Tutor:

New! Get regular updates about newly solved problems via algebra.com's RSS system.

---

Recent problems solved by 'ankor@dixie-net.com'

ankor@dixie-net.com answered: 15632 problems
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 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 4740..4769 , 4770..4799 , 4800..4829 , 4830..4859 , 4860..4889 , 4890..4919 , 4920..4949 , 4950..4979 , 4980..5009 , 5010..5039 , 5040..5069 , 5070..5099 , 5100..5129 , 5130..5159 , 5160..5189 , 5190..5219 , 5220..5249 , 5250..5279 , 5280..5309 , 5310..5339 , 5340..5369 , 5370..5399 , 5400..5429 , 5430..5459 , 5460..5489 , 5490..5519 , 5520..5549 , 5550..5579 , 5580..5609 , 5610..5639 , 5640..5669 , 5670..5699 , 5700..5729 , 5730..5759 , 5760..5789 , 5790..5819 , 5820..5849 , 5850..5879 , 5880..5909 , 5910..5939 , 5940..5969 , 5970..5999 , 6000..6029 , 6030..6059 , 6060..6089 , 6090..6119 , 6120..6149 , 6150..6179 , 6180..6209 , 6210..6239 , 6240..6269 , 6270..6299 , 6300..6329 , 6330..6359 , 6360..6389 , 6390..6419 , 6420..6449 , 6450..6479 , 6480..6509 , 6510..6539 , 6540..6569 , 6570..6599 , 6600..6629 , 6630..6659 , 6660..6689 , 6690..6719 , 6720..6749 , 6750..6779 , 6780..6809 , 6810..6839 , 6840..6869 , 6870..6899 , 6900..6929 , 6930..6959 , 6960..6989 , 6990..7019 , 7020..7049 , 7050..7079 , 7080..7109 , 7110..7139 , 7140..7169 , 7170..7199 , 7200..7229 , 7230..7259 , 7260..7289 , 7290..7319 , 7320..7349 , 7350..7379 , 7380..7409 , 7410..7439 , 7440..7469 , 7470..7499 , 7500..7529 , 7530..7559 , 7560..7589 , 7590..7619 , 7620..7649 , 7650..7679 , 7680..7709 , 7710..7739 , 7740..7769 , 7770..7799 , 7800..7829 , 7830..7859 , 7860..7889 , 7890..7919 , 7920..7949 , 7950..7979 , 7980..8009 , 8010..8039 , 8040..8069 , 8070..8099 , 8100..8129 , 8130..8159 , 8160..8189 , 8190..8219 , 8220..8249 , 8250..8279 , 8280..8309 , 8310..8339 , 8340..8369 , 8370..8399 , 8400..8429 , 8430..8459 , 8460..8489 , 8490..8519 , 8520..8549 , 8550..8579 , 8580..8609 , 8610..8639 , 8640..8669 , 8670..8699 , 8700..8729 , 8730..8759 , 8760..8789 , 8790..8819 , 8820..8849 , 8850..8879 , 8880..8909 , 8910..8939 , 8940..8969 , 8970..8999 , 9000..9029 , 9030..9059 , 9060..9089 , 9090..9119 , 9120..9149 , 9150..9179 , 9180..9209 , 9210..9239 , 9240..9269 , 9270..9299 , 9300..9329 , 9330..9359 , 9360..9389 , 9390..9419 , 9420..9449 , 9450..9479 , 9480..9509 , 9510..9539 , 9540..9569 , 9570..9599 , 9600..9629 , 9630..9659 , 9660..9689 , 9690..9719 , 9720..9749 , 9750..9779 , 9780..9809 , 9810..9839 , 9840..9869 , 9870..9899 , 9900..9929 , 9930..9959 , 9960..9989 , 9990..10019 , 10020..10049 , 10050..10079 , 10080..10109 , 10110..10139 , 10140..10169 , 10170..10199 , 10200..10229 , 10230..10259 , 10260..10289 , 10290..10319 , 10320..10349 , 10350..10379 , 10380..10409 , 10410..10439 , 10440..10469 , 10470..10499 , 10500..10529 , 10530..10559 , 10560..10589 , 10590..10619 , 10620..10649 , 10650..10679 , 10680..10709 , 10710..10739 , 10740..10769 , 10770..10799 , 10800..10829 , 10830..10859 , 10860..10889 , 10890..10919 , 10920..10949 , 10950..10979 , 10980..11009 , 11010..11039 , 11040..11069 , 11070..11099 , 11100..11129 , 11130..11159 , 11160..11189 , 11190..11219 , 11220..11249 , 11250..11279 , 11280..11309 , 11310..11339 , 11340..11369 , 11370..11399 , 11400..11429 , 11430..11459 , 11460..11489 , 11490..11519 , 11520..11549 , 11550..11579 , 11580..11609 , 11610..11639 , 11640..11669 , 11670..11699 , 11700..11729 , 11730..11759 , 11760..11789 , 11790..11819 , 11820..11849 , 11850..11879 , 11880..11909 , 11910..11939 , 11940..11969 , 11970..11999 , 12000..12029 , 12030..12059 , 12060..12089 , 12090..12119 , 12120..12149 , 12150..12179 , 12180..12209 , 12210..12239 , 12240..12269 , 12270..12299 , 12300..12329 , 12330..12359 , 12360..12389 , 12390..12419 , 12420..12449 , 12450..12479 , 12480..12509 , 12510..12539 , 12540..12569 , 12570..12599 , 12600..12629 , 12630..12659 , 12660..12689 , 12690..12719 , 12720..12749 , 12750..12779 , 12780..12809 , 12810..12839 , 12840..12869 , 12870..12899 , 12900..12929 , 12930..12959 , 12960..12989 , 12990..13019 , 13020..13049 , 13050..13079 , 13080..13109 , 13110..13139 , 13140..13169 , 13170..13199 , 13200..13229 , 13230..13259 , 13260..13289 , 13290..13319 , 13320..13349 , 13350..13379 , 13380..13409 , 13410..13439 , 13440..13469 , 13470..13499 , 13500..13529 , 13530..13559 , 13560..13589 , 13590..13619 , 13620..13649 , 13650..13679 , 13680..13709 , 13710..13739 , 13740..13769 , 13770..13799 , 13800..13829 , 13830..13859 , 13860..13889 , 13890..13919 , 13920..13949 , 13950..13979 , 13980..14009 , 14010..14039 , 14040..14069 , 14070..14099 , 14100..14129 , 14130..14159 , 14160..14189 , 14190..14219 , 14220..14249 , 14250..14279 , 14280..14309 , 14310..14339 , 14340..14369 , 14370..14399 , 14400..14429 , 14430..14459 , 14460..14489 , 14490..14519 , 14520..14549 , 14550..14579 , 14580..14609 , 14610..14639 , 14640..14669 , 14670..14699 , 14700..14729 , 14730..14759 , 14760..14789 , 14790..14819 , 14820..14849 , 14850..14879 , 14880..14909 , 14910..14939 , 14940..14969 , 14970..14999 , 15000..15029 , 15030..15059 , 15060..15089 , 15090..15119 , 15120..15149 , 15150..15179 , 15180..15209 , 15210..15239 , 15240..15269 , 15270..15299 , 15300..15329 , 15330..15359 , 15360..15389 , 15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629 , 15630..15659, >>Next

Expressions-with-variables/271729: When 6 gallons of gasoline are put in your car’s tank, the indicator goes from ¼ of a tank to 5/8 of a tank. Find the total capacity of the gasoline tank. 1 solutions Answer 198933 by ankor@dixie-net.com(15647)   on 2010-02-19 16:30:30 (Show Source): You can put this solution on YOUR website! When 6 gallons of gasoline are put in your car’s tank, the indicator goes from ¼ of a tank to 5/8 of a tank. Find the total capacity of the gasoline tank. : Let x = tank capacity x - x = 6 : x - x = 6 : x = 6 : Multiply both sides by 8 3x = 8(6) 3x = 48 x = x = 16 gal tank : : Check solution in original equaltion (16) - (16) = 10 - 4 = 6

Trigonometry-basics/271794: A wheel with a 38- inch radius is marked at two points on the rim. The distance between the marks along the wheel is found to be inches. What is the angle (to the nearest tenth of a degree) between the radii to the two marks? 1 solutions Answer 198932 by ankor@dixie-net.com(15647)   on 2010-02-19 16:21:24 (Show Source): You can put this solution on YOUR website! How many inches?

Percentage-and-ratio-word-problems/271570: When 5 new girls joined a class, the percent of girls increased from 40% to 50%. What is the number of boys in the class 1 solutions Answer 198927 by ankor@dixie-net.com(15647)   on 2010-02-19 15:36:37 (Show Source): You can put this solution on YOUR website! When 5 new girls joined a class, the percent of girls increased from 40% to 50%. What is the number of boys in the class : originally = .4 g = .4(g+b) g = .4g + .4b g - .4g = .4b .6g = .4b multiply by 10 6g = 4b : When 5 girls are added = .6 g + 5 = .5(g+b+5) g + 5 = .5g + .5b + 2.5 g - .5g = .5b + 2.5 - 5 .5g = .5b - 2.5 get rid of all those decimals, multiply by 2 g = b - 5 : In the original equation, replace g with (b-5) 6(b-5) = 4b 6b - 30 = 4b 6b - 4b = 30 2b = 30 b = 15 boys : : Check by finding the girls originally 6g = 4(15) 6g = 60 g = 10 girls, a total class of 25 : 10/25 = .4, 40% : then we had 15 girls which is 50% of the class with 15 boys

Money_Word_Problems/271481: Carmel put $5000 into 3 different accounts at paid interest of 8%, 10%, and 7% . Total itnerest at the end was $405. If carmel invested 500$ more at 10% than at 8%, find amount invested in each. Set it up in a 3 variable system to find. 1 solutions Answer 198922 by ankor@dixie-net.com(15647)   on 2010-02-19 15:11:33 (Show Source): You can put this solution on YOUR website! Carmel put $5000 into 3 different Carmel put $5000 into 3 different accounts at paid interest of 8%, 10%, and 7% . Total itnerest at the end was $405. If carmel invested 500$ more at 10% than at 8%, find amount invested in each. If carmel invested 500$ more at 10% than at 8%, find amount invested in each. ; Let x = amt at 8% Let y = amt at 10% Let z = amt at 7% : Write an equation for each statement : "Carmel put $5000 into 3 different accounts". x + y + z = 5000 : "Total interest at the end was $405." .08x + .10y + .07z = 405 ; "invested 500$ more at 10% than at 8%," y = x + 500 : Replace y with (x+500) in the first equation x + (x+500) + z = 5000 2x + z = 5000 - 500 2x + z = 4500 z = (4500 - 2x); we can use this for substitution later : do the same in the 2nd equation .08x + .10(x+500) + .07z = 405 .08x + .10x + 50 + .07z = 405 .18x + .07z = 405 - 50 .18x + .07z = 355 : Replace z with (4500-2x) in the above equation .18x + .07(4500 - 2x) = 355 .18x + 315 - .14x = 355 .18x - .14x = 355 - 315 .04x = 40 x = x = $1000 invested at 8% : z = 4500 - 2(1000) z = $2500 invested at 7% : y = 1000 + 500 y = $1500 invested at 10% ; : I'll let you check solution by finding the total interest .08(1000) + .10(1500) + .07(2500) =

Problems-with-consecutive-odd-even-integers/271551: four more than the opposite of n equals 6 1 solutions Answer 198918 by ankor@dixie-net.com(15647)   on 2010-02-19 14:51:32 (Show Source): You can put this solution on YOUR website! four more than the opposite of n equals 6 opposite of n is -n : 4 + (-n) = 6 -n = 6 - 4 -n = 2 n = -2 (opposite is +2)

Quadratic_Equations/271680: If the sides of a square are lengthened by 6cm, the area becomes 144cm^2. Find the length of a side of the original square. Please explain answer. Thanks! 1 solutions Answer 198917 by ankor@dixie-net.com(15647)   on 2010-02-19 14:47:57 (Show Source): You can put this solution on YOUR website! If the sides of a square are lengthened by 6cm, the area becomes 144cm^2. Find the length of a side of the original square. : Let x = side of the original square then (x+6) = lengthened side of the square : The area of the lengthened square is given as 144, therefore (x+6)^2 = 144 Find the square root of both sides x + 6 = 12 x = 12 - 6 x = 6 cm is the side of the original square

Rate-of-work-word-problems/271567: A box without a top is to be made by cutting squares measuring 5 cm on a side from each corner of a square piece of tin and folding up the sides. Find the dimensions of the box, if it is to have a volume of 7220 cm^3. 1 solutions Answer 198915 by ankor@dixie-net.com(15647)   on 2010-02-19 14:43:33 (Show Source): You can put this solution on YOUR website! A box without a top is to be made by cutting squares measuring 5 cm on a side from each corner of a square piece of tin and folding up the sides. Find the dimensions of the box, if it is to have a volume of 7220 cm^3. : We know the height of the box is 5 cm and the bottom is square then we can just find the area of the bottom by: 7220/5 = 1440 Find the sides (s) of the square bottom s = s = 38 cm ; The box dimensions: 38 by 38 by 5 : Find the vol to check it 38 * 38 * 5 = 7220

Linear_Equations_And_Systems_Word_Problems/271438: Find two numbers such that twice the first exceeds three times the second by 1, and three times the first exceeds twice the second by 14. 1 solutions Answer 198914 by ankor@dixie-net.com(15647)   on 2010-02-19 14:35:31 (Show Source): You can put this solution on YOUR website! let x = the first number let y = the second number : Write an equation for each statement: : Find two numbers such that twice the first exceeds three times the second by 1, 2x = 3y + 1 : and three times the first exceeds twice the second by 14. 3x = 2y + 14 : Multiply the first equation by 2, and the 2nd equation by 3 4x = 6y + 2 9x = 6y + 42 ---------------subtraction eliminates y, find x -5x = -40 x = +8 : Find y using the 1st equation 2(8) = 3y + 1 16 - 1 = 3y 3y = 15 y = 5 : Check solution in the 2nd equation 3(8) = 2(5) + 14 24 = 10 + 14 : Response to the comment 2x = 3y + 1 is exactly the same thing as 2x - 3y = 1 and 3x = 2y + 14 is exactly the same thing as 3x - 2y = 14 : You can check the solutions in either equation, if you doubt it

Exponential-and-logarithmic-functions/271531: how do i reduce this: 3log base 5 of 2-(5log base 5 of x+log base 5 of 48) ? email address: dianasalerno0ooo@yahoo.com please show all steps so i can understand how to solve this problem. thank you. 1 solutions Answer 198910 by ankor@dixie-net.com(15647)   on 2010-02-19 14:26:37 (Show Source): You can put this solution on YOUR website! how do i reduce this: 3log base 5 of 2-(5log base 5 of x+log base 5 of 48) ? email address: dianasalerno0ooo@yahoo.com please show all steps so i can understand how to solve this problem. thank you. : All have the base of 5, so we can ignore that for this: 3*log(2) - 5*log(x) + log(48) : Write the multipliers as expnonets subtraction is the same as divide Addition is the same as multiply =

Rational-functions/271545: the population of a colony of bateria is growing exponentially according to the function below , where t is the time in hours. how long will it take for the population of the colony to grow to 1,000 B(t)=12*e^0.2t 1 solutions Answer 198778 by ankor@dixie-net.com(15647)   on 2010-02-18 21:39:56 (Show Source): You can put this solution on YOUR website! the population of a colony of bacteria is growing exponentially according to the function below , where t is the time in hours. how long will it take for the population of the colony to grow to 1,000 B(t)=12*e^0.2t : = 1000 = Use the nat logs = = nat log of e is 1, so we have .2t = 4.22848 t = t = 22.1142 hrs to reach 1000 ; Check on a calc using t=22.1142 enter: 12*e^(.2*22.1142) = 999.99 ~1000

Square-cubic-other-roots/271467: What are the steps for simplyfying cubic root of 24 divided by cubic root of 9? 1 solutions Answer 198772 by ankor@dixie-net.com(15647)   on 2010-02-18 21:24:40 (Show Source): You can put this solution on YOUR website! What are the steps for simplifying cubic root of 24 divided by cubic root of 9? : ------ Same as reduce fraction 8 is 2^3, extract that

Exponential-and-logarithmic-functions/271486: what would be the smallest form of the x^16y^8/81 all in the fourth root? 1 solutions Answer 198766 by ankor@dixie-net.com(15647)   on 2010-02-18 21:03:59 (Show Source): You can put this solution on YOUR website! what would be the smallest form of the x^16y^8/81 all in the fourth root? : : Factor to reveal the 4th powers Extract those end up with =

Travel_Word_Problems/271451: During the day a truck driver encounters light ,moderate, & heavy traffic. If he travels 1/3 hour in light, 1/2 hour in moderate, and 1/5 hour in heavy he can cover 21 miles. Ifh e travels 1/5 in light, 1/4 in moderate, and 1 hr in heavy he can cover 16 mi. The sum of his speeds in moderate & heavy is 5 mi less than his speed in light. Find his speed in each type of traffic. Use 3 variable system to solve. 1 solutions Answer 198745 by ankor@dixie-net.com(15647)   on 2010-02-18 19:55:50 (Show Source): You can put this solution on YOUR website! During the day a truck driver encounters light ,moderate, & heavy traffic. If he travels 1/3 hour in light, 1/2 hour in moderate, and 1/5 hour in heavy he can cover 21 miles. If he travels 1/5 in light, 1/4 in moderate, and 1 hr in heavy he can cover 16 mi. The sum of his speeds in moderate & heavy is 5 mi less than his speed in light. Find his speed in each type of traffic. : : Three different speed, fast, medium, slow: a, b, c : A first distance equation a + b + c = 21 Multiply by 30 to get rid of the fractions, results: 10a + 15b + 6c = 30(21) 10a + 15b + 6c = 630 : 2nd distance equation a + b + c = 16 Multiply by 20 to get rid of the fractions, results: 4a + 5b + 20c = 20(16) 4a + 5b + 20c = 320 : "The sum of his speeds in moderate & heavy is 5 mi less than his speed in light." b + c = a - 5 -a + b + c = -5 : Using the matrix feature in a Ti83, 10, 15, 6, 630 4, 5, 20, 320 -1,1, 1, -5 I got a = 30 mph b = 20 c = 5

Surface-area/270921: Square corners, 6 cm on a side, are removed from a 36cm by 42cm piece of cardboard. the cardboard is then folded to form an open box. What is the urface area of the inside of the box? 1 solutions Answer 198705 by ankor@dixie-net.com(15647)   on 2010-02-18 17:02:34 (Show Source): You can put this solution on YOUR website! Square corners, 6 cm on a side, are removed from a 36cm by 42cm piece of cardboard. the cardboard is then folded to form an open box. What is the surface area of the inside of the box? : Find the dimensions of the open box: (36-12) by (42-12) by 6 24 by 30 by 6 are the dimensions : SA = (24*30) + 2(24*6) + 2(30*6) : SA = 720 + 2(144) + 2(180) : SA = 720 + 288 + 360 : SA = 1368 sq/cm

Linear_Equations_And_Systems_Word_Problems/270920: Find the larger of two positive integers if one is 2/3 of the other and their difference is 34 1 solutions Answer 198698 by ankor@dixie-net.com(15647)   on 2010-02-18 16:54:55 (Show Source): You can put this solution on YOUR website! Find the larger of two positive integers if one is 2/3 of the other and their difference is 34. : x = the larger of the two integers x = the smaller : 1x - x = 34 : x = 34 Multiply both sides by 3 x = 102 is the larger : : Check 102 - (102) = 102 - 68 = 32

Linear_Algebra/270919: the lenght of a book cover is 1cm more than twice its widht if its widht is x cm and its perimeter is 92 cm, form an equation useing x to repesent the adove 1 solutions Answer 198694 by ankor@dixie-net.com(15647)   on 2010-02-18 16:43:05 (Show Source): You can put this solution on YOUR website! : the length of a book cover is 1cm more than twice its width if its width is x cm and its perimeter is 92 cm, form an equation using x to represent the above. : L = 2x+1 therefore p = 2(2x+1) + 2x : 2(2x+1) + 2x = 92 4x + 2 + 2x = 92 6x = 92 - 2 x = x = 15 cm is the width then 2(15) + 1 = 31 cm is the length : : Check 2(31) + 2(15) = 92

Numbers_Word_Problems/271141: The sum of the digits of a certain 2-digit number is 13. When you reverse the number, the new number is 9 less than the original number. The difference between the 2 digits is 1. Find the original number. 1 solutions Answer 198685 by ankor@dixie-net.com(15647)   on 2010-02-18 16:15:10 (Show Source): You can put this solution on YOUR website! The two digit number: 10x + y : The sum of the digits of a certain 2-digit number is 13. x + y = 13 : When you reverse the number, the new number is 9 less than the original number. 10y + x = 10x + y - 9 10y - y = 10x - x - 9 9y = 9x - 9 simplify, divide by 9 y = x - 1 Find the original number. : replace y in the 1st equation with (x-1) x + (x-1) = 13 2x = 13 + 1 2x = 14 x = 7 then y = 6 : 76 is the number : : Check solution in the statement: "When you reverse the number, the new number is 9 less than the original" 67 = 76 - 9

Travel_Word_Problems/271105: When Fritz drives to work his trip takes 36 minutes, but when he takes the train it takes 20 minutes. Find the distance Fritz travels to work if the train travels an average of 32 miles per hour faster than his driving. 1 solutions Answer 198590 by ankor@dixie-net.com(15647)   on 2010-02-18 09:54:07 (Show Source): You can put this solution on YOUR website! When Fritz drives to work his trip takes 36 minutes, but when he takes the train it takes 20 minutes. Find the distance Fritz travels to work if the train travels an average of 32 miles per hour faster than his driving. : Let d = the distance to work : Convert to hrs 36/60 = .6 hrs 20/60 = .33 hrs : Write a speed equation, speed = dist/time : train speed - drive speed = 32 - = 32 multiply by 3 to get rid of the denominators, results 9d - 5d = 96 4d = 96 d = d = 24 miles : : Check solution by finding the difference in speed 24/.33 = 72 mph 24/.6 = 40 mph ----------------- diff: = 32 mph

Percentage-and-ratio-word-problems/271160: The ratio of girls to boys in a class is 4 : 5. lf there are 5 more boys than girls, which of the following is the number of students in this class? (A) 9 (B) 18 (c) 45 (D) 90 (E) 180 1 solutions Answer 198567 by ankor@dixie-net.com(15647)   on 2010-02-18 08:53:43 (Show Source): You can put this solution on YOUR website! The ratio of girls to boys in a class is 4:5. If there are 5 more boys than girls, which of the following is the number of students in this class? : Let x = the multiplier then 4x = no. of girls 5x = no. of boys : "there are 5 more boys than girls," 5x = 4x + 5 5x - 4x = 5 x = 5 is the multiplier then 4(5) = 20 girls 5(5) = 25 boys total: 45 students

Radicals/271177: In what sense do exponentials and radicals behave exactly the same way? 1 solutions Answer 198559 by ankor@dixie-net.com(15647)   on 2010-02-18 08:24:28 (Show Source): You can put this solution on YOUR website! When the exponents are fractions like: x^(1/2) = for example

Exponents/271060: CAn someone please help me? I keep trying these but I also keep getting different answers:( a) [16^(1/2) +(2/3)^0]^-2 b)(27/8)^(1/3) + 4^-1 c)(7^0 - 4^-1)^-3 1 solutions Answer 198556 by ankor@dixie-net.com(15647)   on 2010-02-18 08:18:01 (Show Source): You can put this solution on YOUR website! Remember any number raised to the power of 0 = 1 : a) [16^(1/2) +(2/3)^0]^-2 [16^(1/2) + 1]^-2 The exponent of 1/2 is the square root of the number (4 + 1)^-2 5^-2 The reciprocal gets rid of the neg = : : b)(27/8)^(1/3) + 4^-1 Take the cube root of both numerator and denominator + = + = : : c)(7^0 - 4^-1)^-3 (1 - )^-3 = ()^-3 = ()^3 cube both the numerator and denominator

Numbers_Word_Problems/270970: Five times a certain number, X, exceeds 8 by three times the sum of the number and 2. Find the number. 1 solutions Answer 198480 by ankor@dixie-net.com(15647)   on 2010-02-17 21:54:09 (Show Source): You can put this solution on YOUR website! Five times a certain number, X, exceeds 8 by three times the sum of the number and 2. Find the number. 5x = 8 + 3(x+2) : 5x = 8 + 3x + 6 : 5x - 3x = 8 + 6 : 2x = 14 ; x = 7 is the number : Check in the original statement 5(7) = 8 + 3(7+2) 35 = 8 + 27

Graphs/270935: Hourly Wage Your wage is $8.00 per hour plus $0.75 for each unit produced per hour. So, your hourly wage y in terms of the number of units produced x is y = 8 + 0.75x. a. find the inverse function. What does each variable in the inverse function represent. b. Use a graphing utility to graph the funciton and its inverse function. c. Use the trace feature of a graphing utility to find the hourly wage when 10 units are produced per hour. d. Use the trace feature of a graphing utility to find the number of units produced when your hourly wage is $22.25. 1 solutions Answer 198479 by ankor@dixie-net.com(15647)   on 2010-02-17 21:49:38 (Show Source): You can put this solution on YOUR website! Your wage is $8.00 per hour plus $0.75 for each unit produced per hour. So, your hourly wage y in terms of the number of units produced x is y = 8 + 0.75x. : a. find the inverse function. Swap x and y, solve for y .75y + 8 = x .75y = x - 8 y = x - is the inverse What does each variable in the inverse function represent. y = the units, x = wage ; b. Use a graphing utility to graph the function and its inverse function. Graph both equations, should look like this c. Use the trace feature of a graphing utility to find the hourly wage when 10 units are produced per hour. x = 10; y = 15.50 (use the calculate value function, enter 10) d. Use the trace feature of a graphing utility to find the number of units produced when your hourly wage is $22.25. Using the inverse equation x = 22.25; y = 19 units check this on the original equation

Exponential-and-logarithmic-functions/270946: I need help with this problem log(3x+7)=0 1 solutions Answer 198467 by ankor@dixie-net.com(15647)   on 2010-02-17 21:17:48 (Show Source): You can put this solution on YOUR website! log(3x+7)= 0 Write the exponent equiv 10^0 = (3x+7) : 1 = 3x + 7 : 1 - 7 = 3x : -6 = 3x x = x = -2 ; : Check it: log(3(-2)+7) which is log(1) enter in your calc, to get 0

Expressions-with-variables/270948: Need formula and solution so I can do others- Dried apricots worth #4.25 a pound were mixed with dried prunes worth $4.75 a pound to produce a mixture of dried fruit worth $94.75. How much of each kind of fruit was used to produce 25 pounds of mixture? 1 solutions Answer 198403 by ankor@dixie-net.com(15647)   on 2010-02-17 19:37:26 (Show Source): You can put this solution on YOUR website! Need formula and solution so I can do others- Dried apricots worth #4.25 a pound were mixed with dried prunes worth $4.75 a pound to produce a mixture of dried fruit worth $94.75. How much of each kind of fruit was used to produce 25 pounds of mixture? : Find out how much the resulting mixture is worth per pound = 3.79 : Cannot do this. The resulting mixture cost, has to be between 4.25 and 4.75

Travel_Word_Problems/270793: On Monday, Roger drove to work in 45 minutes. On Tuesday he averaged 12 miles per hour more, and it took him 9 minutes less to get to work. How far does he travel to work? 1 solutions Answer 198369 by ankor@dixie-net.com(15647)   on 2010-02-17 16:45:13 (Show Source): You can put this solution on YOUR website! On Monday, Roger drove to work in 45 minutes. On Tuesday he averaged 12 miles per hour more, and it took him 9 minutes less to get to work. How far does he travel to work? : Change 45 min: 45/60 .75 hr Change 9 min: 9/60 = .15 hr : Let d = distance to work we know Monday it took .75 hrs to get to work Tuesday, (.75-.15) = .6 hrs to get to work : Write a speed equation(Speed = dist/time) : Tuesday speed - Monday speed = 12 mph - = 12 Multiply by 3, to clear the denominators, results 5d - 4d = 3(12) d = 36 miles to work ; : See if that is true Find the difference in speed 36/.6 = 60 36/.75 =48 mph ----------- differ = 12

Rectangles/270865: The perimeter of a paved area being built at a playground is going to be 46 meters. If the length and width are each a whole number of meters, what should the length and width of the area be to cover the greatest possible area? Draw a picture and make an organized list to solve. I dont know how to solve this can you please help me!!! 1 solutions Answer 198345 by ankor@dixie-net.com(15647)   on 2010-02-17 16:06:24 (Show Source): You can put this solution on YOUR website! The perimeter of a paved area being built at a playground is going to be 46 meters. If the length and width are each a whole number of meters, what should the length and width of the area be to cover the greatest possible area? Draw a picture and make an organized list to solve. I dont know how to solve this can you please help me!!! : We know: 2L + 2W = 46 Simplify, divide by 2 L + W = 23 : Max area of a rectangle is a square, but since this has to be integer values. the closest we can get is 12 by 11 meters : you can prove that 12 * 11 = 132 13 * 10 = 130 14 * 9 = 126 etc

Travel_Word_Problems/270809: Alana and her father Tim begin skiing the same cross-country ski trail in Elmwood park in sioux Falls, South Dakota, at the same time. If Alana, who averages 9 miles per hour, finishes the trail 0.25 hours sooner than her father, who averages 6 miles per hour, determine the length of the trail? 1 solutions Answer 198340 by ankor@dixie-net.com(15647)   on 2010-02-17 15:56:48 (Show Source): You can put this solution on YOUR website! If Alana, who averages 9 miles per hour, finishes the trail 0.25 hours sooner than her father, who averages 6 miles per hour, determine the length of the trail? : Let t = time it takes A to ski the trail Let (t+.25) = time for daddy to do it : A's dist = D's dist (dist = speed * time) 9t = 6(t+.25) 9t = 6t + 1.5 9t - 6t = 1.5 3t = .5 hrs for A to do it : Find the dist (d's time .5 + .25 = .75) .5*9 = 4.5 mi is the length of the trail Find the dist using daddy's time .75(6) = 4.5 mi also

Miscellaneous_Word_Problems/270807: The following table shows the amount of polonium in milligrams remaining after x days from an original sample of 2 milligrams. x(days) 0 100 200 300 y milligrams 2 1.22 0.743 0.453 a. is the half life pf te polonium less than 200 days? b. give a general formula thatr can be used to approximate the amount A of polonium after x days. c. what is the half-life of the polonium? GRaph A(x) and show th epoint that would show the half-life for x=2 milligrams. 1 solutions Answer 198336 by ankor@dixie-net.com(15647)   on 2010-02-17 15:44:40 (Show Source): You can put this solution on YOUR website! The following table shows the amount of polonium in milligrams remaining after x days from an original sample of 2 milligrams. x(days) 0 100 200 300 y milligrams 2 1.22 0.743 0.453 : a. is the half life of the polonium less than 200 days? Find the half life (h) using values for 100 days and resulting amt of 1.22 mg 2*(2^(-100/h)) = 1.22 : 2^(-100/h) = ; 2^(-100/h) = .61 : log(2^(-100/h)) = log(.61) log(2) = log(.61) = = -.713 h = h ~ 140 days is the half life : b. give a general formula that can be used to approximate the amount A of polonium after x days. A = 2*2^(-x/140) : : c. what is the half-life of the polonium? we found it to be 140 days in (a) : GRaph A(x) and show th epoint that would show the half-life for x=2 milligrams. Graph the equation y = 2*2^(-x/140) You can see that at 140 days there is about 1 mg of the substance

Travel_Word_Problems/270640: A man is walking at an average speed of 4 miles per hour along a railroad track. A train going the same way at a speed of 30 mph requires 5 seconds to pass the man. How long is the train? 1 solutions Answer 198256 by ankor@dixie-net.com(15647)   on 2010-02-17 10:10:35 (Show Source): You can put this solution on YOUR website! A man is walking at an average speed of 4 miles per hour along a railroad track. A train going the same way at a speed of 30 mph requires 5 seconds to pass the man. How long is the train? ; Let x = length of the train : Convert both speeds to ft/sec Man: = 5.867 ft/sec : Train: = 44 ft/sec : Find the length of the train x = 5(44 - 5.867) = 190.67 ft

Unit_Conversion_Word_Problems/270685: A booklet containing the New Testament, the Psalms and the Proverbs has 633 Pages. The booklet, excluding the outer covers is 1.5 cm thick. Calculate the thickness of each page in Millimeters, giving your answer in standard form. 1 solutions Answer 198254 by ankor@dixie-net.com(15647)   on 2010-02-17 09:54:46 (Show Source): You can put this solution on YOUR website! A booklet containing the New Testament, the Psalms and the Proverbs has 633 Pages. The booklet, excluding the outer covers is 1.5 cm thick. Calculate the thickness of each page in Millimeters, giving your answer in standard form. : 1.5 cm = 15 mm : = .0236966825 mm per page