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# Recent problems solved by 'robertb'

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 Linear-equations/431270: which equation represents a line with a y-intecept and (0,4) and an x-intercept of (3,0)?1 solutions Answer 299372 by robertb(4012)   on 2011-04-04 22:25:50 (Show Source): You can put this solution on YOUR website!Use the intercept form: You can just simplify this.
 Linear-equations/431263: which equation represents a line with a slope of 0 and passing through the point (4, 5)?1 solutions Answer 299371 by robertb(4012)   on 2011-04-04 22:23:54 (Show Source): You can put this solution on YOUR website!y = 5.
 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 .
 test/431293: What are the roots of the quadratic equation y=x^2+7x-18 by factoring 1 solutions Answer 299368 by robertb(4012)   on 2011-04-04 22:04:23 (Show Source): You can put this solution on YOUR website!(x+9)(x - 2) = 0 ==> x = -9, 2.
 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.
 Geometry_Word_Problems/431274: a satellite completely orbits earth in 216 days. determine the angle through which the satellite travels over a period of 12 days1 solutions Answer 299355 by robertb(4012)   on 2011-04-04 21:29:01 (Show Source): You can put this solution on YOUR website!radians, or 20 degrees.
 Linear-equations/431268: which is the equation of the line containing points (3,5) and (-2, -20)?1 solutions Answer 299353 by robertb(4012)   on 2011-04-04 21:16:07 (Show Source): You can put this solution on YOUR website! ==> y-5 = 5(x-3) ==> y - 5 = 5x - 15 or y = 5x - 10. You could also use , and still get the same equation in the end.
 logarithm/431228: What is the exact value of 4+2log3(7x)=10? And how do you find that without using a calculator?1 solutions Answer 299352 by robertb(4012)   on 2011-04-04 21:13:31 (Show Source): You can put this solution on YOUR website! <==> <==> <==> ==> x = 27/7. Since this value also satisfies the original equation, this is the final answer.
 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.
 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): You can put this solution on YOUR website!If the hypotenuse is , then each of the two legs must be 12 units long. Hence the perimeter is units.
 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.
 logarithm/430642: evaluate (-9)^(5/2) without using a calculator1 solutions Answer 299146 by robertb(4012)   on 2011-04-04 05:09:51 (Show Source):
 Mixture_Word_Problems/430454: i have 5 liters of water and need to add 15% color 1 solutions Answer 298959 by robertb(4012)   on 2011-04-03 07:53:08 (Show Source): You can put this solution on YOUR website!Hmm..wait a while, I'll just peer through my crystal ball...
 Geometry_Word_Problems/430447: the length of a rectangular field is 6 times its breadth its area is 1350 sq.m find its perimeter?1 solutions Answer 298958 by robertb(4012)   on 2011-04-03 07:50:58 (Show Source): You can put this solution on YOUR website!Area = x*6x = 1350 ==> ==> x = 15 meters, the breadth. ==> 6*15 = 90 meters, the length. ==> perimeter is 2(15 + 90) = 210 meters.
 Radicals/430455: how do i do the square root of 5 over 7? I need to simplify it.1 solutions Answer 298957 by robertb(4012)   on 2011-04-03 07:45:54 (Show Source):
 Mixture_Word_Problems/430437: How many milliliters of water must be added to 60 mL of a 15% iodine solution in order to dilute it to a 10% solution?1 solutions Answer 298956 by robertb(4012)   on 2011-04-03 07:44:14 (Show Source): You can put this solution on YOUR website!0.00x + 0.15*60 = 0.10*(x+ 60) <==> 9 = 0.10x + 6 ==> 3 = 0.10x ==> x = 30 ml of water should be added...
 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.
 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): You can put this solution on YOUR website!g(-3) = 2|1--3| - 7 = 2*4 - 7 = 1 g(b) = 2|1-b| - 7 g(2x-3) = 2|1-2x + 3| - 7 = 2|4 - 2x| - 7 = 4|2-x| - 7
 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. ==>
 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 \$.1681 solutions Answer 298949 by robertb(4012)   on 2011-04-03 06:46:54 (Show Source): You can put this solution on YOUR website!The expectation is \$
 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).
 Exponents/430444: FInd the value of a and b if (5^(n+1)-5^(n-1))/(3x5^(3n))=ax5^(bn)1 solutions Answer 298946 by robertb(4012)   on 2011-04-03 06:21:31 (Show Source): You can put this solution on YOUR website! <==> <==> <==> ==> ==> and b = -2, by direct comparison.
 Sequences-and-series/430417: 140% of what number is 35?1 solutions Answer 298945 by robertb(4012)   on 2011-04-03 06:13:27 (Show Source): You can put this solution on YOUR website!1.40x = 35 ==> x = 25
 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.
 Probability-and-statistics/430446: ∛(a^3+b^3 )/∛(a+b)1 solutions Answer 298943 by robertb(4012)   on 2011-04-03 05:48:01 (Show Source):
 Mixture_Word_Problems/430436: How many liters of water must be added to 50 L of a 30% acid solution in order to produce a 20% acid solution?1 solutions Answer 298942 by robertb(4012)   on 2011-04-03 05:43:14 (Show Source): You can put this solution on YOUR website!0.00x + 0.30*50 = 0.20*(x+50) <==> 15 = 0.20x + 10 <==> 5 = 0.20x <==> x = 25 liters of water must be added.
 Rational-functions/430399: y= For this problem, what would the removable discontinuity be? Please help me!! Thank you and have a nice day :))1 solutions Answer 298926 by robertb(4012)   on 2011-04-03 00:12:03 (Show Source): You can put this solution on YOUR website!. There is a removable discontinuity at x = 1/2. (There is essential discontinuity at x = -10.)
 Rational-functions/430404: =y For this problem, what would the removable discontinuity be? Thank you and have a great day!1 solutions Answer 298924 by robertb(4012)   on 2011-04-03 00:05:29 (Show Source): You can put this solution on YOUR website!. There is a hole on the graph of y = f(x) at x = -4, and hence that is where the removable discontinuity is. (There is an essential discontinuity at x = 4, or a vertical asymptote there.)
 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 Dave1 solutions Answer 298922 by robertb(4012)   on 2011-04-03 00:01:03 (Show Source): You can put this solution on YOUR website!That is right.
 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.
 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, Gina1 solutions Answer 298917 by robertb(4012)   on 2011-04-02 23:37:07 (Show Source): You can put this solution on YOUR website!This experiment follows the binomial distribution, with n = 12, p = 0.20, and q = 1 - p = 0.80. The expectation is