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 Human-and-algebraic-language/107438: Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 1/2 hours. How quickly can all three fill the pool together?1 solutions Answer 78214 by ankor@dixie-net.com(15652)   on 2007-11-01 08:20:35 (Show Source): You can put this solution on YOUR website!Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 1/2 hours. How quickly can all three fill the pool together? : Let t = time required if they work together Let 1 = the full pool Convert 1.5 hrs to minutes: 90 min A simple equation: Multiply equation by 90, this gets rid of the denominators; You then have 3t + 2t + t = 90 6t = 90 t = 90/6 t = 15 minutes working together: : Check solution: 15/30 + 15/45 + 15/90 = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 1
 Geometry_Word_Problems/107378: Martina leaves home at 9am bicycling at a rate of 24 miles per hour, 2 hours later John leaves driving at the rate of 48 miles per hour. At what time will john catch up with Martina?1 solutions Answer 78175 by ankor@dixie-net.com(15652)   on 2007-10-31 21:51:23 (Show Source): You can put this solution on YOUR website!Martina leaves home at 9 am bicycling at a rate of 24 miles per hour, 2 hours later John leaves driving at the rate of 48 miles per hour. At what time will john catch up with Martina? : Let t = M's travel time Then (t-2) = J's travel time : One thing to remember on all these "catch-up" problems is that they will have traveled the same distance when that occurs. Write a distance equation from this fact. : Distance = speed * time : J's dist = M's dist 48(t-2) = 24t 48t - 96 = 24t 48t - 24t = +96 24t = 96 t = 96/24 t = 4 hrs is M's travel time : Find the time: 9:00 AM = 4:00 = 1 PM is when J catches up with M : Confirm our solution by finding the distances: 24*4 = 96 mi 48*(4-2)) = 96 mi ; Did this make sense? Any questions?
 Polynomials-and-rational-expressions/107391: Can anyone help me with the following problem? 36x^2=1 I cant figure out how to work it. I have tried several different ways and keep coming up short. The ^2 is an exponent Thank You1 solutions Answer 78160 by ankor@dixie-net.com(15652)   on 2007-10-31 20:48:48 (Show Source): You can put this solution on YOUR website!36x^2 = 1 : 36x^2 - 1 = 0; recognize this as the difference of squares, : which factor to: (6x+1)(6x-1) = 0 6x = -1 x = and 6x = +1` x =
 Geometry_Word_Problems/107377: A bus leaves a station at 1 pm traveling west at an average rate of 44 miles per hour. One hour later a second bus leaves the same station, traveling east at an rate of 48 miles per hour. At what time will the two buses be 274 miles apart?1 solutions Answer 78159 by ankor@dixie-net.com(15652)   on 2007-10-31 20:41:33 (Show Source): You can put this solution on YOUR website!A bus leaves a station at 1 pm traveling west at an average rate of 44 miles per hour. One hour later a second bus leaves the same station, traveling east at an rate of 48 miles per hour. At what time will the two buses be 274 miles apart? : Let t = travel time of the westbound bus when they are 274 mi apart Then (t-1) = travel time of the eastbound bus when they are 274 mi apart : Write a distance equation: Distance = speed * time : West bus dist + East bus dist = 274 mi 44t + 48(t-1) = 274 44t + 48t - 48 = 274 92t = 274 + 48 92t = 322 t = 322/92 t = 3.5 hrs is the travel time of the west bound bus Then we know: 2.5 hrs is the travel time of the east bound bus : Find the time: 1:00 + 3:30 = 4:30 PM, time they will be 274 mi apart : Check solution by finding the sum of the distances: 44(3.5) + 48(2.5) = 154 + 120 = 274 mi as given : : Did this make sense to you? Any questions?
 Radicals/107263: This question is from textbook sqrt(6)(sqrt(3)-2)] Add or subtract as indicated I have gotten to this point: sqrt(6)sqrt(3) - sqrt(6)-2 But from here, I have NO clue where to go. Can anyone assist me?1 solutions Answer 78158 by ankor@dixie-net.com(15652)   on 2007-10-31 20:30:35 (Show Source): You can put this solution on YOUR website!() : Multiply both terms inside the brackets by Same as: : Extract the sqrt of 9
 Radicals/107290: Simplify: √[49x^12y^4z^8] Thanks for helping out! 1 solutions Answer 78151 by ankor@dixie-net.com(15652)   on 2007-10-31 20:10:02 (Show Source): You can put this solution on YOUR website!Simplify: √[49x^12y^4z^8] Factor it into perfect squares: =
 Probability-and-statistics/107280: Two Russian mathematicians meet on a plane. “If I remember correctly, you have three sons,” says Ivan. “What are their ages today?” “The product of their ages is thirty-six,” says Igor, “and the sum of their ages is exactly today’s date.” “I’m sorry, Igor,” Ivan says after a minute, “but that doesn’t tell me the ages of your boys.” “Oh, I forgot to tell you, my youngest son has red hair.” “Ah, now it’s clear,” Ivan says. “I now know exactly how old your three sons are.” How did Ivan figure out the ages? 1 solutions Answer 78126 by ankor@dixie-net.com(15652)   on 2007-10-31 15:43:16 (Show Source): You can put this solution on YOUR website!Two Russian mathematicians meet on a plane. “If I remember correctly, you have three sons,” says Ivan. “What are their ages today?” “The product of their ages is thirty-six,” says Igor, “and the sum of their ages is exactly today’s date.” “I’m sorry, Igor,” Ivan says after a minute, “but that doesn’t tell me the ages of your boys.” “Oh, I forgot to tell you, my youngest son has red hair.” “Ah, now it’s clear,” Ivan says. “I now know exactly how old your three sons are.” How did Ivan figure out the ages? : I am going guess that Ivan knew a couple things that they didn't tell us: 1. The day of the month is the 13th 2. Two of the 3 brothers are twins : That could make the boys ages (which add up to 13): 6, 6, 1 2, 2, 9 : When he said the youngest had red hair. that made the older ones the twins and confined the answer to: 6, 6, 1 : This is just a guess, there may be other solutions.
 Age_Word_Problems/107157: I do not know how to set up an equation for this word sentence. I was able to come up with an answer that works in my head by I do not know how to write an equation for it on paper. The question is: A father is four times as old as his daughter is now. In 20 years, he will be only twice as old as his daugher. How old are the father and daughter now. The answer I came up with was 7 and 28. Please help.1 solutions Answer 78016 by ankor@dixie-net.com(15652)   on 2007-10-30 20:50:31 (Show Source): You can put this solution on YOUR website!Here's an easy method to these type of problems: : Write an equation for each statement: : A father is four times as old as his daughter is now. F = 4D : "In 20 years," their age will be: F+20 and D+20 : In 20 years, he will be only twice as old as his daughter. F + 20 = 2(D+20) F + 20 = 2D + 40 F = 2D + 40 - 20 F = 2D + 20 : How old are the father and daughter now. From the 1st statement: substitute 4D for F in the above equation: 4D = 2D + 20 4D - 2D = 20 2D = 20 D = 20/2 D = 10 yrs old is the daughter now. Then 4(10) = 40 yrs old is the father now : : Check our solution using the statement: "In 20 years, he will be only twice as old as his daughter." (40 + 20) = 2(10 + 20); confirms out solution : Did this help you understand these type problems?
 Geometry_Word_Problems/106906: Please help! Two designs for and oil storage tank are being considered: spherical and cylindrical. The two tanks would have the same capacity and would each have an inside diameter of 60 feet. a)what would be the height of the cylindrical tank? b) If one cubic foot holds 7.5 gallons of oil, what is the capacity of each tank in gallons? c)Which of the two designs has the smallest surface area and would thus require less material in its construction?1 solutions Answer 78006 by ankor@dixie-net.com(15652)   on 2007-10-30 19:59:40 (Show Source): You can put this solution on YOUR website!Two designs for and oil storage tank are being considered: spherical and cylindrical. The two tanks would have the same capacity and would each have an inside diameter of 60 feet. : a)what would be the height of the cylindrical tank? r = 30 ft Cylinder Vol = Sphere Vol = = Multiply both sides by 3: = Divide both sides by and you have: 3h = 4*30 h = 120/3 h = 40 ft is the height of the cylinder : You can check this by finding the volume of both, see if they equal 113,097.3 cu/ft : b) If one cubic foot holds 7.5 gallons of oil, what is the capacity of each tank in gallons? 113097.3 * 7.5 = 848,230 gal : c)Which of the two designs has the smallest surface area and would thus require less material in its construction? Sphere would have the smallest surface area Sphere: = 11,309.7 sq ft Cylinder: + = 13,194.7 sq ft : Did this make sense to you?
 Average/107185: An alloy of metals is 25% copper another alloy is 50% copper. How much of each alloy is used to make 1000 grams of an alloy with 45% copper. Can you help us write this equations?1 solutions Answer 77998 by ankor@dixie-net.com(15652)   on 2007-10-30 19:19:40 (Show Source): You can put this solution on YOUR website!An alloy of metals is 25% copper another alloy is 50% copper. How much of each alloy is used to make 1000 grams of an alloy with 45% copper. : Let x = amt of 25% copper required Then (1000-x) = amt of 50% copper required: : A simple equation: .25x + .50(1000-x) = .45(1000)
 Numbers_Word_Problems/106896: Two numbers have sum of 32. If the second is five less than four times the first, what are the two numbers?1 solutions Answer 77996 by ankor@dixie-net.com(15652)   on 2007-10-30 19:14:26 (Show Source): You can put this solution on YOUR website!Let x = the 1st number : Two numbers have sum of 32. If the 1st number = x, then the 2nd number = (32-x) : "the second is five less than four times the first," (32 - x) = 4x - 5 32 + 5 = 4x + x 37 = 5x : what are the two numbers? x = 37/5 x = 7.4 is the 1st number : Find the 2nd number: 32 - 7.4 = 24.6 is the 2nd number : : Check solution in the statement: "the second is five less than four times the first," 24.6 = 4(7.4) - 5 24.6 = 29.6 - 5; confirms our solution
 Rational-functions/106877: Here is one of the hardest problems I have even seen! Can you please see if you can help with this one? I feel like I can write some functions, but I am really confused. CAN YOU PLEASE HELP ME WORK THIS PROBLEM OUT IN FULL PLEASE? Product x: Each item sold produces \$100 profit Labor cost: is 3 hours for assembly, 1 hour in detail work, and 2 hours for QA & packing product. Product y: Each item sold produces \$150 profit Labor cost: is 5 hours for assembly, 3 hour in detail work, and 2 hours for QA & packing product. Company has these hours available for production for each accounting period: 3900 hours for assembly, 2100 hours for detail work, & 2200 hours for QA & packing. Questions are: 1) How many products of both x & y should be produced to make a max & min profit? 2) Now what if product y profit goes up to \$170 each. How many products are needed to make a max & min profit? I know this is not an easy question, but do you think you could help with this question please? Thank you kindly. 1 solutions Answer 77923 by ankor@dixie-net.com(15652)   on 2007-10-30 09:44:49 (Show Source): You can put this solution on YOUR website!Product x: Each item sold produces \$100 profit Labor cost: is 3 hours for assembly, 1 hour in detail work, and 2 hours for QA & packing product. : Product y: Each item sold produces \$150 profit Labor cost: is 5 hours for assembly, 3 hour in detail work, and 2 hours for QA & packing product. : Company has these hours available for production for each accounting period: 3900 hours for assembly, 2100 hours for detail work, & 2200 hours for QA & packing. : Assembly: 3x + 5y =< 3900 5y =< -3x + 3900; arrange in the "y=" form for graphing y =< -.6x + 780; divided equation by 5 : Detail 1x + 3y =< 2100 3y =< -x + 2100 y =< .33x + 700; divided equation by 3 : QA & Packing 2x + 2y =< 2200 2y =< -2x + 2200 y =< -x + 1100; divided equation by 2 : Graph this and you should have: Note that the area of feasibility is at or below the the lowest graphing line : Questions are: 1) How many products of both x & y should be produced to make a max & min profit? : Find the coordinates of the corners of the area of feasibility, use these to make an objective profit function for each corner. The x/y values of the corners will be: 0, 700 300, 600 800, 300 1100, 0 : 0,700: 100x + 150y = 100(0) + 150(700) = \$105,000 profit : 300,600 100(300) + 150(600) = 30000 + 90000 = \$120,000 profit : 800,300 100(800) + 150(300) = 80000 + 45000 = \$125,000 profit : 1100, 0 100(1100) + 150(0) = \$110,000 profit : : 2) Now what if product y profit goes up to \$170 each. How many products are needed to make a max & min profit? : I am pressed for time, here. Substitute 170 for 150 and do the same as above. If you have any questions email me, I will respond tonight. I know this is not an easy question, but do you think you could help with this question please? Thank you kindly.
 Polynomials-and-rational-expressions/106756: This question is from textbook Please help me with this problem: Simplify the expression making sure the answer has no negative exponents: -5x^2yz^3 ---------- -5x^2yz the entire problem has an exponent of 5 In this particular instance, doesn't everything cancel out and the answer is z^2? Or, am I missing something? 1 solutions Answer 77698 by ankor@dixie-net.com(15652)   on 2007-10-28 20:39:25 (Show Source): You can put this solution on YOUR website!I think you're right, except if the whole thing is enclosed in brackets, and has )^5 exponent, it would be x^10, wouldn't it?
 Miscellaneous_Word_Problems/106747: Mike and Matthew are each responsible for mowing half of their 60 foot by 100 foot rectangular back yard. MIke starts mowing at an outside corner, gradually working his way toward the middle by mowing around the outside edges. If the mower cuts a 3-foot-wide path, during which trip around the yard should Mike stop and Matthew start mowing?1 solutions Answer 77690 by ankor@dixie-net.com(15652)   on 2007-10-28 19:37:41 (Show Source): You can put this solution on YOUR website!Mike and Matthew are each responsible for mowing half of their 60 foot by 100 foot rectangular back yard. MIke starts mowing at an outside corner, gradually working his way toward the middle by mowing around the outside edges. If the mower cuts a 3-foot-wide path, during which trip around the yard should Mike stop and Matthew start mowing? : Find the total area: 60 * 100 = 6000 sq/ft : Half the area = 3000 sq/ft : Let x = no. of trips by a 3' mower to do 3000 sq/ft (half the lawn : Area of the unmowed area remaining (each round trip cuts 6' off the edge: (60-6x) * (100 - 6x) = 3000 : 6000 - 960x + 36x^2 = 3000 Arrange as a quadratic equation: 36x^2 - 960x + 6000 - 3000 = 0 : 36x^2 - 960x + 3000 = 0 : Simplify, divide equation by 12: 3x^2 - 80x + 250 = 0 : Using the quadratic formula, the lower value solution: x = 3.6 trips : Try to verify this: Remember that each round he would chop 6' off the lawn dimensions : if he mowed exactly 3 times 3(6) = 18 ft The remaining lawn would be: (60 - 18) * (100 - 18) = 3444 sq/ft remaining, not quite a half done : If he mowed exactly 4 time; 4(6) = 24 ft (60 - 24) * (100 - 24) = 2736 sq/ft remaining, over half done : Between the 3rd and 4th round would be the time for Matthew to take over. : Did this help you?
 Polynomials-and-rational-expressions/106711: This question is from textbook Can someone please help me with this division problem? I am totally lost. (3-x+8x^3-10x^2)/(1+2x) 1 solutions Answer 77653 by ankor@dixie-net.com(15652)   on 2007-10-28 14:32:34 (Show Source): You can put this solution on YOUR website!(3-x+8x^3-10x^2)/(1+2x) : Arrange these expression into the general descending form: (8x^3 - 10x^2 - x + 3)/(2x + 1) : Use grade school long division (I'm using .........to keep things lined up): Choose a quotient term that will equal the 1st term, when multiplied by the divisor : ............................4x^2 - 7x + 3 .............---------------------- (2x+1) |8x^3 - 10x^2 - x + 3 ...............8x^3 + 4x^2 .............-------------- ............................14x^2 - x ............................14x^2 -7x ............................---------- .........................................6x + 3 .........................................6x + 3 .........................................------ .................................................0 : You can check our solution by ordinary multiplication: 4x^2 - 7x + 3 Times 2x + 1 ---------------- : : Did this help you find your way?
 Numbers_Word_Problems/106550: The sum of two numbers is 82. The larger number is 17 less than twice the smaller number. What are the two numbers?1 solutions Answer 77595 by ankor@dixie-net.com(15652)   on 2007-10-27 21:41:20 (Show Source): You can put this solution on YOUR website!The sum of two numbers is 82. The larger number is 17 less than twice the smaller number. What are the two numbers? : Just write what it says: : "The sum of two numbers is 82." Let larger number = x; then (82-x) = the smaller number : "The larger number is 17 less than twice the smaller number" x = 2(82-x) - 17 x = 164 - 2x - 17 x + 2x = 164 - 17 3x = 147 x = 147/3 x = 49 Then 82 - 49 = 33 = the smaller number : : Check our solution using the statement: "The larger number is 17 less than twice the smaller number." 49 = 2(33) - 17 49 = 66 - 17; confirms our solution
 Money_Word_Problems/106604: For a recent job, a plumber earned \$28 per hour, adn the plumber's apprentice earned \$15 per hour. The plumber worked 3 hours more htan the apprentice. If together they were paid \$213, how much did each earn? All I know is that I need to find an expression first for the number of hours each worked on the job, which would be something like (28x+3)+ 15x=213 ??? I'm really not sure, please help! Thank you!1 solutions Answer 77592 by ankor@dixie-net.com(15652)   on 2007-10-27 21:29:00 (Show Source): You can put this solution on YOUR website!For a recent job, a plumber earned \$28 per hour, adn the plumber's apprentice earned \$15 per hour. The plumber worked 3 hours more htan the apprentice. If together they were paid \$213, how much did each earn? : All I know is that I need to find an expression first for the number of hours each worked on the job, which would be something like (28x+3)+ 15x = 213 ??? : you're almost right (bracket), just solve for x to find the apprentice hrs 28(x+3) + 15x = 213 28x + 84 + 15x = 213 28x + 15x = 213 - 84 43x = 129 x = 129/43 x = 3 hrs : Find the wages: Plumber: 6 * 28 = 168 Apprent: 3 * 15 = 45 ----------------------- our given total = 213,