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# Recent problems solved by 'nerdybill'

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 Geometry_Word_Problems/316116: Rachel ran 3375 feet.how many feet less than 0.75 mile is this?1 solutions Answer 226125 by nerdybill(7008)   on 2010-06-21 00:57:59 (Show Source): You can put this solution on YOUR website! Rachel ran 3375 feet.how many feet less than 0.75 mile is this? . Since there are 5280 feet in a mile: .75(5280) = 3960 feet . 3960-3375 = 585 feet
 Probability-and-statistics/316100: Tim was ranked 50th in a class of 250. What was his percentile rank?1 solutions Answer 226124 by nerdybill(7008)   on 2010-06-21 00:55:29 (Show Source): You can put this solution on YOUR website!Tim was ranked 50th in a class of 250. What was his percentile rank? . (250-50)/250 * 100 = 200/250 *100 = .8 *100 = 80%
 Mixture_Word_Problems/316114: a pharmacist has 20 L of a 10% drug solution. How many liters of 5% solution must be added to get a mixture that is 8% ? 1 solutions Answer 226123 by nerdybill(7008)   on 2010-06-21 00:52:33 (Show Source): You can put this solution on YOUR website!a pharmacist has 20 L of a 10% drug solution. How many liters of 5% solution must be added to get a mixture that is 8% ? . Let x= liters of 5% solution added then .05x + .10(20) = .08(20+x) .05x + 2 = 1.6+.08x 2 = 1.6+.08x .4 = .08x 5 liters = x
 Travel_Word_Problems/316087: Viral can do a piece of work in 10 days & Raja in 15days. If both of them work together how long will it take to finish the work? a) 6days b) 5days c) 7days d) 8days1 solutions Answer 226121 by nerdybill(7008)   on 2010-06-21 00:48:07 (Show Source): You can put this solution on YOUR website!Viral can do a piece of work in 10 days & Raja in 15days. If both of them work together how long will it take to finish the work? a) 6days b) 5days c) 7days d) 8days . Let x = time it takes for both then x(1/10 + 1/15) = 1 x(15 + 10) = 150 x(25) = 150 x = 6 days
 logarithm/316093: 1. Solve log(6x+5)=0 2. use natural logarithms to solve this equation. Round to the nearest thousandeth. 6e^4x-6=15 3.e^x=3/4 1 solutions Answer 226119 by nerdybill(7008)   on 2010-06-21 00:38:28 (Show Source): You can put this solution on YOUR website!1. Solve log(6x+5)=0 6x+5 = 10^0 6x+5 = 1 6x = -4 x = -4/6 x = -2/3 . 2. use natural logarithms to solve this equation. Round to the nearest thousandeth. 6e^4x-6=15 6e^4x=21 e^(4x)^6=21 (4x)^6 = ln(21) 4x = (ln(21))^(1/6) x = ((ln(21))^(1/6))/4 x = 0.301 . 3.e^x=3/4 x = ln(3/4) x = -0.288
 percentage/316040: Brett a football player made 18 field goals out of 22 attempted field goals. To the nearest whole percent,what persent of the field goals were successful?1 solutions Answer 226075 by nerdybill(7008)   on 2010-06-20 20:06:10 (Show Source): You can put this solution on YOUR website!18/22 * 100 = 0.818*100 = 81.8% rounded to nearest percent: 82%
 Mixture_Word_Problems/316001: twenty pounds of salt-water solution contains fifteen percent salt. How much water must be added to weaken the solution to twelve percent salt?1 solutions Answer 226073 by nerdybill(7008)   on 2010-06-20 19:56:20 (Show Source): You can put this solution on YOUR website! twenty pounds of salt-water solution contains fifteen percent salt. How much water must be added to weaken the solution to twelve percent salt? . Let x = pounds of water to add then .15(20) = .12(20+x) 3 = 2.4 + .12x .6 = .12x .6/.12 = x 5 pounds = x
 Square-cubic-other-roots/315970: in a right triangle, find the length of the sides when a is unknown, b=1 and c=square root 261 solutions Answer 226009 by nerdybill(7008)   on 2010-06-20 15:28:09 (Show Source): You can put this solution on YOUR website!in a right triangle, find the length of the sides when a is unknown, b=1 and c=square root 26 . For any "right triangle", you can apply Pythagorean theorem: .
 Miscellaneous_Word_Problems/315935: filling a tank through a large tube takes 30 minutes. It takes 50 minutes for the tank to fully drain through a smaller tube. how long will it take to fill the tank if both tubes are open1 solutions Answer 226003 by nerdybill(7008)   on 2010-06-20 13:17:55 (Show Source): You can put this solution on YOUR website! filling a tank through a large tube takes 30 minutes. It takes 50 minutes for the tank to fully drain through a smaller tube. how long will it take to fill the tank if both tubes are open . Let x = time it takes to fill tank when both tubes are open then x(1/30 - 1/50) = 1 Multiplying both sides by 1500: x(50 - 30) = 1500 x(20) = 1500 x = 75 minutes
 Polynomials-and-rational-expressions/315936: 2x^2+4x=01 solutions Answer 226002 by nerdybill(7008)   on 2010-06-20 13:15:26 (Show Source): You can put this solution on YOUR website! 2x^2+4x=0 Factor what is common between the two terms first: (2x)(x+2)=0 . Setting each term to zero: x = {0, -2}
 Rational-functions/315903: Find the point of intersection of the two lines: 3x-4y=2 -2x+y=1 Thanks in advance1 solutions Answer 225996 by nerdybill(7008)   on 2010-06-20 10:45:42 (Show Source): You can put this solution on YOUR website!. The point of intersection is simply the solution to: 3x-4y=2 -2x+y=1 Solve by the addition method. Multiply the bottom equation by 4 and add: 3x-4y=2 -8x+4y=4 ----------- -5x = 6 x = -6/5 . Plug above into second equation and solve for y: -2x+y=1 -2(-6/5)+y=1 12/5+y=1 y = 1-12/5 y = 5/5-12/5 y = -7/5 . Point of intersection: (-6/5, -7/5)
 logarithm/315786: log (base x)0.05 = -1/21 solutions Answer 225966 by nerdybill(7008)   on 2010-06-20 00:56:05 (Show Source):
 logarithm/315738: Express as a single logarithm, and, if possible, simplify. logb 5x + 7(logb x - logb y) 1 solutions Answer 225901 by nerdybill(7008)   on 2010-06-19 14:35:54 (Show Source):
 Polynomials-and-rational-expressions/315759: List all numbers for which the rational expression is undefined x^2-4/x^2-8x+15 1 solutions Answer 225900 by nerdybill(7008)   on 2010-06-19 14:31:54 (Show Source): You can put this solution on YOUR website!Undefined if the denominator is zero so we set x^2-8x+15 to zero and solve for x . x^2-8x+15 = 0 (x-5)(x+3) = 0 x = {-3, 5}
 expressions/315755: Please help me to evaluate: a+(b-a)^2, for a=1 and b=2. My answer is 3, but it's answer is 2? Thanks in advance 1 solutions Answer 225899 by nerdybill(7008)   on 2010-06-19 14:30:19 (Show Source): You can put this solution on YOUR website!a+(b-a)^2, for a=1 and b=2 . Plugging in the values: 1+(2-1)^2 1+(1)^2 1+1 2
 Probability-and-statistics/315729: In a box of 14 clocks, it is known that three clocks are defective. Two clocks are selected at random without replacement. Find the probability that both clocks are defective. 1 solutions Answer 225882 by nerdybill(7008)   on 2010-06-19 11:19:01 (Show Source): You can put this solution on YOUR website!In a box of 14 clocks, it is known that three clocks are defective. Two clocks are selected at random without replacement. Find the probability that both clocks are defective. . 3/14 * 2/13 = 6/182 = .033
 Percentage-and-ratio-word-problems/315708: Gwen bought a new Toyota Corolla. The selling price plus the 8% state sales tax was \$15,714. What was the selling price?1 solutions Answer 225881 by nerdybill(7008)   on 2010-06-19 11:15:50 (Show Source): You can put this solution on YOUR website!The selling price plus the 8% state sales tax was \$15,714. What was the selling price? . Let P = selling price then P + .08P = 15714 P(1+.08) = 15714 P(1.08) = 15714 P = 15714/1.08 P = \$14,550
 Finance/315681: a college paid \$1748 for 46 calculators. They paid \$9 for each scientific calculator. all other graphing calculators cost \$55 each how many of each calculator was ordered 1 solutions Answer 225863 by nerdybill(7008)   on 2010-06-19 02:14:44 (Show Source): You can put this solution on YOUR website! a college paid \$1748 for 46 calculators. They paid \$9 for each scientific calculator. all other graphing calculators cost \$55 each how many of each calculator was ordered . Let x = number of scientific calculators then 46-x = number of graphing calculators . 9x + 55(46-x) = 1748 9x + 2530 - 55x = 1748 2530 - 46x = 1748 -46x = -782 x = 17 (number of scientific calculators) . graphing calculators: 46-x = 46-17 = 29
 logarithm/315585: logarithm using the change-of-base formula. Round to the nearest ten-thousandth. log8.1 5.61 solutions Answer 225836 by nerdybill(7008)   on 2010-06-18 21:47:48 (Show Source): You can put this solution on YOUR website!I'll assume you mean: Applying change of base we get: = =
 logarithm/315415: Solve: ln(2x+3)=31 solutions Answer 225700 by nerdybill(7008)   on 2010-06-18 01:49:44 (Show Source): You can put this solution on YOUR website!ln(2x+3)=3 2x+3 = e^3 2x = e^3-3 x = (e^3-3)/2 x = 8.543
 Age_Word_Problems/315294: Gabrielle is 15 years younger than Mikhail. The sum of their ages is 81 . What is Mikhail's age? 1 solutions Answer 225610 by nerdybill(7008)   on 2010-06-17 17:08:50 (Show Source): You can put this solution on YOUR website!Gabrielle is 15 years younger than Mikhail. The sum of their ages is 81 . What is Mikhail's age? . Let x = Mikhail's age then x-15 = Gabrielle's age . x + x-15 = 81 2x-15 = 81 2x = 96 x = 48 years old
 Rate-of-work-word-problems/315312: Two college students have started their own business building computers from kits. Working alone, one student can build a computer in 20 hours. When the second student helps, they can build a computer in 7.5 hours. How long would it take the second student, working alone, to build the computer.1 solutions Answer 225609 by nerdybill(7008)   on 2010-06-17 17:07:12 (Show Source): You can put this solution on YOUR website!Two college students have started their own business building computers from kits. Working alone, one student can build a computer in 20 hours. When the second student helps, they can build a computer in 7.5 hours. How long would it take the second student, working alone, to build the computer. . Let x = time it takes second student to build it alone then 7.5(1/20 + 1/x) = 1 Multiplying both sides by 20x: 7.5(x + 20) = 20x 7.5x + 150 = 20x 150 = 12.5x 12 hours = x
 Travel_Word_Problems/315309: a student took 18 minutes to walk from home to school.given that his average speed is 4km/h,how far he had to travel 1 solutions Answer 225605 by nerdybill(7008)   on 2010-06-17 17:04:23 (Show Source): You can put this solution on YOUR website!a student took 18 minutes to walk from home to school.given that his average speed is 4km/h,how far he had to travel . Apply the distance formula: d = rt . However, begin by changing the 18 minutes into hours: 18min * 1hr/60min = 18/60 = 3/10 hour . distance = 3/10 * 4 distance = 3/5 * 2 distance = 6/5 km or distance is 1.2 km
 Angles/315281: The measure of an angle is 20 less than 3 times its supplement. Find the measure of the angle1 solutions Answer 225604 by nerdybill(7008)   on 2010-06-17 17:01:11 (Show Source): You can put this solution on YOUR website!The measure of an angle is 20 less than 3 times its supplement. Find the measure of the angle . Let x = the angle then 180-x = the supplement . x = 3(180-x) - 20 x = 540-3x-20 x = 520-3x 4x = 520 x = 130 degrees
 logarithm/315283: find the logarith using the change-of-base formula. logn 15001 solutions Answer 225567 by nerdybill(7008)   on 2010-06-17 15:57:28 (Show Source): You can put this solution on YOUR website!That would be log(1500)/log(n)
 logarithm/315262: evaluate the logarithm. 1. log (base 7) 1/49 write the expression as a single logarithm 2. 5log (base b)q+3 log(base b)w 3. 4 log x-6 log (x+2) 4. solve 4^2x=1111 solutions Answer 225542 by nerdybill(7008)   on 2010-06-17 14:40:02 (Show Source): You can put this solution on YOUR website!1. log (base 7) 1/49 write the expression as a single logarithm 2. 5log (base b)q+3 log(base b)w 3. 4 log x-6 log (x+2) 4. solve 4^2x=111
 Quadratic_Equations/315258: A sandbag falls out of a hot air balloon that is 144 feet above the ground how long does it take for the sandbag to reach the ground?1 solutions Answer 225538 by nerdybill(7008)   on 2010-06-17 14:23:47 (Show Source): You can put this solution on YOUR website!h(t) = -(1/2)32t^2 + Vt + Ho where h(t) is height t is time V is initial velocity (0) Ho is initial height (144) . 0 = -(1/2)32t^2 + 0t + 144 0 = -16t^2 + 144 -144 = -16t^2 9 = t^2 3 sec = t
 Exponents/315228: How do you solve problems like this? 324=4(3^n-1) thank you1 solutions Answer 225519 by nerdybill(7008)   on 2010-06-17 12:33:21 (Show Source): You can put this solution on YOUR website!I'm assuming the (n-1) is the exponent -- if not, please write back. .
 logarithm/315214: solve. where appropriate, include approximations to the nearest thousandth. if no solution exists, state this 5^x = 1251 solutions Answer 225510 by nerdybill(7008)   on 2010-06-17 11:55:10 (Show Source): You can put this solution on YOUR website!5^x = 125 x = x = x =3
 logarithm/315212: solve. where appropriate, include approximations to the nearest thousandth. if no solution exists, state this In 8x=51 solutions Answer 225507 by nerdybill(7008)   on 2010-06-17 11:53:50 (Show Source): You can put this solution on YOUR website!ln 8x=5 8x = e^5 x = e^5/8 x = 18.55
 Human-and-algebraic-language/315205: Jim is able to sell a hand-carved statue for \$670 which was a 35% profit over his cost. How much did the statue originally cost him? 1 solutions Answer 225506 by nerdybill(7008)   on 2010-06-17 11:51:59 (Show Source): You can put this solution on YOUR website!Jim is able to sell a hand-carved statue for \$670 which was a 35% profit over his cost. How much did the statue originally cost him? . Let x = original cost then x + .35x = 670 x(1 + .35) = 670 1.35x = 670 x = 670/1.35 x = \$496.30