Friday
December 9, 2016

# Posts by David Q

Total # Posts: 167

October 6, 2008

statistics
You could be right about the standard deviation being 1. I did wonder at the time about whether you ought to be using the standard deviation for the entire population, as opposed to the usual one that's applied to a sample, which would be calculated using n as the divisor ...
October 6, 2008

statistics
The mean of those numbers is 2. The variance is 1.2. The sum of 100 of them should have a mean of 200 and a variance of 120, i.e. a standard deviation of sqrt(120) = 10.95. Now, 250 is (250-200)/10.95 = 4.56 standard deviations above the mean. Assuming the distribution is ...
October 6, 2008

And from me too!
October 6, 2008

Divide 51 by 3: that'll give you the middle one. The other two will be two above it and two below it.
October 6, 2008

Algebra
Suppose you were after the probability of getting four aces in five cards. Suppose also that the four aces were the first four cards out of the five you were dealt. The chances of getting that would be (4/52)x(3/51)x(2/50)x(1/49). But the 5th card could be any of the five you ...
October 6, 2008

Math/Algebra
(a) No, it won't. The remainder will be the same as that for the number that isn't divisible by n. (b) It might be, and it might not. Consider whether (8+4) is divisible by 3, given that neither 8 nor 4 is divisible by 3; then consider whether (8+5) is divisible by 3, ...
October 6, 2008

Calculus
On second thoughts, I don't think you do mean that: if you did, the tangent would be -1 for every point on the curve. If it IS x²y² + 2xy = 3, then put z=xy for a moment, in which case z²+2z=3, in which case z=1 or z=-3. So xy=1 or xy=-3, i.e. y=1/x or y=-3/...
October 6, 2008

Calculus
Do you mean the curve x^2 + y^2 + 2xy = 3?
October 6, 2008

algebra
5x=7+4y, so 5x-4y=7. Multiply both sides by 4, and you get: 20x-16y=28. But that's the other equation you were given - so you've actually only got one equation there, not two. And you can feed any value of x into that equation and get a corresponding value of y out.
October 5, 2008

U.S. History
Just a suggestion: you might want to take a look at "1984" by George Orwell, which was written shortly after WW2 and which describes a fictional dystopian future in which the war never ended, and which includes the following view (which was probably the one held by ...
October 4, 2008

math
And L doesn't require the pencil to be lifted.
October 4, 2008

MS = Moe Singles; MD = Moe Doubles; LS = Larry Singles; LD = Larry Doubles; CS = Curlie Singles; CD = Curlie Doubles. Then: MS = 3 x LS LD = 4 x CD MS + (2 x MD) = LS + (2 x LD) = CS + (2 x CD) MS + LS + CS = MD + LD + SD MS + LS + CS + 2 x (MD + LD + SD) < 200. It seems to...
October 4, 2008

math
900 miles at 50 miles an hour will take him 900/50=18 hours. He wants to do it in 15 hours, so he's going to have to travel at 900/15=60 miles an hour. If he does that, he'll have increased his speed by 10 mph.
October 4, 2008

math easy challenge
The answer is 8²+4²+4². There's an applet on the internet that will do the decomposition for you for any positive integer: just google "Dario Alpern Lagrange" and click on the link at the bottom of the page to find it. It's very fast indeed.
October 3, 2008

Math
(Sorry - the symbols Ó and ì ought to be a sigma sign and a mu respectively. You evidently can't just copy them from another posting - it doesn't work.)
October 3, 2008

Math
Are you sure that second formula isn't Ó(x-ì)²F? Unless it is, I can't see a way of calculating a standard deviation from the statistics supplied. On the assumption that the second statistic is Ó(x-ì)²F, the variance ought to be (1...
October 3, 2008

math algerbra 2
No, it won't be. A function is determined by two collections A and B and an assignment of a unique element of B to each element of A. If you let the function be f(x) = x², and let the domain be -1 to +1, then the range will be 0 to +1. But if you swap the domain and ...
October 2, 2008

math
Suppose you're using C ounces of Cheap and E ounces of Expensive syrup. Then: C + E = 128 5C + 25E = 18 x 128 Multiply the first equation by 5, and you'll get: 5C + 5E = 5 x 128 so: (5C + 25E) - (5C + 5E) = 20E = (18-5) x 128 = 13 x 128 so E = 13 x 128 / 20 = 83.2 so C...
October 1, 2008

math
(That funny symbol ð should be a pi, by the way: it isn't being interpreted correctly.)
September 30, 2008

math
Your string is cut into X and (24-X). Suppose the X part is used to form the circle, and the (24-X) part is used to form the square. Then since the circumference X = 2ðr, the radius r of the circle is X/(2ð), and so the area is ðr² = ðX²/(4ð²...
September 30, 2008

MATH
You need more information than this to solve the problem. Do you know the angle of the wire to the ground, or the height above the ground at which the wire is attached to the tree?
September 30, 2008

Math
1: sin(2x) = 2sin(x)cos(x), so you know that 2sin(x)cos(x)=3cos(x). So either 2sin(x)=3, or cos(x)=0. You now need to find all the values of x such that one or other of these equations is true. 2: e^(sqrt(x))=4 so ln(e^(sqrt(x))=ln(4), but ln(e^y)) = y for any y, so sqrt(x)=ln...
September 30, 2008

MATH
There's nothing wrong with it: it's correct.
September 30, 2008

algebra
Let B = no. of bicycles, U = no. of unicycles and T = no. of tricycles. Then you're told that: B = 88 + U T = 5U B = 40 + T. But T=5U, so B = 40 + 5U So since B = 88 + U, you know that 40 + 5U = 88 + U, so 4U = 48. From there you can work out what all of U, B and T are, ...
September 30, 2008

Maths - Pigeon-hole principle
I don't know what the pidgeon-hole principle is, but I imagine the solution will go something like this: The largest five-digit number is 99999, the sum of whose digits is 45. The smallest five-digit number is 10000, the sum of whose digits is 1. You can find any sum ...
September 30, 2008

Maths
The answer is d=25; N is any of 7, 32, 57, 82, 107, 132 etc etc. It was set up in a spreadsheet and arrived at by trial and error, so just knowing the answer probably won't get many marks. I'd be interested to know if anyone else can produce a formula for deriving the ...
September 30, 2008

math
This is a single equation in two unknowns. You can find X in terms of Y, or vice versa, but you can't calculate the actual value of either of them without more information.
September 29, 2008

Math- repost
This might be easier to read - just ignore the underscores: P_Q_~P_~Q_(Pv(~Q))__~(Pv(~Q)) __(~P)^(Q) T_T__F__F______T__________F__________F T_F__F__T______T__________F__________F F_T__T__F______F__________T__________T F_F__T__T______T__________F__________F
September 28, 2008

Math- repost
It ought not to: a truth table should deliver the same answers. I've just had a go at doing the first one that way, and got the following (these columns probably won't line up, but you should be able to work out which heading relates to which column): P Q ~P ~Q (Pv(~Q...
September 28, 2008

Math- repost
Put p = "Peter is a boy" and q = "Queenie is a girl". Then ~(p v ~q) means "It is not true that (either Peter is a boy or Queenie is a boy)". Doesn't that mean that both Peter is a girl and Queenie is a girl? If so, then p would be false and q...
September 28, 2008

math
The derivative f'(x) of -4x²+bx+3 is the gradient of f(x), which is -8x+b. At x=50 the function takes a maximum value, so the gradient must be zero, so -8x+b=0 at x=50, which means that b=400. Check the above: f(x) = -4x² + 400x + 3, so f'(x) = -8x + 400 = 0...
September 25, 2008

statistics
I don't have a binomial probabilities table, so I've done the math from scratch: you should be able to verify the probabilities against your tables as you go: The probability of a driver being drunk is 0.2, so the probability of a driver NOT being drunk is 1 - 0.2 = 0....
September 25, 2008

math
The power of a quotient is equal to the quotient obtained when the dividend and divisor are each raised to the indicated power separately, before the division is performed - so I'm assuming that this is what the quotient of powers property is. So perhaps the argument would...
September 24, 2008

Math Calculus
It's difficult to see how the problem as stated is related to the Intermediate Value Theorem - but putting that aside, presumably what you're looking for is a good indication that the sweetheart is at home without going over there. You could phone, of course, but if ...
September 24, 2008

math
If he walks 6 feet/second, that's saying that he walks 6 feet in a second. So he walks 3600x6=21600 feet in 3600 seconds, which is 21600 feet in an hour. But 5280 feet equals one mile, so he's walking 21600/5280 miles per hour. Which of the available choices is closest...
September 24, 2008

algebra scales
Presumably it's a scale factor of 70, i.e. (21mm / 0.3mm).
September 24, 2008

Language
Yes - it's correct. I was about to write just that when I realized you'd already done it.
September 23, 2008

math
You're going to have to do just that, I'm afraid. Plot U against V on a piece of graph paper, calculator, spreadsheet or whatever; draw the two lines described by those equations, and see where they intersect. I know where that's going to be: it's at the point...
September 23, 2008

math
First, set up a practical example for yourself to get a feel for what happens. Put X=5, and calculate log(X) to base 5 and you'll get 1.0. If on the other hand you calculate log(X) to base 25, you'll get 0.5. Now try changing X to something else, say 12. log(12) to ...
September 23, 2008

math
Would you settle for (12/2)/(4-3)²? Or is there a limit on the number of times any operator can be used?
September 23, 2008

math
Ah - whoops. Didn't see the condition that the exponents had to be used. Sorry.
September 23, 2008

math
September 23, 2008

Social Studies
It often depends on what's at stake. Dissident voices are a lot easier to tolerate in times of peace than times of war. Also a secure government will tolerate dissent far more comfortably than will an insecure government.
September 23, 2008

Algebra 8
In (a), all values of x make the statement true, because both sides of the equation are actually the same: if you expand the right-hand side, you'll see that all it's saying is that 3x+3=3x+3, so any value of x you care to choose will make that statement true. In (b), ...
September 22, 2008

MATH Matrix Equation
Correction: -58c=-58, so c=1.
September 22, 2008

MATH Matrix Equation
Or to get it algebraically, call the equations P, Q and R respectively, so P: 4a + 3b + c = 27 Q: 3a + b + 4c = 16 R: 9a + 2b + 3c = 33 Solve these for b first, since the multiples are easy: R-2Q = 3a - 5c = 1 P-3Q = -5a - 11c = -21 so 5(R-2Q) = 15a - 25c = 5 3(P-3Q) = -15a - ...
September 22, 2008

Stats
A "random variable" is a technical term: it does not mean a variable that is "random" in the colloquial sense. The definitions above are taken from the "variance" and "covariance" entries in Wikipedia, but can be verified at any site ...
September 22, 2008

Stats
Variance is a measure of dispersion of a single random variable X. Covariance is a measure of how much TWO random variables, say X and Y, change together. (The variance is a special case of the covariance when the two variables are identical.)
September 22, 2008

math
I agree with you about (a). Part (b) is just y=3*f(x), and (c) is y=3*f(2x)). What you're describing in (b) is a translation of the function of 3 units to the right, not a vertical expansion of it by a factor of 3. Having said all that, I can't see where the answers at...
September 21, 2008

science....help
Mass is a measure of how much matter an object has. Weight is a measure of how strongly gravity pulls on that matter. The mass of a stone would be the same irrespective of where you measured it, be it on Earth, the Moon or in deep space. The weight on the other hand is ...
September 21, 2008

You can get a very good idea where to start looking by just calculating the cube root of 1716. (The minus sign isn't a problem: it just means that the three consecutive integers will all be negative.)
September 21, 2008

science ()
And are we talking about some specific cheeky girls - in which case which ones - or cheeky girls in general?
September 21, 2008

MATH
You won't be able to factor it further, so yes: that's the answer.
September 21, 2008

MATH
That equation factorizes as (5x-4)(5x-4), so if the original expression is the area, then one of those two identical factors must represent the side.
September 21, 2008

maths
Here's the brute-force solution, which was produced using MS Excel in about half an hour - so probably not much use if you have show your working and use the clues to get to the answer. There are five solutions that use the digits 0-9 exactly once: 5694 x 3 = 17082 6189 x ...
September 21, 2008

Calculus
I've seen this one before and queried it before. As h tends to zero, (4+h)^3 approaches 64, but 64/h tends to either plus or minus infinity depending on which side h is approaching zero from, so this isn't what you're calculating. Could you check the function please?
September 21, 2008

Mth plz...help
Yes, it is.
September 21, 2008

Mth plz...help
You've got a positive relationship (perhaps not surprisingly) between attendance and success, which you can see from the sign of the coefficient on the X term (+0.5). That means the correlation coefficient (which can only lie between -1 and +1) is positive. Only one of the...
September 21, 2008

Calculus
If that pair of coordinates represents (X,Y), then the easiest way is to do pretty much what you already suggested, but do it systematically in small increments. That is, work out a set of points as follows. -pi/2 is approximately -1.57, so t=-1.57, X=cos(2t)=-1, Y=sin(t)=-1 t...
September 20, 2008

Math
Just a thought... if Jim holds down the first key while he presses the second, then he's only got 35 to choose from for his second press, which would slightly increase his chance of hitting a letter. But I don't think that's what the question meant.
September 19, 2008

Math
Juanita answered 21, and Anna answered three fewer than this, so Anna must have answered 18. Earl answered two more than Anna, so Earl must have answered... what?
September 18, 2008

math
Suppose there are P stamps in Doug's first book. Then there are (P+30) stamps in his second book. The total number of stamps in his collection is 170, and his collection equals the number of stamps in the first book plus the number in the second book. So P + (P+30) = 170, ...
September 18, 2008

Maths
We want to find two real numbers p and q such that (p+qi)(p+qi)=(5+12i). Collect the real and the imaginary terms together into two separate equations: Real terms: p²-q²=5 Imaginary terms: 2pq=12, i.e. pq=6 You could solve the above as a pair of simultaneous ...
September 18, 2008

latin
...which includes such useful phrases as: Radix lecti (Couch potato) Fabricati diem (Make my day) Lege et lacrima (Read it and weep) Ne auderis delere orbem rigidum meum! (Don't you dare erase my hard disk!) Res melius evinissent cum coca (Things go better with Coke) ...
September 18, 2008

latin
I can't actually post a website address here, but if you google "latin phases quotes uk" you should find fairly high on the list a site at the University of Liverpool that has a lot of expressions covering an assortment of subjects. With a little ingenuity, you ...
September 18, 2008

MATH HELP
Do you mean "What does "prime power factorization" mean? If so, it means expressing a number n as the product of its prime factors in the form: n = (p1^a1) x (p2^a2) x (p3^a3) etc etc where p1, p2, p3 etc are prime factors of n, and a1, a2, a3 etc are exponents...
September 17, 2008

math
What I *could* have done instead would be to just multiply the first equation by 2 to make the first one have the same number of Gs as the second: J + G = 28 (items) 5J/3 + 2G = 50 (cents) Multiplying the first one by 2 would give me: 2J + 2G = 56 5J/3 + 2G = 50 so J/3 = 6 If ...
September 17, 2008

math
They come from multiplying the previous two equations by 5 and 3 respectively. What you're trying to do is get two equations that you can use to eliminate one of the two variables, so after I multiplied the equation that reads 5J/3 + 2G = 50 by 3 to clear the fraction, I ...
September 17, 2008

math
Say J = no. of jellybeans and G = no. of pieces of gum then J + G = 28 (items) and 5J/3 + 2G = 50 (cents) so 5J + 6G = 150 and 5J + 5G = 140 You've now got two equations which differ by exactly 1 x G. Can you finish it off?
September 17, 2008

Math
Your answer looks correct to me, but I don't see the relevance of the two intermediate steps. Each tile is one foot square; you've got 10x10=100 of them in a square, so it looks like a 10x10 chessboard. Half of those 100 squares will be black. (Just one thing: 10 feet ...
September 17, 2008

Math!
"New York - deny work"?
September 17, 2008

Math!
I'll guess that "New York" is in there somewhere. Try removing those letters and then feed the remainder through an online anagram solver. I did that and didn't see anything I recognised, but you might be more lucky.
September 17, 2008

drama
Google is usually a good place to start when it comes to definitions. Type in "define:surrealism" and see what you get.
September 17, 2008

math (unit rate)
Do you mean "25 feet/second"? It's almost certainly a measure of speed, expressed as the number of feet travelled divided by the number of seconds it took to travel it.
September 16, 2008

Math
5.688 x 10^12 is in standard form already.
September 16, 2008

Literature
SINGER , Isaac Bashevis (1904-1991): Zlatek the Goat and Other Stories (Cuentos judíos de la aldea de Chelm) Okay - I've found it. What's the question please?
September 16, 2008

year 8 geography
Assuming "waiting street" is supposed to read "Watling Street", Wikipedia says that this was originally Wæcelinga Stræt, and is now the A2 from Dover to London followed by the A5 from London to Wroxeter. (Somehow it doesn't have the same ...
September 16, 2008

Math
I don't believe there's a smaller one than that (I checked it in Excel). The next one is 5039, which is twice the last plus 1. (Incidentally, the one before 2519 corresponds to N=-1.) To work out which number gives a remainder of 1 for all the integers from 1 to P, ...
September 16, 2008

math
Consider a very simple example in which you've only got two numbers. If they're not the same number, the mean won't be included in the set of data. Another reason why it might not be is when all the elements in the data are integers, but the mean is not an integer...
September 15, 2008

trig
The correlation coefficient (r) is just the square root of r² ... but there are two square roots of r², namely +r and -r. However, there's a clue: the line of best fit has a negative slope - so that tells you the sign of r.
September 15, 2008

Math
1 googol = 10^100, i.e. the digit 1 followed by one hundred zeros. The company name Google is a misspelling of the word "Googol".
September 15, 2008

math
It would be, if your original expression was supposed to be: (xy^5)^3/x^2y^4
September 15, 2008

algebra
Hi again Laura: it's putting into words the consequences of one of the assumptions that we made when we worked out the number of animals in that conservation park, namely that the density of animals in a small section of their habitat (in that example that would have been ...
September 14, 2008

algebra
It's referred to as the "mark-and-recapture" technique: you can find it under "Mark and Recapture" in Wikipedia, together with examples of the math involved.
September 14, 2008

trig
Think of the various definitions of these functions in terms of the height, base and hypoteneuse of a right-angled triangle. You're told that tan(x)=8/3, which means that the ratio of the height to the side is 8 to 3. So you can work out the hypoteneuse by Pythagoras. That...
September 14, 2008

Whatever the number of friends is, it has to divide into \$8.41 (i.e. 841 cents) without a remainder - so you need to find out what integers (because there can only be an integer number of friends) divide into 841. As Bob showed, that's easy: you can just do it by trial and...
September 13, 2008

pre-calculus
The answer is yes: you can write y as a function of x. Damon and I were debating whether you can write x as a function of y, which wasn't what you were asked.
September 13, 2008

pre-calculus
Fair enough, though you could presumably define a function by restricting the range to just zero plus either the positive or negative real numbers.
September 13, 2008

pre-calculus
Do you mean "Can y be expressed as a function of x?". If so then the answer is yes it can, if by "x^2y" you mean "x²y" and not "x raised to the power of 2y". The equation x²y - x² + 4y = 0 can be written as (x²+4)y = ...
September 13, 2008

Stats
I still don't understand what "a" or "á" is supposed to represent here. Can you define it please?
September 13, 2008

Stats
We'll need to know rather more about what that "a" is supposed to be - but I don't think your answer is correct. Whatever "a" is, the answer is unlikely to be just 1-0.84, which I suspect is how you've calculated it.
September 13, 2008

Statistics
The standard error of the mean (SEM) is the standard deviation divided by the square root of the sample size - which in this instance is 9 - so the SEM here is 16/sqrt(9)=5.33. The question actually contains a little clue that you're probably on the right track in that ...
September 13, 2008

math
Biased surveys generate answers that are unrepresentative of the population about which you want to draw general conclusions. In this case, the population consists of all the students in your school. As Ms Sue says, what would you conclude if only you survey kids who work out ...
September 13, 2008

writting
A compelling argument or counterargument is one which it's very difficult to refute. Do you have a particular thesis in mind, or is this a general request for help in how to set about doing it?
September 13, 2008

statistics
Have you been given some data upon which to perform the hypothesis testing procedure? If so, we'll need to see it too in order to help.
September 13, 2008

education
By "top ten", do you mean the ten most positive characteristics of such an environment, or just the ten characteristics that most strikingly differentiate a multicultural school environment from a non-multicultural one? And should these characteristics be the most ...
September 12, 2008

Maths
You're welcome! :)
September 12, 2008

Maths
Oh - and one more constraint, namely that the total quantity of Sunflower, Sorghum, Maize and Wheat equals one kilogram, since you're trying to find the optimal mix in that amount of feed. This isn't actually part of the problem you've been set, but if you're ...
September 12, 2008

Maths
It's going to be something like this (but do check my algebra)... You've been told what the Energy, Protein, Vitamin and Price are for unit quantities of Sunflower, Sorghum, Maize and Wheat. This gives you four equations - one in each of Energy, Protein, Vitamin A and ...
September 12, 2008

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