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Mixture_Word_Problems/311236: how much pure alcohol must be added to 15 oz of a 60% solution of rubbing alcohol to change it to a 70% solution? 1 solutions Answer 222580 by mananth(12270)   on 2010-06-04 01:12:10 (Show Source): You can put this solution on YOUR website! let quantity of 100% alcohol required be x oz rubbing alcohol = 60% 15 oz Mixture 70% alcohol quantity = (x+15) oz add the concentrations of individual and equate it to total concentration . 1x+0.6*15 =0.7(x+15) x+9=0.7x +10.5 x-0.7x = 10.5-9 0.3x = 1.5 x=5 oz of pure alcohol

Trigonometry-basics/311234: ³√175/³√75 1 solutions Answer 222578 by mananth(12270)   on 2010-06-04 00:59:59 (Show Source): You can put this solution on YOUR website! cuberoot of 175 / cuberoot of 75 . cuberoot of (7/3)

Linear-systems/311160: The larger of two numbers is one more than twice the smaller. The sum of the numbers is twenty less than three times the larger. Find the numbers. 1 solutions Answer 222542 by mananth(12270)   on 2010-06-03 21:01:57 (Show Source): You can put this solution on YOUR website! let one number be x the other number be y . y=2x+1 y-2x=1 . x+y=3y-20 x-2y=-20 . 2(y-2x)+x-2y=2-20 2y-4x+x-2y=-18 -3x=-18 x= 6 y=2x+1 y=12+1 y=13 .

Linear-systems/311172: A group of students go out for lunch. If two have hamburgers and five have hot dogs, the bill will be $8.00. If five have hamburgers and two have hot dogs, the bill will be $9.50. What is the price of a hamburger? 1 solutions Answer 222541 by mananth(12270)   on 2010-06-03 20:52:27 (Show Source): You can put this solution on YOUR website! A group of students go out for lunch. If two have hamburgers and five have hot dogs, the bill will be $8.00. If five have hamburgers and two have hot dogs, the bill will be $9.50. What is the price of a hamburger? Let hamburgers cost $x each Let hot dogs cost $y each 2x+5y==8.00 5x+2y=9.50 . 5(2x+5y)-2(5x+2y)= 5*8 - 2*9.50 10x+25y-10x -4y = 40-19 21y=21 y=1 . plug value of y in any equation 2x+5*1 =8 2x=3 x=1.5 Hamburger cost is $ 1.5

Linear-systems/311078: Trains A & B are traveling in the same direction on parallel tracks. Tran A is traveling 80 miles per hour and Train B is traveling 90 miles per hour. Train A passes a station at 12:00am. If Train B passes the same station 12:40am, at what time will Train B catch up to Train A? When will Train B catch up with Train A? What is the time and if am or pm? Please help. Thank you. 1 solutions Answer 222540 by mananth(12270)   on 2010-06-03 20:45:38 (Show Source): You can put this solution on YOUR website! Train A speed = 80 mph Train B 90 mph Train A is ahead of train B at the station by 40 minutes.( 2/3 hours) By the time train B reaches the station train A has traveled 80 * 2/3 miles =160/3 miles to a point say P. Let the distance from point P to the point where train B overtakes train A be x . Train B travels 160/3 + x miles in the same time the train A travels x miles time taken by train A = x/80 hours time taken by train B = x+160/3 / 90 . x/80 = 3x+160 / 3 divided by 90 x/80 = 3x+160 /3 * 1/90 x/80= 3x+ 160 / 270 270x = 80(3x+160) 270x=240x +12800 30x= 12800 x=426.66 miles time taken by train A t travel x miles = 426.66/80 =5.33 hours. This is the same time taken by train B to cross train A

Angles/311080: the second angle of a triangle is 3 times as large as the first. the third angle is 25% more than the first. find the measure of the smallest angle? 1 solutions Answer 222505 by mananth(12270)   on 2010-06-03 17:09:54 (Show Source): You can put this solution on YOUR website! let the first angle be x the second angle will be 3x. \the third angle will be x+0.25x x+3x+1.25x= 180 deg 5.25x= 180 x=34.28 deg Check 34.28+(3*34.28)+(1.25*34.28)=179.97

Travel_Word_Problems/311048: If I drive 540 miles and drive and average of 80 miles per hour and I stop 2 times for 30 minutes how long will the trip take me? 1 solutions Answer 222502 by mananth(12270)   on 2010-06-03 17:03:17 (Show Source): You can put this solution on YOUR website! The time taken to travel 540 miles at 80 mph 540/80 = 6.75 hours. stops for 1 hour. so total time for trip = 7.75 hours

Miscellaneous_Word_Problems/310946: Can you please help me with this problem? I'm confused. A square light switch plate is made which measures 4 inches on each side. A square hole measuring 1 inch on each side is left in the center. If the cost to construct the plate is 2.75 per square inch, what is the construction cost? (use A=s^2) 1 solutions Answer 222391 by mananth(12270)   on 2010-06-03 09:40:49 (Show Source): You can put this solution on YOUR website! The area of the switch plate = area of square plate - the area of the square hole. Area of sq. plate = 4*4 = 16 sq. inches .. Area of square hole = 1*1=1 sq. in Area of plate = 16-1= 15 sq. in 1 sq. inch cost $2.75 15 sq. in costs 2.75 * 15 =41.25

Miscellaneous_Word_Problems/310947: Will you please help me with this problem? For a holiday party, Laura is making a seven layer torte, which consists of seven 8 inch diameter layers with a cream topping on each layer. She knows that one recipe of cream will cover 55 square inches of cake. How many batches of the topping must she make to complete her torte? ( use pi=3.14 as an approx. value) please show work. 1 solutions Answer 222387 by mananth(12270)   on 2010-06-03 09:35:38 (Show Source): You can put this solution on YOUR website! Area of topping = area of circle with diameter 8" Radius = 4" area = pi*r^2 pi^4^2 =pi*16 . 7 layers = 7*pi*16 = 351.85 sq. in . one recipe covers 55 sq in 351.85 sqin will require 351.85/55 = 6.39 = 7 batches

Exponential-and-logarithmic-functions/310896: solve the quadratic equation x^2+2x-4=0 I get 1 & -3 however, when i plug them into the equation i get -1 for both solutions. Is there no solution to this equation? 1 solutions Answer 222358 by mananth(12270)   on 2010-06-03 02:01:36 (Show Source): You can put this solution on YOUR website! x^2+2x-4=0 find the roots of the equation x1 , x2 x1 = -2 + sqrt ((2^2 - (-16)) /2 = -2 + sqrt20 /2 =1.23 . x2=-2 -sqrt ((2^2 - (-16)) /2 = -3.23

Polynomials-and-rational-expressions/310901: Multiplication problem to be solved 4x^2 * 4x^3 = ? 1 solutions Answer 222357 by mananth(12270)   on 2010-06-03 01:52:12 (Show Source): You can put this solution on YOUR website! 4x^2 * 4x^3 This is actually 4*x*x*4*x*x*x x is multiplied 5 times = x^5 4*4 = 16 Answer = 16 x^5 .. By following the indices rule you have to multiply the co-efficients and add the indices of the same terms = 16x^(2+3) 16^5

Surface-area/310904: Earth's radius is approximately 4000 mi. About two-thirds of Earth's surface is covered by water. Estimate the land area on Earth. 1 solutions Answer 222356 by mananth(12270)   on 2010-06-03 01:48:43 (Show Source): You can put this solution on YOUR website! Diameter = 4000 miles surface area of the earth = 4*pi*r^2 = 4*pi*2000^2 = 50 265 482.5 If 2/3 is water 1/3 will be land . 1/3 of this will be 1/3 *50265482 16 755 160 .8 square miles will be land area

Miscellaneous_Word_Problems/310558: Shanon and Piper are on the golf team. Shanon buys 10 cheap golf balls and 7 expensive ones for $31.75. Piper buys 8 cheap and 5 expensive balls for $23.75. Find the prices of the two kinds of golf balls. 1 solutions Answer 222076 by mananth(12270)   on 2010-06-02 00:59:01 (Show Source): You can put this solution on YOUR website! cheap ball be $x expensive ball be $y Shanon - cost equation 10x+7y= 31.75 Piper - cost equation 8x+5y= 23.75 8(10x+7y)-10(8x+5y)= 8*31.75 - 10*23.75 80x+56y-80x-50y=252-237.5 6y=14.5 y=2.42 Plug the value of in one equation 10x+7*2.42 =31.75 10x= 31.75-16.94 10x= 14.81 x=1.48 CHECK 10*1.48+7*2.42=31.74

Surface-area/310563: what is the length of the diagonal of a cube with a surface area of 24units squared? 1 solutions Answer 222074 by mananth(12270)   on 2010-06-02 00:42:12 (Show Source): You can put this solution on YOUR website! the surface area of cube = 24 Let side be x area of one face of cube = x^2 Total surface area = area of 6 faces =6x^2 6x^2=24 x^2=4 x=2 .. Use pythagoras theorem to find diagonal D 2^2 +2^2 = D62 8=D^2 d= sqrt 8

Miscellaneous_Word_Problems/310566: The first day at a baseball game you purchase 3 colas and 2 hotdogs worth $5.75. The next day you purchase 2 colas and 5 hotdogs worth $7.50. Find the cost of one cola and one hotdog. 1 solutions Answer 222073 by mananth(12270)   on 2010-06-02 00:28:41 (Show Source): You can put this solution on YOUR website! let the cost of cola be $x the cost of burger be $y First day 3x+2y= 5.75 Second day 2x+5y=7.50 . 2(3x+2y)-3(2x+5y)=2*5.75 - 3*7.50 6x+4y-6x-15y=11.50-22.50 -11y=-11 y= 1 y=$1.00 the cost of a burger Plug the value of y 3x+2=5.75 3x=3.75 x=$1.25 cost of a cola

Surface-area/310564: what is the length of the diagonal of a regular cube with a surface area of 54 units squared? 1 solutions Answer 222071 by mananth(12270)   on 2010-06-02 00:19:57 (Show Source): You can put this solution on YOUR website! surface area of cube = 54 let the side be x x^2 is the area of one face of the cube. there are 6 faces. 6x^2 = 54 x^2= 54/6 x^2=9 x=3 units apply pythagoras theorem to find the diagonal. 3^2 +3^2 = diagonal^2 9+9= diagonal ^2 diagonal = sqrt18

Numbers_Word_Problems/310514: in a child's coin bank, there is a collection of nickels, dimes, and quarters that amount to $3.20. There are 3 times as many quarters as nickels, and 5 more dimes that nickels. How many coins of each kind are there? Solution: Count of coins Let X = numbers of nickels 3x = the numbers of quarters x + 5 = the numbers of dimes Value of the count .05x = value of the quarters 0.25(3x) = value of the quarters 0.10(x + 5) = value of the dimes 1 solutions Answer 222021 by mananth(12270)   on 2010-06-01 20:56:40 (Show Source): You can put this solution on YOUR website! in a child's coin bank, there is a collection of nickels, dimes, and quarters that amount to $3.20. There are 3 times as many quarters as nickels, and 5 more dimes that nickels. How many coins of each kind are there? Solution: Count of coins . Let x = numbers of nickels 3x = the numbers of quarters x + 5 = the numbers of dimes Value of the count .05x = value of the quarters 0.25(3x) = value of the quarters 0.10(x + 5) = value of the dimes .. You are on the right track .. 0.05x+0.75x+0.1x+0.5 = 3.20 0.90x= 3.20-0.50 0.90x = 2.70 Multiply by 100 90x = 270 x= 3. the number of nickels 3x = 9 the number of quarters x+5 = 3+5 = 8 number of dimes CHECK 3*5 + 9*25+8*10 = 320 cents

Numbers_Word_Problems/310515: if the sum of two consecutive odd integers is divided by 4, the quotient is 10. find the numbers. 1 solutions Answer 222018 by mananth(12270)   on 2010-06-01 20:42:27 (Show Source): You can put this solution on YOUR website! Let the consequtive odd numbers be x & x-2 x+x-2 / 4 = 10 2x-2 = 40 2x=40+2 2x=42 x=21 the other number = 19. Check 19+21 / 4 = 10

Travel_Word_Problems/310506: Transport a and transport b left the loading dock at noon and headed in opposite directions. If transport a traveled at 60mph and transport b traveled at 68mph, how many hours was it before they were 348 miles apart? I need an equation for this kind of problem. Thank you so much! 1 solutions Answer 222017 by mananth(12270)   on 2010-06-01 20:39:44 (Show Source): You can put this solution on YOUR website! Transport A speed = 60mph. Transport B speed = 68 mph . Assume they travel x hours when they are 348 miles away. Distance traveled by transport A = 60x Distance traveled by transport B = 68x 60x+68x=348 128x=348 x= 348/128 x= 2.7 hours After 2.7 hours they will be 348 miles away

Numbers_Word_Problems/310512: if the sum of two consecutive integers is divided by 3, the quotient is 9. find the numbers 1 solutions Answer 222016 by mananth(12270)   on 2010-06-01 20:32:31 (Show Source): You can put this solution on YOUR website! let one number be x the other number will be x+1 . x+x+1 / 3= 9 2x+1=9*3 2x=27-1 2x=26 x=13 the numbers are 13 and 14

Linear_Equations_And_Systems_Word_Problems/310466: 1)Ivana invested her savings of $4800. SHe invested part in a mutual fund, which paid her 9% interest per year, and the rest went into a GIC, which paid her 10% per year. After one year, the interest she earned from the mutual fund was $43 less than the interest she earned from the GIC. How much did Hailey invest into each? 1 solutions Answer 222013 by mananth(12270)   on 2010-06-01 20:29:57 (Show Source): You can put this solution on YOUR website! Let her invest $ x in Mutual funds & $y in GIC x+y= 4800 . Interest on mutual fund = 9% Interest accrued = 0.09x . Interest on GIC is 10% Interest accrued = 0.1y . 0.09x=0.1y -43 0.09x -0.1y =-43 ( multiply by 100) . 9x -10y=-4300 10x+10y+9x-10y = 48000-4300 19x=43700 x= $2300 the amount she invested in Mutual fund. y=$2500 in GIC

Numbers_Word_Problems/310477: They gave away ¼ of what they had to friends and still had 11,462 left. How many did they start with? 1 solutions Answer 221977 by mananth(12270)   on 2010-06-01 19:36:03 (Show Source): You can put this solution on YOUR website! let them have x They gave away 1/4th = x/4 . x-x/4 =11462 4x-x / 4 = 11462 3x= 45848 x=45848/3 They had about 15,282

Miscellaneous_Word_Problems/310467: The speed of the current in the Yankaton River is 3 kilometers per hour. If a boat travels 18 kilometers downstream in this river and then returns to its starting point all in 4 1/2 hours, what is the rate of the boat in still water? 1 solutions Answer 221973 by mananth(12270)   on 2010-06-01 19:31:19 (Show Source): You can put this solution on YOUR website! the speed of the boat in still water be x km/hr. Downstream the speed will be x+3 km/hr. Distance traveled is 18 km. So time taken = 18/x+3 -- Upstream the speed of the boat is x-3 mph. Distance is 18km. Time 18 / x-3 . Add up the two . 18/x+3 + 18/x-3 = 9/2 hours 18(x-3)+18(x+3)= 9/2(x^2-9) 18x-54+1854 = 9x^2-81 / 2 2(36x)= 9x^2-81 72x=9x^2-81 9x^2-72x-81=0 ( divide by 9) x^2-8x-9=0 x^2-9x+x-9=0 x(x-9)+1(x-9)=0 (x+1)(x-9)=0 x= -1 Or x=9 Speed cannot be negative so boat speed in still water = 9 km/hr

Miscellaneous_Word_Problems/310469: Two pumps operating together can fill a cistern in 4 hours. If one of the pumps working alone can fill the cistern in 6 hours, how long would it take the other pump working alone? 1 solutions Answer 221967 by mananth(12270)   on 2010-06-01 19:11:16 (Show Source): You can put this solution on YOUR website! Let filling the cistern be = 1 job. Both pumps can do the job in 4 hours. So they can do 1/4 of the job in 1 hour. . one pump does the job in 6 hours . So it does 1/6th. of the job in 1 hour. . Job done by both - job done by one of them = job done by the other in 1 hour. . 1/4 - 1/6 =3-2 / 12 =1/12. The other pump does 1/12th job in 1 hour. . So it takes 12 hours to do the complete job of filing the cistern alone.

Geometry_proofs/310458: Given: Parallelogram ABCD is inscribed in a circle Prove: ABCD is a rectangle I was thinking to start out saying that since parallelograms have congruent opposite sides, then the congruent chords would have congruent arcs, but then I got stuck. Could you please help me? I need this answer ASAP. 1 solutions Answer 221966 by mananth(12270)   on 2010-06-01 19:07:05 (Show Source): You can put this solution on YOUR website! Solution: LBAC= LBCD( opposite angles of a parallelogram are equal) . LBAC + LBCD = 180° ( opp. angles of a cyclic quadrilateral are supplementary) . LBAC=LBCD= 90° . Similarly LABC=LADC=90° . ABCD is a rectangle ( all the angles are =90°) L stands for angle

Volume/310287: Find the surface area of a cylindrical water tank that is 6 meters tall and has has a diameter of 8 meters. 1 solutions Answer 221860 by mananth(12270)   on 2010-06-01 07:35:49 (Show Source): You can put this solution on YOUR website! Surface arae of a cylinder = 2*pi*r*h r= 4 meters height = 6 meters . 2*pi*4*6 =48pi square meters OR 150.8 sq. m

Volume/310288: Calculate the surface-area-to-volume ratio of a cube 3 inches on each side. 1 solutions Answer 221859 by mananth(12270)   on 2010-06-01 07:32:34 (Show Source): You can put this solution on YOUR website! surface area of a cube = 6x^2 where x is the side Volume of cube = x^3 where x is the side surface area = 6*9=54 Volume = 3*3*3= 27 Ratio = 54/27 =2

Geometry_Word_Problems/310291: The perimeter of a rectangle, given that the length is x yards and the width is 10 yards shorter 1 solutions Answer 221858 by mananth(12270)   on 2010-06-01 07:28:27 (Show Source): You can put this solution on YOUR website! LENGTH = X YARDS WIDTH = X-10 YARDS PERIMETER = 2X + 2(X-10) = 4X-10 YARDS

Length-and-distance/310200: A piece of rope 36 feet long is to be cut into two piecies so that one piece is 1/3 as long as the other piece. How many feet long will the shorter piece be? 1 solutions Answer 221835 by mananth(12270)   on 2010-05-31 20:54:52 (Show Source): You can put this solution on YOUR website! Rope length = 36 feet ratio of small to long piece = 1/3 There are 4 parts. 1/4 * 36 is one part = 9 feet the other is 3/4 * 36 = 27 feet . 27-9 = 18 feet is the difference.

Rectangles/310194: the perimeter of a rectangle is 65 inches. The ratio of the lenth to the width is 4:1. what is the lenth and width The perimeter is 24, the ratio is 2:1, what is the lenth and width 1 solutions Answer 221833 by mananth(12270)   on 2010-05-31 20:43:14 (Show Source): You can put this solution on YOUR website! The perimeter = 65 inches 1/2 perimeter = 32.5 inches x/y = 4:1 x=4y x+y =32.5 Plug the value of x in the equation. 4y+y= 32.5 5y= 32.5 y=6.5 So x = 4*6.5 = 26 The dimensions ar 6.5 by 26 Check 26+26+6.5+6.5= 65

Rational-functions/310172: Subtract: 1 solutions Answer 221827 by mananth(12270)   on 2010-05-31 19:43:08 (Show Source): You can put this solution on YOUR website! 3/x+5 - 4/x+1 3(x+1)-4(x+5) / (x+1)(x+5) 3x+3 -4x-20 / (x+1)(x+5) -x-17 /(x+1)(x+5) -(x+17) /(x+1)(x+5)