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# Recent problems solved by 'robertb'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019, >>Next

 Radicals/367892: 1 solutions Answer 262248 by robertb(4012)   on 2010-11-08 16:44:30 (Show Source): You can put this solution on YOUR website! , , after squaring both sides. , after transposition and cancellation. , 4 = x-3, after squaring again, or x = 7. This value satisfies the original equation, so this is the final answer.
 Expressions-with-variables/367960: Jules's Verne's fictional submarine, the Nautilus, traveled 20,000 leagues under the sea. Let m leagues equal 1 mile. How many mailes dd the Natulis travel? write the problem as an expression1 solutions Answer 262240 by robertb(4012)   on 2010-11-08 16:37:55 (Show Source): You can put this solution on YOUR website!let x = # of miles. Then 1 mile/m leagues = x/20,000, or , or miles.
 Probability-and-statistics/367953: Eight people are entered in a race. If there are no ties, in how many ways can the first two places come out? 1 solutions Answer 262236 by robertb(4012)   on 2010-11-08 16:34:56 (Show Source): You can put this solution on YOUR website!P(8,2) = 8*7 = 56.
 Numeric_Fractions/367949: what is 2/3 + (-1/6) please show work1 solutions Answer 262233 by robertb(4012)   on 2010-11-08 16:33:02 (Show Source):
 Numeric_Fractions/367954: what is -1/2-(-5/8)1 solutions Answer 262232 by robertb(4012)   on 2010-11-08 16:31:45 (Show Source):
 Numeric_Fractions/367952: what is -5/9-7/181 solutions Answer 262231 by robertb(4012)   on 2010-11-08 16:30:40 (Show Source):
 Probability-and-statistics/367569: A new medication for migraine sufferers is known to be successful in 70% of cases. Jessica selects ten migraine sufferers to take part in the testing of the drug. Find the probability that: a) 2 people are cured b) no people are cured1 solutions Answer 262032 by robertb(4012)   on 2010-11-08 06:10:40 (Show Source): You can put this solution on YOUR website!a) b)
 Equations/367593: Solve by factoring 4x^2 - 3x -6 = 0 1 solutions Answer 262030 by robertb(4012)   on 2010-11-08 06:08:19 (Show Source): You can put this solution on YOUR website!It cannot be factored into linear factors having rational coefficients: the discriminant is equal to 105, which is a positive real number but not a perfect square.
 Probability-and-statistics/367577: Niall rolls a fair die 50 times. Find: a) the expected number of odd numbers b) the variance of odd numbers c) the standard deviation of odd numbers 1 solutions Answer 262029 by robertb(4012)   on 2010-11-08 06:05:04 (Show Source): You can put this solution on YOUR website!The exercise becomes a binomial experiment with P(odd)= p = 0.5 and P(even) = q= 0.5. a)the expectation is odd numbers. b) the variance is c) the SD is just the square root of (b)--around 3.54.
 absolute-value/367597: 6+3│p-4│>121 solutions Answer 262027 by robertb(4012)   on 2010-11-08 05:58:48 (Show Source): You can put this solution on YOUR website!3/p-4/>6, /p-4/>2. This inequality is the same as the pair of inequalities p-4< -2 or p - 4>2, p <2 or p>6. In interval notation, (, 2)U(6, ).
 Quadratic_Equations/367622: For what value of k will the roots of 4x^2 + 4x + k be equal?1 solutions Answer 262023 by robertb(4012)   on 2010-11-08 05:52:32 (Show Source): You can put this solution on YOUR website!The discriminant has to be 0. . This gives 16 = 16k, or k = 1.
 Sequences-and-series/367620: The first term of a geometric sequence is 5 and the third term is 7.2.Which of the following can be the fifth term? (A) 8.85 (B) 9.4 (C) 10.368 (D) 11.646 (E) 12.44161 solutions Answer 262022 by robertb(4012)   on 2010-11-08 05:50:02 (Show Source): You can put this solution on YOUR website!B) 9.4. the difference between the 1st and 3rd terms is 2.2. Dividing this by 2 gives 1.1, and this is the common difference d. Adding 2.2 to 7.2 gives the 5th term , which is 9.4.
 Problems-with-consecutive-odd-even-integers/367616: find two consecutive integers whose sum is 383 1 solutions Answer 262020 by robertb(4012)   on 2010-11-08 05:47:06 (Show Source): You can put this solution on YOUR website!x+x+1 = 383, 2x = 382, x = 191, x+1 = 192
 Problems-with-consecutive-odd-even-integers/367618: find two consecutive multiples of 7 whose sum is 841 solutions Answer 262017 by robertb(4012)   on 2010-11-08 05:44:49 (Show Source): You can put this solution on YOUR website!7x + (7x+7) = 84, 14x = 77, 2x = 11. The equation has no integer solution,and thus the problem itself has no solution.
 Probability-and-statistics/367615: Let ⌊x ⌋ = the greatest integer that is less than or equal to x. For example ⌊4.23⌋ = 4 and ⌊8⌋ = 8 What is the average of ⌊10.75⌋ and ⌊-3.68⌋ ?1 solutions Answer 262013 by robertb(4012)   on 2010-11-08 05:38:04 (Show Source): You can put this solution on YOUR website!(10+(-4))/2 = 6/2 = 3
 Polynomials-and-rational-expressions/367550: Find the polynomial function that has the given zeros a) 1+ square root 3, 1 – square root 3 b) 0, -2, -3 1 solutions Answer 262012 by robertb(4012)   on 2010-11-08 05:36:05 (Show Source): You can put this solution on YOUR website!a) b)
 Equations/367588: Solve this quadratic inequality and show answer in interval notation: 4x^2 - 12x + 9 > 0 1 solutions Answer 262002 by robertb(4012)   on 2010-11-08 02:31:52 (Show Source): You can put this solution on YOUR website! is the same as . All real numbers will satisfy this except x = 3/2, when it is zero. Thus the solution set is (, 3/2)U(3/2, ). 4x^2 - 3x - 6 = 0 Check the discriminant:. The value of the discriminant is positive but is not a perfect square, so the quadratic expression cannot be factored into linear factors with rational coefficients.
 Equations/367591: Find the discriminant of this equation and tell if the quadratic equation has 2 real solutions, one real solution, or two imaginary solutions: 9x^2 - 64 = 0 1 solutions Answer 262001 by robertb(4012)   on 2010-11-08 02:28:15 (Show Source): You can put this solution on YOUR website!. Thus there are two distinct real roots.
 Quadratic_Equations/367586: Find the value of k so that the equation 3x²-(5+k)x-17=0 will have roots numerically equal but opposite sign.Please answer the question.1 solutions Answer 262000 by robertb(4012)   on 2010-11-08 02:25:21 (Show Source): You can put this solution on YOUR website!For the roots to be numerically equal but opposite in signs, the factorization of the expression would have to be (ax+b)(ax-b) = , a difference of two squares. This means , and . The middle term has to disappear, and so -(5+k) = 0, or k = -5.
 Rational-functions/367578: horizontal asymptote 4x/x-21 solutions Answer 261999 by robertb(4012)   on 2010-11-08 02:18:15 (Show Source): You can put this solution on YOUR website!. Dividing 4x by x - 2, we get . As x goes to positive or negative infinity, the expression goes to 4. Thus the horizontal asymptote has equation y = 4.
 Triangles/367583: The area of a triangle is 40 and its base is 32. Find the base of a similar triangle whose area is 90. . 1 solutions Answer 261998 by robertb(4012)   on 2010-11-08 02:12:30 (Show Source): You can put this solution on YOUR website!Let k = constant of proportionality between the two similar triangles(bigger-to-smaller.)Then . or k = 3/2. Thus the base of the bigger triangle is .
 Human-and-algebraic-language/367580: Can anyone tell me if I did this correctly? The sum of two consecutive integers is 35. This is what I have: x+(x+1)=351 solutions Answer 261997 by robertb(4012)   on 2010-11-08 02:04:18 (Show Source): You can put this solution on YOUR website!Yup.
 Probability-and-statistics/367510: An instructor gives his class a set of 15 problems with the information that the next quiz will consist of a random selection of 4 of them. If a student has figured out how to do 7 of the problems, what is the probability the he or she will answer correctly at least 3 questions?1 solutions Answer 261992 by robertb(4012)   on 2010-11-08 00:45:52 (Show Source): You can put this solution on YOUR website!# of ways 3 correct answers: , # of ways 4 correct answers: . # of ways getting 4 questions out of 15: , thus the probability is
 Linear-systems/367575: Will you help me solve for y in the equation: 3x-4y=101 solutions Answer 261991 by robertb(4012)   on 2010-11-08 00:30:33 (Show Source): You can put this solution on YOUR website!3x-10 = 4y, so that
 Finance/367576: A bottle of perfume contains 10 1/2 ounces and sells for .98 cents. What is the cost per ounce?1 solutions Answer 261990 by robertb(4012)   on 2010-11-08 00:29:11 (Show Source): You can put this solution on YOUR website!98 cents/10.5 = 9.33 cents/ounce.
 Rectangles/367571: a rectangle is three times as long as it is wide. its perimeter is 36. find each side1 solutions Answer 261989 by robertb(4012)   on 2010-11-08 00:27:50 (Show Source): You can put this solution on YOUR website!2(w + 3w) = 36, 2(4w) = 36, 8w = 36, w = 36/8 = 9/2, the width of the rectangle. l = 3w = 27/2, the length of the rectangle.
 Miscellaneous_Word_Problems/367507: If, in the ordered pair (a, b), a and b have different signs, then the point (a, b) is ________ in the second quadrant.1 solutions Answer 261988 by robertb(4012)   on 2010-11-08 00:18:30 (Show Source): You can put this solution on YOUR website!possibly
 Sequences-and-series/367543: The first three terms in the binomial expansion of (1+ kx)n are 1− 21x +189x2. Find the value of n and the value of k. Please show all the steps etc... I know the answer, but I don't understand the solution at all... thanks1 solutions Answer 261987 by robertb(4012)   on 2010-11-08 00:14:52 (Show Source): You can put this solution on YOUR website!The first three terms of the expression are . Hence nk = -21, and , after equating coefficients. The foregoing equation is the same as . Hence by substitution, , or , or 21k = -63, or k = -3. From nk = -21, n = 7.
 Exponents-negative-and-fractional/367540: (6x)^-21 solutions Answer 261986 by robertb(4012)   on 2010-11-08 00:02:05 (Show Source):
 Polynomials-and-rational-expressions/367516: which numbers cannot be used in place of the variable in the rational expression: 3x/x^2-491 solutions Answer 261984 by robertb(4012)   on 2010-11-08 00:00:46 (Show Source): You can put this solution on YOUR website!. So the numbers x = 7 or x = -7 cannot be used into the expression.
 Quadratic_Equations/367502: find the vertex, line of symmetry, and maximum/minimum value -2x^2+2x+3 I have tried everything and am completely lost, any help would be appreciated1 solutions Answer 261983 by robertb(4012)   on 2010-11-07 23:57:56 (Show Source): You can put this solution on YOUR website!The x-coordinate of the vertex is . The y-coordinate of the vertex is . The line of symmetry is x = 1/2, and the maximum value is 7/2.