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 'venugopalramana'

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, >>Next

 Triangles/48583: HELP i have two triangles ans the order from the bottom left corner is A the point is B and the right corner C inbetween the B AND C line there is the number 18 and between A AND C there is an x the other one is a triangle same order but D E AND F between E AND F There is a 12 and between D AND F there is a 6 . . WHAT DO THEY WANT?? the directions say triangle ABC~ triangle DEF and solve for x1 solutions Answer 32168 by venugopalramana(3286)   on 2006-08-09 09:36:12 (Show Source): You can put this solution on YOUR website!HELP i have two triangles ans the order from the bottom left corner is A the point is B and the right corner C inbetween the B AND C line there is the number 18 and between A AND C there is an x the other one is a triangle same order but D E AND F between E AND F There is a 12 and between D AND F there is a 6 . . WHAT DO THEY WANT?? the directions say triangle ABC~ triangle DEF and solve for x THIS MEANS BC=18......AC=X.........EF=12.......DF=6 TRIANGLE ABC IS SIMILAR TO TRIANGLE DEF... THEN AB/DE=BC/EF=CA/FD..HENCE.. 18/12=X/6 12X=6*18 X=18*6/12=9
 Quadratic_Equations/48343: complete the square, and find the roots of the quadratic equation. x^2 + 16x = 0 1 solutions Answer 31993 by venugopalramana(3286)   on 2006-08-07 12:18:23 (Show Source): You can put this solution on YOUR website!complete the square, and find the roots of the quadratic equation. x2 + 16x = 0 X^2+2*X*8+8^2-8^2=0 (X+8)^2=8^2 X+8=+8...........OT..-8 X=0........OR........-16
 Quadratic_Equations/48344: apply the quadratic formula to find the roots of the given function, and then graph the function. f(x) = x2 - 41 solutions Answer 31992 by venugopalramana(3286)   on 2006-08-07 12:16:48 (Show Source): You can put this solution on YOUR website!apply the quadratic formula to find the roots of the given function, and then graph the function. f(x) = x2 - 4=0 X=2..OR...-2 X.....0.......1......2.......3........4.....ETC Y.....-4......-3.....0.......5........12
 Quadratic_Equations/48346: use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Note: It is not necessary to find the roots; just determine the number and types of solutions. x2 + 6x - 7 = 0 z2 + z + 1 = 0 (3)1/2y2 - 4y - 7(3)1/2 = 0 2x2 - 10x + 25 = 0 2x2 - 6x + 5 = 01 solutions Answer 31988 by venugopalramana(3286)   on 2006-08-07 12:12:30 (Show Source): You can put this solution on YOUR website!use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Note: It is not necessary to find the roots; just determine the number and types of solutions. x2 + 6x - 7 = 0 DEL=6^2-4*1*(-7)=36+28=64..2 SOLUTIONS,REAL z2 + z + 1 = 0 DEL=1-4=-3..-VE........IMAGINARY SOLUTION ..2 (3)1/2y2 - 4y - 7(3)1/2 = 0...????PLEASE TYPE PROPERLY 2x2 - 10x + 25 = 0 DEL=100-4*2*25=-VE......IMAGINARY..2 2x2 - 6x + 5 = 0 DEL=36-40=-VE...IMAGINARY..2
 Problems-with-consecutive-odd-even-integers/48351: The product of two consecutive positive even integers is 360. Find the integers. Thanks1 solutions Answer 31985 by venugopalramana(3286)   on 2006-08-07 12:08:08 (Show Source): You can put this solution on YOUR website!The product of two consecutive positive even integers is 360. Find the integers. LET ANY EVEN INTEGER=2N...NEXT EVEN INTEGER =2N+2 2N(2N+2)=360 N(N+1)=90 N^2+N-90=0 (N+10)(N-9)=0 N=9 THE 2 EVEN INTEGERS ARE 2*9=18 AND 20
 Linear-equations/48350: Write the equation of the line that passes through point (6,4) with a slope of 2 Thanks1 solutions Answer 31984 by venugopalramana(3286)   on 2006-08-07 12:05:23 (Show Source): You can put this solution on YOUR website!Write the equation of the line that passes through point (6,4) =(X1,Y1)with a slope of 2 =M Y-Y1=M(X-X1) Y-4=2(X-6) Y=2X-8
 Linear_Equations_And_Systems_Word_Problems/48347: Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle. 1 solutions Answer 31981 by venugopalramana(3286)   on 2006-08-07 12:03:46 (Show Source): You can put this solution on YOUR website!Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle. let his speed be =x mph speed at 10 mph faster=x+10 mph time to go 200 miles 1.at normal speed =200/x at faster speed =200/(x+10) difference = 200[(1/x)-1/(x+10)]=200(x+10-x)/x(x+10)=1 2000=x^2+10x x^2+10x-2000=0 (x+50)(x-40)=0 x=40 mph x=
 Linear_Equations_And_Systems_Word_Problems/48348: The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water?1 solutions Answer 31979 by venugopalramana(3286)   on 2006-08-07 11:58:20 (Show Source): You can put this solution on YOUR website!The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water? let the boat speed in still water =b speed of water be =3 speed up river =b-3..time to travel 60 miles=60/(b-3) speed down river =b+3..time to travel down river=60/(b+3) total time =60[{1/(b+3)}+{1/(b-3)}]=9 60*(b+3+b-3)=9(b+3)(b-3) 40b=3(b^2-9)=3b^2-27 3b^2-40b-27=0 b=13.978 mph
 real-numbers/48319: In ratios, how would you represent the following: 4 minutes to 1 hour and 125 hits to 500 times at bat1 solutions Answer 31977 by venugopalramana(3286)   on 2006-08-07 11:49:27 (Show Source): You can put this solution on YOUR website!In ratios, how would you represent the following: 4 minutes to 1 hour in general as a rule ratios are dimensionless.so if n.r is in minutes d.r should also be in minutes..hence=4 mts/1 hr=4mts/60 mts=1/15 and 125 hits to 500 times at bat =125/500=1/4..ratios are usually simplified to get smallest possible integers in n.r.and d.r.
 Miscellaneous_Word_Problems/48330: A solar collector is 2.5m long by 2.0m wide. It is held in place by a frame of uniform width around its outside edge. If the exposed collector area is 2.5m^2 , what is the width of the frame, to the nearest tenth of a centimeter?1 solutions Answer 31976 by venugopalramana(3286)   on 2006-08-07 11:45:24 (Show Source): You can put this solution on YOUR website!A solar collector is 2.5m long by 2.0m wide. It is held in place by a frame of uniform width around its outside edge. If the exposed collector area is 2.5m^2 , what is the width of the frame, to the nearest tenth of a centimeter? let the width of frame = x length of frame=x+2.5+x=2.5+2x width of frame =x+2+x=2x+2 area of frame & reflector assembly=(2x+2.5)(2x+2)=4x^2+9x+5 area of collector=2.5*2=5 exposed area =4x^2+9x+5-5=2.5 4x^2+9x-2.5=0 8x^2+18x-5=0 x={-18+sqrt(18^2+4*5*8)}/16=1/4 metre=100/4 cm = 25 cm.
 Quadratic-relations-and-conic-sections/48302: This question is from textbook College Algebra I need help, I can't seem to grasp this concept. The question is.. identify the center, vertices, foci, and equations of the asymptotes of the hyperbola: 25y^2 - 9x^2 - 100y - 54x - 206 = 0. If you can help it would be greatly appreciated. Thank you lots. 1 solutions Answer 31949 by venugopalramana(3286)   on 2006-08-07 00:57:56 (Show Source): You can put this solution on YOUR website!I need help, I can't seem to grasp this concept. The question is.. identify the center, vertices, foci, and equations of the asymptotes of the hyperbola: 25y^2 - 9x^2 - 100y - 54x - 206 = 0. If you can help it would be greatly appreciated. ---------------------------------------------------------------------------------- FIRST COMPLETE SQUARES 25(Y^2-4y)-9(X^2+6X)-206=0 25{Y^2-2*Y*2+2^2-2^2}-9{X^2+2*X*3+3^2-3^2}-206=0 25(Y-2)^2-100-9(X+3)^2+81-206=0 -9(X+3)^2+25(Y-2)^2=-81+100+206=225 -[{(X+3)^2}/(225/9)]+[{(Y-2)^2}/(225/25)]=1 [(Y-2)^2/5^2]-[(X+3)^2/3^2]=1 NOW SEE THE FOLLOWING AND YOU SHOULD BE ABLE TO SOLVE YOUR PROBLEM BY YOUR SELF.. Quadratic-relations-and-conic-sections/28184: What is the vertices, foci, and slope of the asymptotes for the hyperbola whose equation is, y^2/16 - x^2/25 =25? 1 solutions Answer 15970 by venugopalramana(1088) About Me on 2006-03-04 03:12:07 (Show Source): SEE THE FOLLOWING AND YOU SHOULD BE ABLE TO SOLVE YOUR PROBLEM BY YOUR SELF..... THE ANSWERS FOR YOUR CASE...H=0...K=0..A=4...B=5....EQN IS OF THE TYPE (Y-K)^2/B^2-(X-H)^2/A^2=1.... SO VERTICES ARE...(H,(K-B)) AND (H,(K+B)) ...(0,-5) AND (0,5) FOCI ARE {H,(K-BE)} AND {H,(K+BE)}...WHERE E IS ECCENTRICITY =SQRT{(A^2+B^2)/B^2}=SQRT((16+25)/25)=SQRT(41/25) SO FOCI ARE =(0,-5SQRT(41/25) AND (0,5SQRT(41/25)... OR....(0,-SQRT(41)) AND (0,SQRT(41) ASYMPTOTES ARE GIVEN BY Y^2/16-X^2/25=K 25Y^2-16X^2-400K=0 (5Y+4X+A)(5Y-4X+B)=0 SLOPES OF ASYMPTOTES ARE -4/5 AND 4/5 THE GRAPHS LOOK LIKE THIS
 Equations/48288: Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. 1 solutions Answer 31948 by venugopalramana(3286)   on 2006-08-07 00:34:35 (Show Source): You can put this solution on YOUR website!Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. 9k^2+6k+1=0 discr.=(6)^2-4*9*1=36-36=0....perfect square...equal roots ....equal to ...-6/2*9=-6/18=-1/3 hence.....9k^2+6k+1=(3k+1)^2
 Equations/48289: Find the imaginary solutions of the equation. 1 solutions Answer 31947 by venugopalramana(3286)   on 2006-08-06 23:29:34 (Show Source): You can put this solution on YOUR website!Find the imaginary solutions of the equation. 5x^2+3x+6=0 discriminant=3^2-4*5*6=9-120=-111 x=[{-3+i(sq.rt(111)}/10] or x=[{-3-i(sq.rt(111)}/10]
 Triangles/47823: Hi i have a question concerning similar triangles: A six foot man is standing 10 feet away from a 20 foot lamppost. What is the lenght of his shadow? i tried to work it out and thought maybe i should use a proportion 20/10 X 6/a ----= 3 ft thats what i got is that the correct answer? if not can you show me what is ? thanks!1 solutions Answer 31642 by venugopalramana(3286)   on 2006-08-01 12:30:56 (Show Source): You can put this solution on YOUR website!Hi i have a question concerning similar triangles: A six foot man is standing 10 feet away from a 20 foot lamppost. What is the lenght of his shadow? i tried to work it out and thought maybe i should use a proportion 20/10 X 6/a ----= 3 ft LET AB BE THE LAMP POST WITH A ON GROUND AND B AT THE TOP. LET CD BE THE MAN WITH C...FEET ON GROUND AND D ..HEAD LET THE SHADOW BE CE. WE HAVE 2 SIMILAR TRIANGLES.ABE AND CDE. AB/CD=AE/CE=(AC+CE)/CE=(10+CE)/CE=1+10/CE WE ARE GIVEN AB=20...CD=6.......AC=10 20/6=1+10/CE 10/CE=20/6 -1 =14/6=7/3 CE=3*10/7=30/7=SHADOW=4.285 FEET thats what i got is that the correct answer? if not can you show me what is ? thanks!
 Radicals/47824: Show that each equattion is true by simplifying the following: a.) b.) can someone PLEASE help me with this? any help will be appreciated!!!1 solutions Answer 31641 by venugopalramana(3286)   on 2006-08-01 12:22:17 (Show Source): You can put this solution on YOUR website!Show that each equattion is true by simplifying the following: USE A^-B^2=(A+B)(A-B)...RATIONALISE THE IRRATIONAL N.R....OR...D.R BY MULTIPLYING WITH CONJUGATE FACTOR. a.) 1/(sqrt(x)+sqrt(y)) = (sqrt(x)-sqrt(y))/(x-y) MULTIPLY N.R AND D.R WITH {SQRT(X)-SQRT(Y)} {SQRT(X)-SQRT(Y)}/[{SQRT(X)}^2-{SQRT(Y)}^2]=(sqrt(x)-sqrt(y))/(x-y) b.) (sqrt(x+h)- sqrt(x))/h = 1/(sqrt(x+h)+sqrt(x)) SAME WAY AS ABOVE ..MULTIPLY N.R AND D.R WITH (sqrt(x+h)+ sqrt(x))
 Quadratic-relations-and-conic-sections/47825: Find the x & y intercepts of: a.) b.) can someone show me the process of how to find the x & y intercepts for the above?? thank you for any of your help!!:-)1 solutions Answer 31640 by venugopalramana(3286)   on 2006-08-01 12:17:46 (Show Source): You can put this solution on YOUR website!Find the x & y intercepts of: a.) (x^2)/4 -(y^2)/9 = 1 PUT Y=0 AND FIND X TO GET X INTERCEPTS X^2/=1....X=+2..AND...-2...ARE THE 2 X INTERCEPTS. PUT X=0 AND FIND Y TO GET X INTERCEPTS Y^2/9=-1 Y^2=-9 Y IS IMAGINARY...HENCE THERE ARE NO Y INTERCEPTS. b.) x^2+y^2 = 9 PUT Y=0 X=+3...AND -3 ARE THE X INTERCEPTS PUT X=0 Y=+3...AND...-3 ARE THE Y INTERCEPTS.
 Rectangles/47837: Geometry. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle? Thanks!1 solutions Answer 31639 by venugopalramana(3286)   on 2006-08-01 12:13:05 (Show Source): You can put this solution on YOUR website!The length of a rectangle is 1 cm longer than its width. LET WIDTH =W LENGTH=W+1 If the diagonal of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle? DIAGONAL^2=L^2+W^2 4^2=(W+1)^2+W^2 W^2+2W+1+W^2=16 2W^2+2W-15=0 =2.28 W=2.28 AND L=3.28 Thank You!
 Graphs/47835: Find the x intercept y = x^2 - 5x + 3 Thank You1 solutions Answer 31638 by venugopalramana(3286)   on 2006-08-01 12:11:44 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING EXAMPLE AND TRY.IF STILL IN DIFFICULTY PLEASE COME BACK ---------------------- Y INTERCEPT IS DETERMINED BY THE POINTS WHERE THE CURVE INTERSECTS X AXIS.HENCE THIS IS OBTAINED BY EQUATING THE EQN. TO ZERO AND FINDING VALUES OF X SATISFYING THE EQN. What is the y-intercept of the function, y=f(x)=2x^2+4x-6?=0 x^2+2x-3=0 x^2+3x-x-3=0 x(x+3)-1(x+3)=0 (x+3)(x-1)=0 x=-3 and x=1 ARE THE 2 Y INTERCEPTS. -------------------- i need help with this quadratic using the formula.. i did the work and my answer came out to be irrational is this true? a=3x^2+ b=8x+ c=2 3x^2+8x+2=0 yes you are correct.the roots are irrational
 Graphs/47836: Find the x intercept -x^2 + 6x - 2 Thanks! 1 solutions Answer 31637 by venugopalramana(3286)   on 2006-08-01 12:11:00 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING EXAMPLE AND TRY.IF STILL IN DIFFICULTY PLEASE COME BACK ---------------------- Y INTERCEPT IS DETERMINED BY THE POINTS WHERE THE CURVE INTERSECTS X AXIS.HENCE THIS IS OBTAINED BY EQUATING THE EQN. TO ZERO AND FINDING VALUES OF X SATISFYING THE EQN. What is the y-intercept of the function, y=f(x)=2x^2+4x-6?=0 x^2+2x-3=0 x^2+3x-x-3=0 x(x+3)-1(x+3)=0 (x+3)(x-1)=0 x=-3 and x=1 ARE THE 2 Y INTERCEPTS. -------------------- i need help with this quadratic using the formula.. i did the work and my answer came out to be irrational is this true? a=3x^2+ b=8x+ c=2 3x^2+8x+2=0 yes you are correct.the roots are irrational
 Coordinate-system/47827: Find the equations for the horizontal and vertical asypmtotes of each function: a.) b.) c.) 1 solutions Answer 31636 by venugopalramana(3286)   on 2006-08-01 12:06:05 (Show Source): You can put this solution on YOUR website!Find the equations for the horizontal and vertical asypmtotes of each function: a.) y=1/(x-1).........D.R=0 WHEN X-1=0..AND... X=1 IS THE ASYMPTOTE b.) y=x/(sqrt(x^2-9))...D.R=0 WHEN X^2=9...OR...X=3..AND..X=-3 ARE THE 2 ASYMPTOTES. FURTHER AS X TENDS TO ZERO Y TENDS TO ZERO.....Y=0 IS ANOTHER ASYMPTOTE c.) y=x^3/(x^3-1)...D.R=0 WHEN X^3-1=0...OR...X=1..IS THE ASYMPTOTE FURTHER AS X TENDS TO ZERO Y TENDS TO ZERO....Y=0 IS ANOTHER ASYMPTOTE.
 Sequences-and-series/47828: Can somebody show me how to solve this. Evaluate the factorial expression 100!/98! 2! Thanks!1 solutions Answer 31635 by venugopalramana(3286)   on 2006-08-01 11:51:41 (Show Source): You can put this solution on YOUR website!Evaluate the factorial expression 100!/98! 2! 100!=[100*99*{98*97*96*.........*3*2*1}] 98!=98*97*96*.........*3*2*1 HENCE 100!/98!=100*99....AS 98,97,96,......3,2,1 CANCEL EACH OTHER IN FACT WE CAN WRITE 100!=100*99*98! SO WE GET 100!/98!2! = 100*99/2*1=50*99=4950
 Geometry_Word_Problems/47831: What is the y-intercept of the function, f(x)=2x^2+4x-6?1 solutions Answer 31634 by venugopalramana(3286)   on 2006-08-01 11:47:32 (Show Source): You can put this solution on YOUR website!Y INTERCEPT IS DETERMINED BY THE POINTS WHERE THE CURVE INTERSECTS X AXIS.HENCE THIS IS OBTAINED BY EQUATING THE EQN. TO ZERO AND FINDING VALUES OF X SATISFYING THE EQN. What is the y-intercept of the function, y=f(x)=2x^2+4x-6?=0 x^2+2x-3=0 x^2+3x-x-3=0 x(x+3)-1(x+3)=0 (x+3)(x-1)=0 x=-3 and x=1 ARE THE 2 Y INTERCEPTS.
 Quadratic-relations-and-conic-sections/47800: find the asymptotes: f (x)=2 --- x squared -9 i hope that equation made sense it should be right on top of eachother but i cant seem to do that. thanks for your help1 solutions Answer 31633 by venugopalramana(3286)   on 2006-08-01 11:42:27 (Show Source): You can put this solution on YOUR website!find the asymptotes: f (x)=2 --- x squared -9 i hope that equation made sense it should be right on top of eachother but i cant seem to do that. thanks for your help y=2/(x^2-9)=2/(x+3)(x-3) hence y tends to infinity as x+3 tends to zero or x tends to -3 and also as x-3 tends to zero...that is x tends to 3. hence the asymptotes are x=-3 and x=3
 Linear_Equations_And_Systems_Word_Problems/47820: a motorboat travels 60 kms upstream in 10 hrs if it returns in 8 hrs. . Find th rate of the current and the boat rates are constant during the trip.1 solutions Answer 31629 by venugopalramana(3286)   on 2006-08-01 09:21:20 (Show Source): You can put this solution on YOUR website!a motorboat travels 60 kms upstream in 10 hrs if it returns in 8 hrs. . Find th rate of the current and the boat rates are constant during the trip. LET SPEED OF BOAT IN STILL WATER=B SPEED OF WATER=W UP STREAM SPEED =B-W T=10 HRS....D=60 KM 10(B-W)=60 B-W=6................I DOWN STREAM SPEED = B+W T=8 HRS.....D=60 KM 8(B+W)=60 B+W=60/8=7.5.................II EQN.I+EQN.II 2B=13.5 B=6.75 KMPH W=7.5-6.75=0.75 KMPH
 expressions/47821: For what values of x is the following expression undefined: (3x - 2)(5x - 4) ________________ (9x - 6)(7x - 1)1 solutions Answer 31628 by venugopalramana(3286)   on 2006-08-01 09:16:25 (Show Source): You can put this solution on YOUR website!For what values of x is the following expression undefined: (3x - 2)(5x - 4) ________________ (9x - 6)(7x - 1) IT IS UNDEFINED WHEN DENOMINATOR IS ZERO 9X-6=0...OR...X=6/9=2/3...AND 7X-1=0....OR...X=1/7
 Probability-and-statistics/47810: 1. From a box containing 6 red bulbs, 8 yellow bulbs and blue bulbs, two bulbs is drawn. Dteremine the probability that the first is a red and the second is yellow. 2. Five girls and 3 boys are to be seated in a row. If seats are taken randomly, waht is the probability that the girls will be seated together? 3. A box of 15 batteries contains defectives, what is the probability that out of the 3 baterries selected without replacement, two is not defective? 4. A box contains 5 white and 3 green marbles. A second box contains 4 white and 6 green marbles. Suppose that a marble is drawn from the first box and placed unseen in the second box. What is the probability that a marble now drawn from the second box is green? 1 solutions Answer 31627 by venugopalramana(3286)   on 2006-08-01 08:59:14 (Show Source): You can put this solution on YOUR website! 1. From a box containing 6 red bulbs, 8 yellow bulbs and (??????HOW MANY )blue bulbs, two bulbs is drawn. Dteremine the probability that the first is a red and the second is yellow. 2. Five girls and 3 boys are to be seated in a row. If seats are taken randomly, waht is the probability that the girls will be seated together? TOTAL NUMBER OF POSSIBILITIES TO SEAT 8 PERSONS=8! FOR THE 3 GIRLS TO BE SEATED TOGETHER,CONSIDER 3 GIRLS TOGETHER AS ONE UNIT..THEN TOTAL =5+1=6 THEY CAN BE SEATED IN 6! WAYS HENCE P=6!/8!=1/(8*7)=1/56 3. A box of 15 batteries contains( ?????HOW MANY ??)defectives, what is the probability that out of the 3 baterries selected without replacement, two is not defective? 4. A box contains 5 white and 3 green marbles. A second box contains 4 white and 6 green marbles. Suppose that a marble is drawn from the first box and placed unseen in the second box. What is the probability that a marble now drawn from the second box is green? CASE 1....LET A GREEN MARBLE BE DRAWN FROM BOX 1 ITS PROBABILITY = 3/8 NOW WHEN IT IS PUT IN THE SECOND BOX THERE ARE 4 WHITE AND 7 GREEN MARBLES P OF DRAWING GREEN MARBLE = 7/11 SO COMBINED PROBABILITY = (3/8)(7/11)=21/88 CASE 2......LET A WHITE MARBLE BE PICKED UP FROM BOX 1 ITS PROBABILITY = 5/8 NOW WHEN IT IS PUT IN THE SECOND BOX THERE ARE 5 WHITE AND 6 GREEN MARBLES P OF DRAWING GREEN MARBLE = 6/11 SO COMBINED PROBABILITY = (5/8)(6/11)=30/88 HENCE P OF EITHER HAPPENING = 21/88 + 30/88 = 51/88 You may edit the question. Maybe convert formulae
 Travel_Word_Problems/47811: This question is from textbook travelling at the full speed against the current of a river a motorboat moves at the rate of 12 kilometers per hour relative to the land.Travelling at a half speed with the current,it moves at 8 kilometers per hour. Find the maximum speed of the boat in still water. 1 solutions Answer 31617 by venugopalramana(3286)   on 2006-08-01 06:24:14 (Show Source): You can put this solution on YOUR website! travelling at the full speed against the current of a river a motorboat moves at the rate of 12 kilometers per hour relative to the land.Travelling at a half speed with the current,it moves at 8 kilometers per hour. Find the maximum speed of the boat in still water. FULL SPEED OF BOAT IN STILL WATER =B SPEED OF CURRENT OF WATER =W SPEED OF BOAT AT FULL SPEED AGAINST CURRENT =B-W=12..............I HALF SPEED OF BOAT IN STILL WATER =B/2=0.5B SPEED OF BOAT AT HALF SPEED WITH THE CURRENT = 0.5B+W=8..............II EQN.I+EQN.II 1.5B=20 B=20/1.5=13.333
 Rational-functions/47813: Given f(x)=3x+1 and g(x)=1/2, what is the domain of f,g & fog1 solutions Answer 31616 by venugopalramana(3286)   on 2006-08-01 06:12:13 (Show Source): You can put this solution on YOUR website!Given f(x)=3x+1 and g(x)=1/2, what is the domain of f,g & fog DOMAIN OF F(X) IS ALL REAL NUMBERS DOMAIN OF G(X) IS ALL REAL NUMBERS FOG=3*1/2+1=2.5 ITS DOMAIN IS ALL REAL NUMBERS
 Linear-systems/47817: The sum of the digits of a 2 digit no. is 9, when the digits are reversed the new no. is 27 more than the original no. Find the no. 1 solutions Answer 31615 by venugopalramana(3286)   on 2006-08-01 06:07:31 (Show Source): You can put this solution on YOUR website!The sum of the digits of a 2 digit no. is 9, when the digits are reversed the new no. is 27 more than the original no. Find the no. LET XY BE THE NUMBER...SUM OF DIGITS =X+Y=9.....................I ITS VALUE =10X+Y WHEN DIGITS ARE REVERSED WE GET YX...ITS VALUE = 10Y+X DIFFERENCE BETWEEN THE 2 NUMBERS =27=10Y+X-10X-Y=9Y-9X=9(Y-X) Y-X=3.............II EQN.I+EQN.II.... 2Y=9+3=12 Y=12/2=6 X=9-Y=9-6=3 THE NUMBER IS 36
 Linear-systems/47818: SUBSTITUTION METHOD 3X - 3Y = 2 EQUATION 1 X + 2 = 3Y EQUATION 2 1 solutions Answer 31614 by venugopalramana(3286)   on 2006-08-01 06:02:14 (Show Source): You can put this solution on YOUR website! SUBSTITUTION METHOD 3X - 3Y = 2 EQUATION 1 X + 2 = 3Y EQUATION 2 X=3Y-2 PUT IN EQN.I 3(3Y-2)-3Y=2 9Y-6-3Y=2 6Y=6+2=8 Y=8/6=4/3 X=3*(4/3)-2=4-2=2
 Quadratic_Equations/47789: i need help with this quadratic using the formula.. i did the work and my answer came out to be irrational is this true? a=3x^2+ b=8x+ c=21 solutions Answer 31613 by venugopalramana(3286)   on 2006-08-01 05:57:27 (Show Source): You can put this solution on YOUR website!i need help with this quadratic using the formula.. i did the work and my answer came out to be irrational is this true? a=3x^2+ b=8x+ c=2 3x^2+8x+2=0 yes you are correct.the roots are irrational