books be arranged on a shelf if no two of the $3$ cooking books are together?   b) There are $5$ comic books, $3$ cooking books, $2$ grammar books. In how many ways can these books be arranged on a shelf if one of the grammar books is on the left of all cooking books, and the other grammar book is on the right of all cooking books.  For b) after calculation I got $5!\times2!\times10\times9\times8\times7\times6$. Did I solve it correctly?  For a) I'm kind of confused... Any help will be very much appreciated! Thanks
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how is this possible? I know there is some trick, should someone please explain?!
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If percentage points can equal decimal points, then $1.25$ should equal $125$% when multiplying $1.25$ by any number.  Therefore $125$% of $0.75$ should equal $1$ if $0.75$ is also $75$% of $1$.   Am I missing something super obvious here or what?!  Please help. Thank you!
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I was on the tube and overheard a dad questioning his kids about maths.  The children were probably about 11 or 12 years old.   After several more mundane questions he asked his daughter what $1/0$ evaluated to. She stated that it had no answer. He asked who told her that and she said her teacher. He then stated that her teacher had "taught it wrong" and it was actually $∞$.  I thought the Dad's statement was a little irresponsible.  Does that seem like reasonable attitude? I suppose this question is partly about morality.
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Suppose we have $10$ red balls and $10$ blue balls. We pick $5$ balls. What is the expected number of red balls we have?  Let $X_i$ be the event that the $i$th ball is red. Then the answer is $E[\sum _1 ^5 X_i]= \sum _1 ^5 E[x_i]$. Buy why are all the $E[X_i]=\frac12$? Obviously I can verify this for $X_1$ and the computation works out for $X_2$, but it is not intuitive to me at all why this is true for all $X_i$, especially when it seems to me like $X_i$ is dependent on all the $X_j$s before it- what is the intuitive reason for why this computation works out so nicely?
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I am reading paper on . I am trying to understand the following statement:     I would like to ask how the Ball doesnot contain the minimum of f? I would appreciate if this could be graphically shown something like following taken from Bayesian Optimization and Data Science
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A ball is shot directly upward, and then it comes back to the place where it was shot. Suppose we have air resistance. Suppose $t_1$ is the time period from the moment that the ball was shot to the moment that it reached its highest altitude, and $t_2$ is the time period from the moment it reached its highest altitude to the moment it reached its original position. Is $t_1=t_2$? Why or why not?
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My question is 1 -Why it's my low to calculate what I spend each month and not on my salary 2- how much you need for a holiday in Uk knowing that my brother who will host me  3- to get an estimate how many meters per day are needed