Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

# 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

 Probability-and-statistics/401617: If you have a six-sided dice and you roll that dice 90 times, what is the expected probability your dice will land on a 2 and a 3?1 solutions Answer 284214 by robertb(4012)   on 2011-01-29 23:35:56 (Show Source): You can put this solution on YOUR website!1)die = singular, dice = plural 2) The probability that a die, thrown once, will show 2 AND 3 is 0. The probability that a die, thrown once, will show 2 OR 3 is 2/6, or 1/3. Thus the expected number of times a 2 or a 3 will show is (1/3)*90 =30 times.
 Polynomials-and-rational-expressions/401615: solve and write in interval notation: -3/2 < 4-2m < 7/21 solutions Answer 284207 by robertb(4012)   on 2011-01-29 23:09:56 (Show Source): You can put this solution on YOUR website!-3/2 - 4 < -2m < 7/2 - 4 ==> -11/2 < -2m < -1/2 ==> 11/4 > m > 1/4, or (1/4, 11/4) in interval notation.
 Graphs/401356: My 14 year old son has Asperger Syndrome and, up until this year, has always excelled in math, scoring very high in California Achievement Tests and working above grade level. I home school my children and have used various math programs, looking for the best fit (I have several on the autism spectrum and another with ADHD). My son is having a horrible time with Algebra 1 (which many children on the spectrum do) and I am hoping for any advice you can give. We have tried Kinetic textbooks, but it was not a good fit. We are now using Math U See, which seems to work, but he is still struggling...we are working on slope/standard formula and graphing at the moment. I would appreciate any advice you could give on teaching Algebra to someone who is a very concrete thinker so that I can get him through this. Thank you!1 solutions Answer 284062 by robertb(4012)   on 2011-01-29 07:24:24 (Show Source): You can put this solution on YOUR website!Sir/Madam, The basis of all graphing exercises, from the simplest (plotting points) to the the most complicated (e.g., algebraic geometry), is an appreciation of the basic Cartesian coordinate system. Give your son lots of exercises on plotting random points on the Cartesian system. Then ask him if he can form geometrical objects, any geometrical object, by connecting dots (points) on the coordinate system. After doing this for some time (probably after having had enough of this simple exercise), introduce order and structure by illustrating how to form a straight line using two points (, ) and (, ). Always keep in mind the position of the line with respect to the origin (0,0), and whether the line falls or rises from left to right. Don't be discouraged if he doesn't get it right away: for many people it takes time to understand the most basic of mathematical concepts (which might actually include me.) =)
 Geometry_proofs/401390: Prove that 2TanA/1+Tan^2A=Sin2A1 solutions Answer 284058 by robertb(4012)   on 2011-01-29 06:45:31 (Show Source):
 Inequalities/401391: Hi! Could you solve this inequalitiy and show me the steps please? Thank you!1 solutions Answer 284057 by robertb(4012)   on 2011-01-29 06:36:11 (Show Source): You can put this solution on YOUR website! <==> <==> ==> The critical numbers of the inequality are 0 and 3. At the interval (, 0), . At the interval (0,3), . At the interval (3, ), . The critical numbers 0 and 3 don't satisfy the inequality. Therefore the solution set is (, 0)U(3, ).
 Probability-and-statistics/401386: Twelve dice are cast. What is the probability that each of the six faces will appear at least once?1 solutions Answer 284056 by robertb(4012)   on 2011-01-29 05:50:23 (Show Source):
 Trigonometry-basics/400656: an equilateral triangle has side lengths of 8. what is the lenght of its altitude1 solutions Answer 284043 by robertb(4012)   on 2011-01-29 03:26:49 (Show Source):
 Probability-and-statistics/400727: There are 9 marbles in a bag. Some are red, some are white, and some are blue. The probability of selecting a red marble, a white marble, and then a blue marble is 1/21. How many of each color are in the bag?1 solutions Answer 284042 by robertb(4012)   on 2011-01-29 03:21:36 (Show Source): You can put this solution on YOUR website!Without replacement: ==> rwb = 24 = 2*3*4. Since r+w+b = 9, there 6 possibilities for the ordered triple(r,w,b): (2,3,4) (2,4,3) (3,2,4) (3,4,2) (4,3,2) (4,2,3) With replacement: ==> , which is impossible, because r,w, b are positive integers satisfying r+ w + b = 9
 Probability-and-statistics/400649: A committee of 12 students must select from their group a president, a vice-president, and a secretary. In how many possible ways can this be accomplished? 1 solutions Answer 284041 by robertb(4012)   on 2011-01-29 03:07:28 (Show Source): You can put this solution on YOUR website!12*11*10 = 1,320 ways
 Linear-systems/400641: line 1: y= -1/4(x) -1 line 2: x+4y=-4 Is this system of the equation a) consistent independent b) consistnt dependent c) inconsistent This means the system has a) a unique solution (_ , _) b) infinitly many solutions c) no solutions'1 solutions Answer 284040 by robertb(4012)   on 2011-01-29 03:04:31 (Show Source): You can put this solution on YOUR website!Consistent dependent, meaning infinitely many solutions.
 Linear_Algebra/400630: let{u1,u2....uk}be a linearly independent set of vector in R^n and c1,c2,....ck are scalars. prove that {c1u1, c2u2....., ckuk}is also limearly independent.1 solutions Answer 284039 by robertb(4012)   on 2011-01-29 02:58:21 (Show Source): You can put this solution on YOUR website!Since { ,, , ..., } are linearly independent, then the equation + ...+ has only the trivial solution = ...= . (is the zero vector, and 's are scalars.) We have to assume that none of the 's are equal to zero, otherwise, { ,, , ..., } would contain the zero vector, automatically making the set linearly dependent. Hence + ...+ ==> for every n = 1,2,3,...,k, and { ,, , ..., } is a linearly independent set.
 Trigonometry-basics/400604: u=2i-5j,v=-3i+7j and w=-i-6j find each specified vector or scalar 4w-3v1 solutions Answer 284036 by robertb(4012)   on 2011-01-29 02:30:40 (Show Source): You can put this solution on YOUR website!4w - 3v = 4(-i-6j) - 3(-3i + 7j) = -4i - 24j + 9i - 21j = 5i - 45j
 Travel_Word_Problems/401299: Find the length of the diagonal and the area of a square with perimeter equal to 1.2√2 inches.1 solutions Answer 284022 by robertb(4012)   on 2011-01-28 23:40:04 (Show Source): You can put this solution on YOUR website!Area = square inch. Diagonal = inch.
 Probability-and-statistics/401312: What is the critical value for the following Chi- square test? A manufacturer has 4 locations and is looking to see if shipments with defects are dependent on the manufacturer location. The defects are categorized in two rows (with defects and no defects). The researcher is testing using a 95% confidence level. Write the null and alternative hypothesis for the scenario. 1 solutions Answer 284020 by robertb(4012)   on 2011-01-28 23:32:40 (Show Source): You can put this solution on YOUR website!: Defects are independent of manufacturer location : Defects are associated with manufacturer location p = 0.05, with degrees of freedom = df = (2 - 1)(4 - 1) = 3. Critical value is 7.82.
 Inequalities/401358: How would I solve and graph the compound inequality. Thank you 7x+4≥-24 or 7x+1≥-131 solutions Answer 284017 by robertb(4012)   on 2011-01-28 23:24:52 (Show Source): You can put this solution on YOUR website! <==> <==> ==> {x: }U {x:} = {x:}
 Miscellaneous_Word_Problems/401346: Pablo's gas tank is 1/2 full. After he buys 7 gallons of gas, it is 5/6 full. How many gallons can Pablo's tank hold? 1 solutions Answer 284014 by robertb(4012)   on 2011-01-28 23:05:29 (Show Source): You can put this solution on YOUR website! ==> ==> x = 21, the total number of gallons Pablo's tank can hold.
 Miscellaneous_Word_Problems/401294: Rob can complete his bus route in 4 hours. Joan can complete her route in 2 hours. If they both leave the terminal at 5:00 am and after each completed route return to the terminal, when is the next time they both leave the terminal at the same time?1 solutions Answer 284013 by robertb(4012)   on 2011-01-28 22:57:20 (Show Source): You can put this solution on YOUR website!9:00 am.
 Equations/401144: Angle A is acute and such that tanA=√6/3. (a) Show clearly that the exact value of sin A can be written in the form 1/5√k and state the value of k. (b) Hence, or otherwise, show that the value of cos2A is exactly 1/51 solutions Answer 284011 by robertb(4012)   on 2011-01-28 22:45:32 (Show Source): You can put this solution on YOUR website!(a) ==> . (b)
 Polynomials-and-rational-expressions/401340: factor completly u^3-125v^31 solutions Answer 284008 by robertb(4012)   on 2011-01-28 22:34:10 (Show Source):
 Inequalities/401339: 5[3m-(m+6)]>-6(m-5) I need to use set-builder notations to describe the complete solution.{m/m__ __} Thanks for the help!1 solutions Answer 284003 by robertb(4012)   on 2011-01-28 22:31:22 (Show Source): You can put this solution on YOUR website!15m - 5(m+6) > -6m + 30, 15m - 5m - 30 > -6m + 30, 10m - 30 > -6m + 30, 16m > 60, m > 60/16 = 15/4, or {m| m > 15/4}.
 Equations/401136: Express the function f(x)=5cos(2x)°-3sin(2x)° in the form f(x)=kcos(2x-α)°, where k>0 and 0≤α≤3601 solutions Answer 284002 by robertb(4012)   on 2011-01-28 22:27:20 (Show Source): You can put this solution on YOUR website! Let and , where is in the 4th quadrant. Then
 Radicals/401298: Find (if it exists) each function value of f(t)=the square root of t^2+1 and so f(-6)=?1 solutions Answer 284001 by robertb(4012)   on 2011-01-28 22:19:46 (Show Source): You can put this solution on YOUR website!If the function is , then f(-6) exists, and is equal to .
 Equations/401332: solve the equation 1/(x+3) - 1/(x+4) = 1/21 solutions Answer 283999 by robertb(4012)   on 2011-01-28 22:12:40 (Show Source): You can put this solution on YOUR website! ==> ==> ==> <==> 0 = (x + 2)(x+ 5) ==> x = -2, -5. Both values will never make the denominator 0, so they are the final answers.
 Quadratic_Equations/401141: During the first part of a trip a canoeist travels 48 miles at a certain speed. The canoeist travels 19 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 3 hours. What was the speed on each part of the trip?1 solutions Answer 283995 by robertb(4012)   on 2011-01-28 22:00:53 (Show Source): You can put this solution on YOUR website!Let r = speed at the 1st part of trip ==> time for 1st part = 48/r ==> r - 5 = speed at 2nd part of trip ==> time for 2nd part = 19/(r-5). both from the formula t = d/r = distance/rate. Then <==> 48(r-5) + 19r = 3r(r-5) <==> <==> <==> (r - 24)(3r - 10) = 0 ==> r = 24, 10/3 Eliminate r = 10/3, because it would make r - 5 negative. Hence the speed in the 1st part is 24 mph, and the speed in the 2nd part is 19 mph.
 Functions/400822: what is the domain of √ ̅ (x-3) divided by x^2-8x+12?1 solutions Answer 283732 by robertb(4012)   on 2011-01-27 21:02:41 (Show Source): You can put this solution on YOUR website!If your rational function is , then the domain is obtained as follows: From the expression , the critical numbers are 2, 3, and 6. These critical numbers partition the real number line into the intervals (, 2), (2, 3), (3, 6), (6, ). At (, 2), by using the test point x = 0. At (2, 3), by using the test point x = 2.5. At (3, 6), by using the test point x = 4. At (6, ), by using the test point x = 7. The critical numbers 2 and 6 are not included in the domain, as these will make the denominator equal to 0. We want those intervals that will make , because the whole expression is under the square root symbol. The critical number x = 3 is included in the domain. Hence the domain of the rational function is (2,3]U(6, ).
 Trigonometry-basics/400480: Given the following values, the value of c is ________. b = 4.5 ft a = 10 ft C = 1051 solutions Answer 283497 by robertb(4012)   on 2011-01-27 00:43:39 (Show Source): You can put this solution on YOUR website!Cosine Law: ==> ==> ==> c = 11.981, to 3 decimal places.
 Graphs/400494: What is a slope of a line?1 solutions Answer 283488 by robertb(4012)   on 2011-01-27 00:21:37 (Show Source): You can put this solution on YOUR website!Measure of steepness of a line = Rise/Run = for two points (,) and (,) on the line.
 Linear-equations/400510: Find the equation of the line passing through (-3, 4) and parallel to 2x + 5y = 12.1 solutions Answer 283487 by robertb(4012)   on 2011-01-27 00:17:13 (Show Source): You can put this solution on YOUR website!The line must have the equation 2x + 5y = c. To find c, use the coordinates of the point (-3,4): 2*-3 + 5*4 = -6 + 20 = 14 Therefore the equation of the line is 2x + 5y = 14.
 Trigonometry-basics/400477: Given the following values, how many triangles are there? a = 16 b = 18 A = 60 1 solutions Answer 283477 by robertb(4012)   on 2011-01-26 22:40:47 (Show Source): You can put this solution on YOUR website!2 triangles are possible. From the sine law, , we get to 5 decimal places. ==> 58'36" 1st possibility: A = B = 58'36" C = 1'24" 2nd possibility: A = B = - 58'36" = 1'24" C = 58'36" Just get the sides using several applications of the sine law.
 Miscellaneous_Word_Problems/400475: speed is 20mph leave at 10:20am how for will you have gone by 5:00 pm1 solutions Answer 283473 by robertb(4012)   on 2011-01-26 22:27:09 (Show Source): You can put this solution on YOUR website! miles.
 Percentage-and-ratio-word-problems/400342: The percent of pure gold in 14-karat gold is about 58.3%. A 14- karat gold ring has a mass of 5.6 grams. About how many grams of pure gold are in the ring?1 solutions Answer 283470 by robertb(4012)   on 2011-01-26 22:23:54 (Show Source): You can put this solution on YOUR website!5.6*0.583 =3.2648 grams of pure gold.