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Equations/431282: Find the quadratic equation with integral coefficients having the given roots.
4 + 2i, 4 - 2i
Thanks!!
1 solutions
Answer 299370 by robertb(4012)   on 2011-04-04 22:11:58 (Show Source):
You can put this solution on YOUR website!The coefficient of x is equal to -(4 + 2i + 4- 2i) = -8.
The constant term is equal to (4+2i)(4-2i) = 16 - 4(-1) = 20.
Hence the quadratic equation is  .
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Probability-and-statistics/431284: What is the probability that a random 2 digit number is a multiple of 7?
1 solutions
Answer 299361 by robertb(4012) on 2011-04-04 21:47:17 (Show Source):
You can put this solution on YOUR website!Without loss of generality, assume only positive integers. There are 90 2-digit positive integers, while there are 13 2-digit positive integers divisible by 7.
Hence the probability is 13/90.
Why 13 2-digit positive integers divisible by 7?
98 = 14 + (n-1)7, from the arithmetic sequence formula.
==> 84 = (n-1)7
==> 12 = n-1
==> n = 13.
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Probability-and-statistics/431234: The annual income of residents in a county is $42,000 with a standard deviation of $10,000. Between what two values do 95% of the incomes of county residents lie?
1 solutions
Answer 299350 by robertb(4012) on 2011-04-04 21:08:50 (Show Source):
You can put this solution on YOUR website!Assuming a normal distribution, then by the empirical rule, 95% of the incomes lie within two standard deviations, or between $22,000 and $62,000.
Assuming non-normality, and using Chebyshev's theorem, then
 ,
==>  ==> 
==> 
<==> 
Since the left endpoint is negative, the bounds are 0 and 86,721.36.
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Triangles/431242: If the length of the hypotenuse of a 45°-45°-90° triangle is 12√2, what is the perimeter of the triangle?
1 solutions
Answer 299345 by robertb(4012) on 2011-04-04 20:50:36 (Show Source):
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Probability-and-statistics/430559: There are two sets of marbles. Both have 1,000 in them. Bag 1 has 700 blue and 300 red. Bag 2 has 300 blue and 700 red. Picking a bag at random you draw out 10 marbles with replacement. If 7 are red and 3 are blue, what is the exact probability of you picking Bag 1?
1 solutions
Answer 299148 by robertb(4012) on 2011-04-04 05:32:00 (Show Source):
You can put this solution on YOUR website!The assumptions that
P(7R3B|bag1) = C(10,3)[(.7)^7(.3)^3]
P(7R3B|bag2) = C(10,3)[(.3)^7(.7)^3]
are wrong.
The experiment of drawing balls from each bag doesn't follow a binomial distribution, but a hypergeometric distribution.
They should be
P(7R3B|bag1) = 
P(7R3B|bag2) =  .
The use of Bayes' rule is correct.
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Functions/430440: How do i find the inverse of the function:
f(x) =(x^3 -7) /(x^2-4)
1 solutions
Answer 298955 by robertb(4012) on 2011-04-03 07:39:24 (Show Source):
You can put this solution on YOUR website!The function is not one-to-one, and hence cannot have an inverse function. (Fails the horizontal line test!)
x-intercept at  ,
vertical asymptotes at x = -2 and x = 2,
y-intercept at 7/4,
slant asymptote is the line y = x.
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logarithm/430316: for the given g(x), evaluate the following.
a) g(-3)
b) g(b)
c) g(x^3)
d) g(2x-3)
g(x) = 2 │1 - x │ - 7
1 solutions
Answer 298954 by robertb(4012) on 2011-04-03 07:20:05 (Show Source):
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Probability-and-statistics/287629: Probability Density. HELP PLEASE !!!!
A broom stick of length 1 meter is split into two substicks at a point that is uniformly distributed. Let X be the length of the shorter substick and Y be the length of the longer substick.
Find
(a) the density of X
(b) the density of Y
(c) E(X)
(d) Var(X)
(e) E(Y - X)2
As no one is attempting to answer this question (that I have posted several times), can I assume it's unsolvable ?
Someone PLEASE reply !!!!
1 solutions
Answer 298952 by robertb(4012) on 2011-04-03 07:13:39 (Show Source):
You can put this solution on YOUR website!f(x) = 1, x in [0,1],
f(y) = 1, y in [0,1]. (Here, Y = 1 - X.)
Now 
<==>  .
var(Y-X) = varY + varX = var(1-X) + var X = var 1 + var X + var X = 2var X = 2/12 = 1/6.
E(Y - X) = E(Y) - E(X) = E(1 - X) - E(X) = E1 - E(X) - E(X) = 1 - 2E(X) =
1 - 1 = 0.
==> 
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Probability-and-statistics/430411: Oh I forgot an important part of the problem.I submitted but forgot choice of answers.
you have 10 coins in your pocket 4 quarters 3 nickels 3 dimes you pull out 1 coin calculate the expected value of the tip in cents
$.145
$.132
$.083
$.183
$.168
1 solutions
Answer 298949 by robertb(4012) on 2011-04-03 06:46:54 (Show Source):
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Rational-functions/430397: y=
For this equation I need to give the domain, asymptotes, and removable discontinuities. I get both of the asymptotes but I just have no idea what the domain and removable discontinuities are. :( Please help me! Thank you and have a great day!!
1 solutions
Answer 298948 by robertb(4012) on 2011-04-03 06:42:52 (Show Source):
You can put this solution on YOUR website!One restriction on the value of x is that it should not be equal to 0. Another restriction is that  should not be equal to 0. This is the same as saying that  should not be equal to 0,  is not equal to 0, or x is not equal to 2.
The DOMAIN is then all real numbers not equal to 0 or 2. This said,
 .
As x goes to infinity, the expression goes to y = 0, because the degree of the numerator is less than the degree of the denominator. (Because the expression will have no real roots.)
Hence y = 0 is a HORIZONTAL ASYMPTOTE.
Since the denominator is a quadratic irreducible over the real numbers, the expression has NO VERTICAL ASYMPTOTES.
There are REMOVABLE DISCONTINUITIES at x = 0 and x = 2, because they cancel out in the process of simplification. They correspond to "holes" at the graph at the point (0,1) and (2, 2/3).
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Sequences-and-series/430428: The 4th term of an arithmetic sequence is 16.The 8th term is four times the 1st term.
(a)find the general term T(n)of the sequence.
(b)Find the smallest term which is greater than 500.
1 solutions
Answer 298944 by robertb(4012) on 2011-04-03 06:11:07 (Show Source):
You can put this solution on YOUR website!(a)  , and 
<==> 
==> 
==> 
==> 
==> d = 3
==> 
==> T(n) = 7 + (n-1)3 = 7 + 3n - 3 = 3n + 4
(b) We want 3n + 4 > 500, or n > 165.333..... Hence when n = 166, we get the smallest term greater than 500, which is 3*166 + 4 = 502.
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Probability-and-statistics/430408: A $1 lottery game has following payouts and probabilities
$5000 .000002
$1000 .00001
$500 .0002
$50 .001
$5 .03
$1 .12
what is the expected value of this game?
a) .35
b) 1.64
c) .06
d) .44
e) 1.53
I chose .44, am I right?
Thanks
Dave
1 solutions
Answer 298922 by robertb(4012) on 2011-04-03 00:01:03 (Show Source):
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Probability-and-statistics/430376: You are given the probabilities below:
P(a) = 0.25
P(B) = 0.30
P(C) = 0.55
P(A and C) = 0.05
P(b and C) = 0
P(B|A) = 0.48
A.) Are A and B independent events? Why or Why not?
B.) Find P(A and B)
C.) Find P (A or B)
D.) Find P(A|B)
E.) Are B and C mutually exclusive events? Why or why not?
F.) Are B and C independent events? Provide mathematical proof.
1 solutions
Answer 298921 by robertb(4012) on 2011-04-02 23:57:04 (Show Source):
You can put this solution on YOUR website!A) A and B are not independent: P(A)*P(B)= 0.25*0.30 = 0.075. This is not equal to P(A and B) = P(B|A)*P(A) = 0.48*0.25 = 0.12.
B) P(A and B) = P(B|A)*P(A) = 0.48*0.25 = 0.12.
C) P(A or B) = P(A) + P(B) - P(A and B) = 0.25 + 0.30 - 0.12 = 0.43
D) P(A|B) = P(A and B)/P(B) = 0.12/0.30 = 0.40
E) B and C are mutually exclusive, because it is given that P(B and C)=0 (Definition of mutual exclusivity.)
F) P(B)*P(C) = 0.30*0.55 = 0.165
P(B and C) = 0
==> The two quantities are not equal, hence B and C are not independent.
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Probability-and-statistics/430393: If I could just get some help with this one. The probability that a person is left handed is .20. you interview 12 people for a study what is the expected number of left handed people out of 12
Thanks,
Gina
1 solutions
Answer 298917 by robertb(4012) on 2011-04-02 23:37:07 (Show Source):
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