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David Q
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David Q
Answers (167)
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
How about (11-3)*(24-21)?
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
And from me too!
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
Do you mean the curve x^2 + y^2 + 2xy = 3?
(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
Divide 51 by 3: that'll give you the middle one. The other two will be two above it and two below it.
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
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
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
And L doesn't require the pencil to be lifted.
(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.)
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 (1/150) times this
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 /
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.
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)
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
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.
(That funny symbol ð should be a pi, by the way: it isn't being interpreted correctly.)
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) =
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?
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
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.
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
There's nothing wrong with it: it's correct.
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
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
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
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
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
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 would be
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
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
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
Presumably it's a scale factor of 70, i.e. (21mm / 0.3mm).
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
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
Yes - it's correct. I was about to write just that when I realized you'd already done it.
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.
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 containing a
Correction: -58c=-58, so c=1.
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
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.
Would you settle for (12/2)/(4-3)²? Or is there a limit on the number of times any operator can be used?
Ah - whoops. Didn't see the condition that the exponents had to be used. Sorry.
How about (12/2)/(4-3)?
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
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.)
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
