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 Miscellaneous_Word_Problems/209457: a 39 ounce can of hills bros. coffee requires 188.5 square inches of aluminum. if its height is 7 inches, what is its radius?1 solutions Answer 158378 by ankor@dixie-net.com(15624)   on 2009-08-29 15:25:33 (Show Source): You can put this solution on YOUR website!a 39 ounce can of hills bros. coffee requires 188.5 square inches of aluminum. if its height is 7 inches, what is its radius? : The cylinder surface area formula: S.A. = + S.A. = 188.5; h = 7 + = 188.5 + = 188.5 Divide by r^2 + 7r = r^2 + 7r = 30 : A quadratic equation r^2 + 7r - 30 = 0 : Factor this to (r+10)(r-3) = 0 ; Positive solution r = 3 inches is the radius : : Check solution + = 56.55 + 131.95 = 188.5
 Linear-systems/209212: When Mr. Reader packed his books into bundles of 12 books there were 2 books left unpacked. When he repacked his books in bundles of 9, there were 2 books left again. Finally, when Mr Reader packed his books in bundles of 7, there were no books left unpacked. Find the smallest number of books that Mr. Reader could have.1 solutions Answer 158330 by ankor@dixie-net.com(15624)   on 2009-08-29 10:03:46 (Show Source): You can put this solution on YOUR website! Mr. Reader packed his books into bundles of 12 books there were 2 books left unpacked. When he repacked his books in bundles of 9, there were 2 books left again. Finally, when Mr Reader packed his books in bundles of 7, there were no books left unpacked. Find the smallest number of books that Mr. Reader could have. : Find a common multiple of 12 & 9; add 2 and see if it is a multiple of 7. Using this method, I arrived at 180 (started at 108), added 2 to make 182 books :
 Polynomials-and-rational-expressions/209285: 4+9xy-18y-2x OK, I'm supposed to factor this by grouping, but i'm not sure how to do that.1 solutions Answer 158214 by ankor@dixie-net.com(15624)   on 2009-08-28 13:19:48 (Show Source): You can put this solution on YOUR website!4 + 9xy - 18y - 2x Easier to see if you group it like this: 9xy - 18y - 2x + 4 ; Factor out 9y and you have 9y(x - 2) - 2x + 4 : factor out -2 9y(x - 2) - 2(x - 2) : Factor out (x - 2) leaving: (x - 2) (9y - 2) : Did this make sense to you?
 Volume/209222: URGENT QUESTION. help needed. THanks the question is- a box in the shape of a cuboid with a square base and the sum of all its dimensions is 20cm . Find the dimensions fos maximum volume and find the maximum volume. Thanks. Heaps 1 solutions Answer 158211 by ankor@dixie-net.com(15624)   on 2009-08-28 12:54:33 (Show Source): You can put this solution on YOUR website!a box in the shape of a cuboid with a square base and the sum of all its dimensions is 20cm . Find the dimensions for maximum volume and find the maximum volume. : max volume is a perfect cube, therefore: 20/3 = 6cm on each side : max vol = 296.296 cu/cm
 percentage/209151: This question is from textbook Longman mathematics for IGCSE book 1 A survey showed that the ratio of telephones to people in the world was 1:8. Of the world's telephones 0.012% were in Ethopia . In ethopia 0.2% of the population had telephones. At the time of the survey there were 4000 million people in the world. What was the population of Ethopia? I an having great problem solving this question. Therefore I request you to help me.It is really urgent! Thankyou very much indeed.1 solutions Answer 158132 by ankor@dixie-net.com(15624)   on 2009-08-27 21:48:40 (Show Source): You can put this solution on YOUR website!A survey showed that the ratio of telephones to people in the world was 1:8. Of the world's telephones 0.012% were in Ethopia. In ethopia 0.2% of the population had telephones. At the time of the survey there were 4000 million people in the world. What was the population of Ethopia? ; let p = population of Ethiopia : Find out how many telephones in the world (in millions) : *4000 = 500 million telephones : It says,"the world's telephones 0.012% were in Ethiopia." therefore Change .012% to decimal .00012 * 500,000,000 = 60,000 telephones : It says,"In Ethiopia 0.2% of the population had telephones.", therefore: Change .2% to decimal .002p = 60000 p = p = 30,000,000 people
 Linear-systems/208974: When I am as old as my father is now, I will five times as old as my son is now. By then, my son will be eight years older than I am now. The sum of my father's age and my age is 100 years. How much older am I than my son?1 solutions Answer 158118 by ankor@dixie-net.com(15624)   on 2009-08-27 21:05:04 (Show Source): You can put this solution on YOUR website!When I am as old as my father is now, I will five times as old as my son is now. By then, my son will be eight years older than I am now. The sum of my father's age and my age is 100 years. How much older am I than my son? : m = my age now f = father's age now s = son's age now d = f - m; (me and dad's age difference) : "When I am as old as my father is now, I will five times as old as my son is now." father now is 5 times son now f = 5s we can substitute 5s for f and we have difference of d = 5s - m : "By then, my son will be eight years older than I am now." (s + d) = m + 8 Substitute (5s-m) for d s + (5s - m) = m + 8 6s - m - m = 8 6s - 2m = 8 : "The sum of my father's age and my age is 100 years." f + m = 100 Substitute 5s for f 5s + m = 100 Multiply this equation by 2 and add to eq: 6s - 2m = 8 10s + 2m = 200 6s - 2m = 8 ----------------adding eliminates m, find s 16s = 208 s = s = 13 yrs is son's present age then 5(13) = 65 yrs is father's present age : It's easy to find my age 65 + m = 100 m = 35 yrs is my age ; ; Check solutions in the statement: (d = 65 - 35 = 30 yrs difference) "By then, my son will be eight years older than I am now." 13 + 30 = 35 + 8 : Dad: 65, me 35, son 13
 Mixture_Word_Problems/208984: How many ounces of a metal other than gold must be added to 56 ounces of pure gold to make a composition 70% gold?1 solutions Answer 158045 by ankor@dixie-net.com(15624)   on 2009-08-27 16:32:28 (Show Source): You can put this solution on YOUR website!How many ounces of a metal other than gold must be added to 56 ounces of pure gold to make a composition 70% gold? : Let x = amt of metal to be added : Write an "amt of gold" equation 56 = .7(x+56) 56 = .7x + 39.2 56 - 39.2 = .7x 16.8 = .7x x = x = 24 oz of metal ; : Check solution .7(24+56) = 56
 Numbers_Word_Problems/209076: I am a 3-digit number. All of my digits are odd. Iam less than 600. I am greater than 400. If you add my digits you get 15. My last digit is 7. What am I?1 solutions Answer 158043 by ankor@dixie-net.com(15624)   on 2009-08-27 16:21:29 (Show Source): You can put this solution on YOUR website!I am a 3-digit number. All of my digits are odd. I am less than 600. I am greater than 400. If you add my digits you get 15. My last digit is 7. What am I? : All digits odd, >400, <600, first digit has to be 5 : Last digit given as 7 : 2nd digit: 15 - 5 - 7 = 3 : 537 is the number
 Word_Problems_With_Coins/209071: A childs coin bank contains 2.58 in pennies and nickels.If the number of pennies is 36 less than 2 times the number of nickels, how many pennies are in the bank?1 solutions Answer 158038 by ankor@dixie-net.com(15624)   on 2009-08-27 15:49:18 (Show Source): You can put this solution on YOUR website!A childs coin bank contains 2.58 in pennies and nickels. If the number of pennies is 36 less than 2 times the number of nickels, how many pennies are in the bank? : Let p = no. pennies let n = no. of nickels : Write an equation for each statement: : "coin bank contains 2.58 in pennies and nickels." .01p + .05n = 2.58 Multiply equation by 100 to get rid of the decimals, use cents 1p + 5n = 258 : "the number of pennies is 36 less than 2 times the number of nickels," p = 2n - 36 : Substitute (2n-36) for p in the cents amt equation (2n-36) + 5n = 258 2n + 5n = 258 + 36 7n = 294 n = n = 42 nickels then p = 2(42) - 36 p = 84 - 36 p = 48 pennies : : Check solution in original \$amt equation .01(48) + .05(42) = .48 + 2.10 = 2.58
 Travel_Word_Problems/209035: Jim leaves work at 6am going 60mph. Pat leaves at 7am going 78mph. How long till they are at the same point?1 solutions Answer 158031 by ankor@dixie-net.com(15624)   on 2009-08-27 14:43:44 (Show Source): You can put this solution on YOUR website!Jim leaves work at 6am going 60 mph. Pat leaves at 7am going 78 mph. How long till they are at the same point? ; Let t = travel time of Jim then (t-1) = Pat's travel time : When P and J are at the same point, they will have traveled the same distance. Write a distance equation. Dist = speed * time : P's dist = J's dist 78(t-1) = 60t : 78t - 78 = 60t : 78t - 60t = 78 : 18t = 78 t = t = 4 hrs, that's 4 hr, 20 min : They will be at the same point at 10:20 AM ; ; Check solution; find the distances 60 * 4.33 ~ 260 mi 78 * 3.33 ~ 260 mi
 Rate-of-work-word-problems/208993: Eva can wallpaper a room in 4 hours and Kathy can wallpaper the same room in 6 hours. Kathy works on her own for one hour, and is then joined bye Eva. Assuming these rates, how many hours did Kathy and Eva together take to finish the job?1 solutions Answer 158025 by ankor@dixie-net.com(15624)   on 2009-08-27 14:20:05 (Show Source): You can put this solution on YOUR website!Eva can wallpaper a room in 4 hours and Kathy can wallpaper the same room in 6 hours. Kathy works on her own for one hour, and is then joined bye Eva. Assuming these rates, how many hours did Kathy and Eva together take to finish the job? : Let t = time required when they work together : Let the completed job = 1 : Each will do a fraction of the job. the two fractions add up to 1 + = 1 Multiply equation by 12 12* + 12* = 12*1 Cancel denominators 3t + 2t = 12 : 5t = 12 t = t = 2.4 hrs working together ; ; Check solution: + = .6 + .4 = 1
 Travel_Word_Problems/208998: Tilda's car get 34 miles per gallon of gasoline and Naomi's car gets 8 miles per gallon. When traveling from Washington D.C. to Philadelphia, they both used a whole number of gallons of gasoline. How far is it from Philadelphia to Washington D.C.? 1 solutions Answer 157993 by ankor@dixie-net.com(15624)   on 2009-08-27 07:26:41 (Show Source): You can put this solution on YOUR website!Tilda's car get 34 miles per gallon of gasoline and Naomi's car gets 8 miles per gallon. When traveling from Washington D.C. to Philadelphia, they both used a whole number of gallons of gasoline. How far is it from Philadelphia to Washington D.C.? : The lowest common multiple: 8 * 34 = 272 mi
 Equations/208929: Johnny's lawn is 2/3 of an acre in size. if 7 1/2 bags of fertilizers are needed for a lawn that is 1 acre in size. How many bags will Johnny need to fertilize his lawn? Do we multiply, subtract or divide?1 solutions Answer 157970 by ankor@dixie-net.com(15624)   on 2009-08-26 21:37:09 (Show Source): You can put this solution on YOUR website!Johnny's lawn is 2/3 of an acre in size. if 7 1/2 bags of fertilizers are needed for a lawn that is 1 acre in size. How many bags will Johnny need to fertilize his lawn? Do we multiply, subtract or divide? : Convert 7 to an improper fraction and multiply by : * = = 5 bags (it will also cancel nicely)
 Equations/208889: A 2.00 kg sample of bituminous coal is composed of 1.30 kg of carbon, 0.20 kg of ash, 0.15 kg of water and 0.35 kg of volatile material. Using this information, determine how many kilograms of carbon are in 125 kg of coal. thank u 1 solutions Answer 157963 by ankor@dixie-net.com(15624)   on 2009-08-26 20:31:59 (Show Source): You can put this solution on YOUR website! 2.00 kg sample of bituminous coal is composed of 1.30 kg of carbon, 0.20 kg of ash, 0.15 kg of water and 0.35 kg of volatile material. Using this information, determine how many kilograms of carbon are in 125 kg of coal. : Use a ratio equation(Let C = amt of carbon in 125 kg): = 2C = 125 * 1.3 2C = 162.5 C = C = 81.25 kg of carbon in 125 kg of coal : : Check using percent 1.3/2 = .65 81.25/125 = .65
 Problems-with-consecutive-odd-even-integers/208784: This question is from textbook algebra 1 an integrated approach solve the variable in each equation below. show all you work. provide a check for each answer. if a solution is undefined, state that in your answer. 1-y/1+y=2/31 solutions Answer 157961 by ankor@dixie-net.com(15624)   on 2009-08-26 20:16:26 (Show Source): You can put this solution on YOUR website! = Cross multiply 3(1-y) = 2(1+y) : 3 - 3y = 2 + 2y : 3 - 2 = 2y + 3y : 1 = 5y y = : : Check solution using .2 for 1/5 = =
 percentage/208811: The question from the text book is this "Bill invested three times as much money at 9% as at 7.5%. If he wanted his interest at the end of the year to be \$1725, what amount of money should he inves a 7.5%?" 1 solutions Answer 157927 by ankor@dixie-net.com(15624)   on 2009-08-26 16:41:42 (Show Source): You can put this solution on YOUR website!"Bill invested three times as much money at 9% as at 7.5%. If he wanted his interest at the end of the year to be \$1725, what amount of money should he invest a 7.5%?" ; Let x = amt invested at 7.5% then "three times as much money at 9% as at 7.5%" therefore: 3x = amt invested at 9% ; Write the interest equation: .09(3x) + .075x = 1725 .27x + .075x = 1725 .345x = 1725 x = x = \$5000 invested at 7.5% : : Check solution (15000 invested at 9%) .09(15000) + .075(5000) = 1350 + 375 = 1725
 Bodies-in-space/208717: A sphere with a diameter 1 meter has a mass of 120 kilograms. What is the mass, in kilograms, of a sphere of the same kind of material that has a diameter of 2 meters? 1 solutions Answer 157920 by ankor@dixie-net.com(15624)   on 2009-08-26 16:22:39 (Show Source): You can put this solution on YOUR website!A sphere with a diameter 1 meter has a mass of 120 kilograms. What is the mass, in kilograms, of a sphere of the same kind of material that has a diameter of 2 meters? : Using the volumes of two sphere, we can see: = Therefore 8 * 120 = 960 kilgrams
 Exponents-negative-and-fractional/208707: This question is from textbook Algebra and Trigonometry Structure and Method Book 2 Please, help me with this, step by step: Wrtite in simplest form without negative or zero exponents. (2x^-1)^-2 over 2(y^-1)^-21 solutions Answer 157917 by ankor@dixie-net.com(15624)   on 2009-08-26 16:15:13 (Show Source): You can put this solution on YOUR website!Write in simplest form without negative or zero exponents. Multiply exponents when raising one power to another power, (2 has an exponent of 1) = The reciprocal makes 2's exponent positive = = : : Did this help you understand? ankor@att.com
 Exponents-negative-and-fractional/208710: This question is from textbook Algebra and Trigonometry Structure and Method Book 2 Please, help me with this, step by step: Wrtite in simplest form without negative or zero exponents. p^-1q^-2 over p^-31 solutions Answer 157913 by ankor@dixie-net.com(15624)   on 2009-08-26 15:52:07 (Show Source): You can put this solution on YOUR website!Write in simplest form without negative or zero exponents. Remember the reciprocal changes the sign of the exponent, to make them positive, we can: Add exponents when you multiply =
 Geometric_formulas/208543: what dimensions should the rancher use to obtain the area of 350 with 100 meters of fence?"1 solutions Answer 157910 by ankor@dixie-net.com(15624)   on 2009-08-26 15:33:57 (Show Source): You can put this solution on YOUR website!what dimensions should the rancher use to obtain the area of 350 with 100 meters of fence?" : Using the perimeter equation, get L in terms of W 2L + 2W = 100 Simplify, divide by 2 L + W = 50 L = (50-W) : The area equation L * W = 350 Substitute (50-W) for L (50-W) * W = 350 -W^2 + 50 W = 350 -W^2 + 50W - 350 = 0 W^2 - 50W + 350 = 0 Will not factor use the quadratic formula: a=1, b=-50; c=350 : You should get the lesser solution: W = 8.416 is the width then (the greater solution) L = 50 - 8.416 = 41.584 is the length
 Miscellaneous_Word_Problems/208712: Two pounds of pears and one pound of peaches cost \$1.40. 3 pounds of pears and two pounds of peaches cost \$2.40. How much is the combined cost of one pound of pears and one pound of peaches?1 solutions Answer 157906 by ankor@dixie-net.com(15624)   on 2009-08-26 15:17:36 (Show Source): You can put this solution on YOUR website!Two pounds of pears and one pound of peaches cost \$1.40. 3 pounds of pears and two pounds of peaches cost \$2.40. How much is the combined cost of one pound of pears and one pound of peaches? : Let x = no. of lbs of pears Let y = no. of lbs of peaches ; 2x + 1y = 1.40 y = 1.40 - 2x; this form for substitution 3x + 2y = 2.40 : Substitute (1.4-2x) for y in the above equation 3x + 2(1.4-2x) = 2.40 3x + 2.8 - 4x = 2.4 3x - 4x = 2.4 - 2.8 -x = -.4 x = .40 a lb; pears then y = 1.4 - 2(.40) y = 1.4 - .8 y = .60 a lb; peaches : A pound of each, pear and peach: .40 + .60 = \$1.00
 Miscellaneous_Word_Problems/208716: In a three-person, 100-meter race,Amy finishes 10 meters ahead of Brooke and 20 meters ahead of Carol. Assuming constant speeds for each runner, by how many meters did Brooke finish ahead of Carol?1 solutions Answer 157904 by ankor@dixie-net.com(15624)   on 2009-08-26 15:00:54 (Show Source): You can put this solution on YOUR website!In a three-person, 100-meter race,Amy finishes 10 meters ahead of Brooke and 20 meters ahead of Carol. Assuming constant speeds for each runner, by how many meters did Brooke finish ahead of Carol? : Let t = A's time to run 100 meters then During this time; B ran 90m and C ran 80m : Find their speed: speed = Dist/time : = B's speed and = C's speed : Find B's time to run 100 yds (time = dist/speed) B's time = = 100 * = = Find how far C runs in ; (Dist = speed * time) C's dist = * Cancel t: 80* = = 88.89 ft therefore 100 - 88.89 = 11.11 meters; C is behind when B crosses the finish line : : Hope this makes sense to you?
 Numbers_Word_Problems/208625: THE SUM OF TWO CONSECUTIVE ODD NUMBERS IS 196. WHAT ARE THE NUMBERS?1 solutions Answer 157797 by ankor@dixie-net.com(15624)   on 2009-08-25 21:54:48 (Show Source): You can put this solution on YOUR website!Two consecutive odd numbers: x, (x+2) : THE SUM OF TWO CONSECUTIVE ODD NUMBERS IS 196. x + (x+2) = 196 2x + 2 = 196 2x = 196 - 2 2x = 194 x = x = 97, 99 are the two numbers
 Age_Word_Problems/208630: A man who is 40 years old has three sons, ages 6,3,and 1 . in how many years will the combined age of his three sons equal 80% of his age ?1 solutions Answer 157792 by ankor@dixie-net.com(15624)   on 2009-08-25 21:32:34 (Show Source): You can put this solution on YOUR website!A man who is 40 years old has three sons, ages 6,3,and 1 . in how many years will the combined age of his three sons equal 80% of his age? : Let x = no. of years for this to be true : (x+6) + (x+3) + (x+1) = .8(x+40) : 3x + 10 = .8x + 32 : 3x - .8x = 32 - 10 : 2.2x = 22 x = x = 10 years : : See if that is true 16 + 13 + 11 = .8(50) 40 = 40
 Travel_Word_Problems/208618: The average speed of today's plane is twice that of a plane of 5 years ago and takes 1 1/4 hours less time to fly the same distance of 1500 miles. find the average speed of a plane of 5 years ago ?1 solutions Answer 157790 by ankor@dixie-net.com(15624)   on 2009-08-25 21:25:32 (Show Source): You can put this solution on YOUR website!The average speed of today's plane is twice that of a plane of 5 years ago and takes 1 1/4 hours less time to fly the same distance of 1500 miles. find the average speed of a plane of 5 years ago? : let s = speed 5 yrs ago then 2s = speed today : Write a time equation: Time = - = 1.25 Multiply 2s, results 2(1500) - 1500 = 1.25(2s) : 3000 - 1500 = 2.5s : 1500 = 2.5s : s = s = 600 mph speed 5 yrs ago : : Check solution by finding the times 1500/600 = 2.5 hrs 1500/1200 =1.25 hrs ------------------- time diff: 1.25 hrs
 Angles/208490: I am having trouble setting up this problem: In Triangle ABC, the measure of angle A is 141 degree's more than the measure of angle B. The measure of angle B is the same as the measure of angle C. What is the measure of each angle. 1 solutions Answer 157752 by ankor@dixie-net.com(15624)   on 2009-08-25 18:52:58 (Show Source): You can put this solution on YOUR website!I am having trouble setting up this problem: In Triangle ABC, the measure of angle A is 141 degree's more than the measure of angle B. The measure of angle B is the same as the measure of angle C. What is the measure of each angle. : Let x = angle B then (x+141) = angle A; " A is 141 degree's more than the measure of angle B." x = C; "measure of angle B is the same as the measure of angle C." : A + B + C = 180 (x+141) + x + x = 180 : Find x and you have angle B
 Radicals/208512: 7. What is the conjugate of 6+ 3√8?1 solutions Answer 157720 by ankor@dixie-net.com(15624)   on 2009-08-25 15:56:38 (Show Source): You can put this solution on YOUR website!What is the conjugate of 6 + 3√8? :
 Travel_Word_Problems/208453: a plane flies 500 miles with the wind and 300 miles against the wind in the same length of time. If the speed is 30mph, what is the speed of the plane?1 solutions Answer 157716 by ankor@dixie-net.com(15624)   on 2009-08-25 15:32:14 (Show Source): You can put this solution on YOUR website!a plane flies 500 miles with the wind and 300 miles against the wind in the same length of time. If the wind speed is 30 mph, what is the speed of the plane? ; Let s = speed of the plane in still air then (s+30) = speed with the wind and (s-30) = speed against the wind : Write time equation: Time = : Time with = time against = Cross multiply: 500(s-30) = 300(s+30) : 500s - 15000 = 300s + 9000 : 500s - 300s = 9000 + 15000 : 200s = 24000 s = s = 120 mph, plane in still air : : : Check solution, find the times: 500/150 = 3.33 300/90 = 3.33
 Numbers_Word_Problems/208352: This question is from textbook tennessee prentice hall mathematics algebra 1 find five consecutive odd intergers such that the first and fifth isone lessthan three times the fourth 1 solutions Answer 157709 by ankor@dixie-net.com(15624)   on 2009-08-25 14:32:14 (Show Source): You can put this solution on YOUR website!find five consecutive odd integers such that the first and fifth is one less than three times the fourth : "find five consecutive odd integers" x, (x+2), (x+4), (x+6), (x+8) : "such that the first and fifth is one less than three times the fourth" x + (x+8) = 3(x+6) - 1 : 2x + 8 = 3x + 18 - 1 : 2x + 8 = 3x + 17 : 8 - 17 = 3x - 2x : -9 = x : The numbers: -9, -7, -5, -3, -1 ; ; Check solution: -9 + -1 = 3(-3) - 1 -10 = -9 - 1
 Numbers_Word_Problems/208372: Find four consecutive integers such that twice the first is subtracted from the sum of the other three is 16.1 solutions Answer 157705 by ankor@dixie-net.com(15624)   on 2009-08-25 14:18:09 (Show Source): You can put this solution on YOUR website!Find four consecutive integers such that twice the first is subtracted from the sum of the other three is 16. : Four consecutive integers: x, (x+1), (x+2), (x+3) : Write an equation for the statement: "twice the first is subtracted from the sum of the other three is 16." -2x + (x+1)+(x+2)+(x+3) = 16 3x - 2x + 6 = 16 x = 16 - 6 x = 10 : 10, 11, 12, 13 : : Check solution -2(10) + 11 + 12 + 13 = -20 + 36 = 16