here's the problem.\n\nThere's a cylinder with a d=3in and a h=5in\n\nThe Volume of a cylinder is V=(pi)times(radius square)times(height)\n\n"If the company fills 86400 iced tea cans in 24 hrs.(all shifts), how many gallons of iced tea are packaged in 24 hrs.?"\n\nPlease help me out!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
213906
Well here's some extra info you need to solve the problem:\n\n1 cubic inch = 0.00432900431 US gallons\n\nSo one can has a volume of:\n\nV=(pi)(5)(3/2)^2=35.34291 cubic inches\n\nThey filled 86400 cans which has a volume of:\n\nVtotal = V*86400 = 35.34291*86400 = 3053627.424 cubic inches\n\nThen you need to convert this to gallons so:\n\nVgallons = 0.00432900431 * 3053627.424 = 13219.1662 Gallons
469917
It is always understandable when a student feels overwhelmed by "word problems" because they are often presented in an intimidating manner.  If only they could be FUN again ... if YOU wrote the problem, I believe you might find it fun!  :-)\n\nBut let's allow ourselves some joy once we uncover all the unknowns in this problem.  Perhaps we'll get results from converting "written words" into "mathematical expressions."\n\nWhat's most important is that you understand the shape involved (think "shoe box") and how the "openings" are placed (think "windows" on three faces of the shoe box).  All the openings are understood to be identical.\n\nUsing only the letter X -- which stands for the length of an opening -- we can indeed come up with expressions for every other dimension of the container, as well as the openings.\n\nX = Opening LENGTH (given)\nX-2 = Opening HEIGHT ("length is 2 more than height")\n\n2X+8 = Container LENGTH ("8 more than twice X")\n3 = Container HEIGHT (given)\nX+2 = Container WIDTH ("2 more than length of opening")\n\nThe surface area of the container's sides (minus the three openings) is given as 300 square meters.  The equation is also given as 2 (sides) + 2 (front/back) + 2 (top/bottom) - 3 (openings), so let's just set these equal:\n\n300 = 2 (sides) + 2 (front/back) + 2 (top/bottom) - 3 (openings)\n\nAll we need to do is to write, and then substitute, expressions for the areas in parentheses.\n\nSide area = length * height = 3 (2X+8) = 6X + 24\nFront or back area = width * height = 3 * (X+2) = 3X + 6\nTop or bottom area = length * width = (2X+8) * (X+2)\n____________________________ = 2X^2 + 12X + 16\nOpening area = length * height = X (X-2) = X^2 - 2X\n\nTime to substitute:\n\n300 = 2 (6X+24) + 2 (3X+6) + 2 (2X^2+12X+16) - 3 (X^2-2X)\n\nNow that this (long) equation has been written, it is necessary to solve for X, since we need that value in order to calculate what the problem asks for:  The area of each element.\n\nCollect like terms:\n\n300 = 2 (6X+24) + 2 (3X+6) + 2 (2X^2+12X+16) - 3 (X^2-2X)\n300 = 12X + 48 + 6X + 12 + 4X^2 + 24X + 32 - 3X^2 + 6X\n300 = X^2 + 48X + 92\nX^2 + 48X - 208 = 0\n\nWhat we hope is that the trinomial on the right-hand side of this equation is able to be factored easily!  Does it?\nMy approach is to factor '-208' and see whether I can 'build' the linear term's coefficient ('48') from the factors.\n\n-208 = -2 * 104 = -2 * 2 * 52 = -2 * 2 * 2 * 26 = -2 * 2 * 2 * 2 * 13\n\nCan we group these factors into (one positive, one negative) numbers that produce 48 when added together?  Yes!\n\n(-2*2) + (2*2*13) = -4 + 52 = 48\n\nWe got lucky ... the '-4' and '52' provide the perfect pair of factors needed to create a 48 (through addition), so we can now factor.\n\n0 = (X-4)(X+52)\n\nThings are getting better still, because only one of the zeros (some call them 'roots') from the right-hand side will be positive.  The zeros are 4 and -52, and we will only choose the 4, since it represents a physical measurement of length (of an opening).\n\nWe can go back to the expressions above and substitute X=4.\n\nSide area = 6X + 24 = 6(4)+24 = 48 sq. m\nFront/back area = 3X + 6 = 3(4)+6 = 18 sq. m\nTop/bottom area = 2X^2+12X+16 = 2(4^2)+12(4)+16 = 96 sq. m\nOpening area = X^2 - 2X = 4^2-2(4) = 8 sq. m\n\nI hope this helps!
138273
Hi frenz here is the pattern of FCG Software,\nThere were totally 70 ques, and the duration is 60 mins, out of 70 ques, 30 are english language , based on Antonyms, Synonyms, Sentence completion etc. And the other 40 ques r aptitude. Iam sending only apti ques , bcoz only these ques I remembered. These may not be in the same order, anyway go thru it,\n\n\n1.Judy is now twice as old as Adam,but 6 years ago, she was 5 times as old as he was . How old is judy now?\nA) 10          B) 16         C) 20             D) 24           E) 32\n\n2. if 3x=2(5-2x), then x = ?\nA) –10/7          B) 0         C) 3/7             D) 1           E) 10/7\n\n3. If a is equal to the sum of b and c, which of the following is equal to the difference of  b and c\nA) a-b-c          B) a-b+c         C) a-c             D) a-2c           E) a-b-2c\n\n4.if the sum of five consecutive even integers is t, then, in terms of t, what is the greatest of these integers?\nA) (t-20)/5          B) (t-10)/5         C) t/5             D) (t+10)/5           E) (t+20)/5\n\n5. If a school cafeteria needs c cans of soup each week for each student, and if there are s students  in the school, for how many weeks will x cans of soup last?\nA) csx          B) xs/c         C) s/cx             D) x/cs           E) cx/s\n\n6. A vendor sell h hot dogs and s sodas. If a hot dog costs twice as much as  a soda, and if the vendor takes in a total of d dollars , how many cents  does a soda cost?\nA)100d/(s+2h)          B) (s+2h)/100d         C)d(s+2h)/100\nD) 100d(s+2h)           E) d/100(s+2h)\n\n7.Yann will be x year old y years from now . How old was he z years ago?\nA)x+y+z          B) x+y-z         C)x-y-z             D)y-x-z           E)z-y-x\n\n8.At Medison High school each student studies exactly one foreign language. Three-fifth of the students take Spanish,and one-fourth of the remaining students take German. If all of the others take French, what percent of the students take French?\nA)10          B)15         C) 20             D) 25           E) 30\n\n9.From 1994 to 1995 the sales of a book decreased by 80%. If the sales in 1996 were the same as in 1994, by what percent did they increase from 1995 to 1996?\nA)80%         B)100%         C) 120%             D) 400%           E) 500%\n\n10. if 25% of 260 equals 6.5% of a, what is a?\nA) 10          B) 65         C) 100             D) 130           E) 1000\n\n11. in a certain club , the ratio of the number of boys to girls is 5:3. what percent of the members of club are girls?\nA) 37.5%          B) 50%         C) 60%             D) 62.5%           E) 80%\n\n12. From 1980 to 1990 , Lior’s weight increased by 25% . if his weight was k kilograms in 1990, what was it in 1980?\nA)1.75k          B) 1.25k         C) 1.20k             D) 0.80k           E) 0.75k\n\n13. Evan has 4 times as many books as David and 5 times as many as Jason .If Jason has more than 40 books , what is the least number of books that Evan could have ?\nA)200          B)205         C) 210             D) 220           E) 240\n\n14. Alison is now three times as old as Jermy, but 5 years ago , she was 5 times as old as he was . How old is Alison now?\nA) 10          B) 12         C) 24             D) 30           E) 36\n\n15. What is the largest prime factor of 255?\nA) 5          B) 15         C) 17             D) 51           E) 255\n\n16. if w widgets cost c cents , how many widgets can you get for d dollars?\nA) 100dw/c          B) dw/100c         C) 100cdw             D) dw/c           E) cdw\n\n17. if 120% of a is equal to 80% of b, which of the following is equal to a+b? \nA) 1.5a       B) 2a       C) 2.5a         D) 3a         E) 5a\n\n18. if x and y are integers such that x3=y2 , which couldnot be the value of y?\nA) -1        B) 1        C) 8           D) 16          E) 27\n\n19. what is a devided by  a% of a ?\nA) a/100    B) 100/a    C) a2 /100      D) 100/a2     E) 100a\n\n20. If an object is moving at a speed of 36 kilometers per hour , how many m
58722
You all thought way too hard on this one. There is no way to know who has more because the asker did not tell what size the containers were. \nWhoever had the biggest container had more because the numbers he gave are more than 1, you can not fill a container 1 and 2/3 of the way, nor can you fill one 7/4 of the way. Once they get to the top, they are full at 1 each. For example, if you try to pour 1 and 3/4 gallons (which is 7/4) into a one gallon container, you will only have one gallon in the container.\nIf both containers were the same size they both have the same amount.
45728
OK, let T be the time (in days) that the job takes.  You know that x can do one fourth of the job in a day, y can do a sixth, and z can do a half.  You have one job to do.  so the equation is set up:\n\n1/4T+1/2T+1/6T=1\n\n24 is a common denominator, so:\n6/24T+12/24T+4/24T=1\n\nNow add the fractions, you get:\n\n22/24T=1\n22T=24\nT=24/22, or 12/11 days (little better than 1 day)
56977
Pay more attention in class! And assuming it is an ideal gas, use PV=nRT. Since there is not change in volume you can basically drop it from the equation and make P=nRT. If you like algebra you can leave it in but it will cancel out eventually. You could solve for 'n' first using initial P and T, and then plug and chug.
28833
In case you want more than just the answer so you can do similar problems on your next test:\n\nQ: What do have to find? \nA: The number of bottles of apple juice (call it A)\nand the number of bottles of orange juice (call it B).\n\nQ: What do you already know about A and B?\nA: You know that together A and B total 12 bottles.\n(A + B = 12)\n\nYou also that you paid $15 for the 12 bottles. You paid $1 for each bottle of apple juice (1xA) and you paid $1.50 for each bottle of orange juice (1.5B)\n\nSo $15 = $1xA + 1.5xB\n\nQ: What next?\n\nA: You have two equations with two unknowns:\n\nA + 1.5 B = 15\nA +     B = 12\n\nSubtract the left hand sides and the right hand sides to get\n      .5B = 3\n\nDivide both sides by .5 to get\n    B = 6\nso  A = 12-6 = 6\nCheck:\n$1x6 + $1.5x6 = $6 + $9 = $15
187995
Given that the volume of the cylindrical can is 100 cm^2...\n\n100 = (pi)r^2h\n\ndivide both sides by (pi)r^2 to isolate h\n\nh = 100/(pi)r^2\n\nSo, if the radius is 2 cm...\n\nh = 100/((pi)*4) - r^2 = 2^2 = 4\n\nh = 7.96 cm, rounded to first two decimal places, using 3.14 as the value for pi.
502362
The formula for a cylindrical volume is (pi)(radius)^2(depth)\nSo the total volume of water we are working with is:\n(Vtot) = (pi)(4)^2(12.5) = 200(pi)                  [eq1]\n\nThe volume of water in Tank1 and Tank2 at particular depths d1 and d2 are:\n(Vtank1) = (pi)16(d1)                                    [eq2]\n(Vtank2) = (pi)9(d2)                                      [eq3]\n\nWe also know that at any given moment...\n(Vtank1)+(Vtank2) = (Vtot)                            [eq4]\n\nWe want to know the volume in Tank2 when the water depth in both tanks are the same, so let d1 = d2 = d, and solve equation [eq4]  using [eq1], [eq2] and [eq3]:\n\n(pi)16(d) + (pi)9(d) =  200(pi)\n\n16(d) + 9(d) = 200\n\n25d = 200\n\nd = 8\n\nUsing [eq3], determine out how much water Tank2 has in it when its depth is 8.\n\n(Vtank2) = (pi)9(8) = 72(pi) =  226.1952 m^3\n\nIf the pump is running at 10 m^3/min, then Tank2 will have 226.1952 m^3 of water in it after 226.1952/10 minutes.\n\nAnswer:  22.6 minutes
407738
For your first, |x - 3| > 10\n\nFor your second, if two cans of soda cost $1.40, how much would 7 cans cost?
552029
1. Bob's favorite ice cream used to cost $1.50.... Then the price was raised to $1.75. Find the percent increase.\n(175/150)-1)*100%=16 2/3% increase\n\n2. Jenny paid $12,000 for her car. Five yrs later she sold it for $8500. What percent decrease was this?\n(8500/12000-1)*100%= -29 1/6% 29 1/6% decrease\n\n3. The Music Box marked up their CD's 75%. If the music box charges $20 for a special cd, how much did it cost before the mark-up? (hint: the answer is not $15)\n$20=1.75x\nx=20/1.75=$11.43\n\n4. Quinn deposits $2000 in a savings account that pays 4% compounded semi-annuallly. HOw much money will Quinn have in her account after two years? Give the expression. (you do not have to simplify) \n\n$2000(1.02)^4=$2164.86
673698
The volume of the sphere is 4/3*pi*r^3\n\nThe volume of the cylinder is pi*r^2*h\n\nSince the cylinder's h is the same as 2r, then the volume becomes pi*r^2*2r which is the same as 2*pi*r^3.\n\nThe fraction of the space taken up by the sphere is the same as:\n\n4/3*pi*r^3\n-------------\n2*pi*r^3\n\nwhich is the same as:\n\n4/3\n----\n2\n\nwhich reduces down to 2/3
234264
1(A) 1 L = 1000 cm^3 therefore 2L = 2000 cm^3\n1(B) 1 L = 1 Kg therefore 2L = 2Kg\n\n*******************\n\n2)\nTwo thirds less than half of what number is five sixths\n(1/2)X - (2/3) = (5/6)\n\nmultiply every term by 6\n3x - 4 = 5\n\nadd 4 to both sides\n3x = 9\nx = 3\n\n*******************\n\n3)\nvolume of a cube = side^3 = 12^3 = 1728 cubic inches\nvolume of square pyramid = (1/3)(b^2)(h)\n where b = 12 and h = 8 (because the total height = 20)\n\n v = (1/3)(144)(8) = 384 cubic inches\n\n total volume = 2112 cubic inches\n\n*******************\n\n4)\nwe do not know the relation ship between the segments, if they form a line, if they form a right triangle, or if they lie on top of each other....\n\nif they form a line segment, where "b" is between "a" and d", then the total meximum length is 12 + c. if they lie on top of each, then they have a minimum distance of |12 - c| (absolute value of 12 - "c")\n\n*******************\n\n5)\nyou would need (1 x 10^3 or 1000) to form 1 meter multiplied by 1000 to form 1 KM\n1000 x 1000 = 1,000,000 or 1 x 10^ 6\n\n*****************\n6)\nx^2 + x  : GCF = x\nx(x + 1)\n\n\n12m^2n^3 + 18mn^2 - 24m^2n^3 \n12m^2n^3 and 24m^2n^3 are like terms\ntherefore\n\n= -12m^2n^3 + 18mn^2\n\nGCF = 6mn^2\n\n6mn^2(-2mn + 3) or 6mn^2(3 - 2mn)\n\n*****************\n\n7)\n-2 2/3w - 1 1/3 = 4 \n\nadd 1 1/3 to both sides\n\n-2 2/3w = 5 1/3\n\n= -(8/3)w = (16/3)\n\nmultiply both sides by -(3/8)\n\nw = -2
417035
32h + 24c = 432  --> drove a total of 432 miles, need to find h and c, highway and city gallons.\n\nh + c = 16  ---> used 16 gallons\n\nUse substitution:  h = 16 - c\n\n32(16 - c) + 24c = 432\n\n512 - 32c + 24c = 432\n\nCombine like terms:\n\n512 - 8c = 432\n\n-8c = -80\n\nc = 10 gallons.  At 24 miles/gallon city, drove 240 miles in the city, \nso must have driven 432 - 240 = 192 miles on the highway.\n\nCheck your work:\n\n32(6) + 24(10) = 432.  (6 gallons on the highway)
131556
If x is the time it will take, then\n\n4x + 2x + 4x/3 = 20\n\nSolve for x and get 2.73 minutes.\n\nThe answers below are more complete.  They've pointed out that in real-world time, it would take 3 mins because you can't serve half a drink.
245302
28 buckets of water needed...\n\nVolume of a sphere (primary water tank) = 4/3 x pi x r^3\n\nso v= 4/3 x 3.14 x 4.5^3\n\nv= 381.7 L (primary tank)\n\nthe mayor wants to fill it up to 6.5 meters from the bottom. If the radius of the primary water tank is 4.5, the diameter is 9 because d=2r. Because the diameter is 9, you take 6.5/9 to find out what percent of the tank he wants filled, which equals 72%. Then take the 381.7 L total x 72% which says the mayor wants to fill the tank with 275.7 L of water. If one bucket holds 10 L which equals .01 m^3, then take 275.7L/.01m^3 to find out how many buckets you need... which equals  27,500 buckets...\n\ni had to recalculate everything because i forgot about the area and having the meters cubed..\n\n27,500 buckets is the right answer\n\nim leaving mine up here...\n\nhere is the CORRECT answer though.  ALL credit is given to Philo who calculated this.  Thank him for the correct answer.\n\n1st, the volume of the tank is (4/3)π(4.5)^3 = 381.7035 cubic meters. The part left unfilled is a spherical cap whose volume formula is (π/6)(3r1² + h²)h, where r1 is the radius of the base of the cap, and h is its height. The height here is 9 - 6.5 = 2.5, and r1² = 4.5² - (6.5-4.5)² = 16.25. \n\nSo the volume of the unfilled cap is (π/6)(3*16.25 - 2.5²)*2.5 = 55.6324 cubic meters. We subtract that from the volume of the tank to get 326.0711 cubic meters of water when the tank is filled 6.5 meters deep. \n\nNow one liter fills a cube 1/10 of a meter on a side (10 cm), so a bucket is 1/100 of a cubic meter. Multiplying the required volume gives 32,607.11 buckets, which rounds up to 32,608.\n\nI mistakenly assumed the volume of the tank was proportional to the depth of water, which would be true for a cylinder, but not for a sphere.
196125
Let's think about how to solve these and maybe that will help you with others,\n\n1. Christian makes the trip twice as fast as Eloise.  Therefore his trip would take half the time.  If his trip was three hours shorter, then 3 hours is half the time.  His trip was 3 hours, Eloises was 6 hours.  So if Christian traveled at 30 mph for 3 hours, and Eloise traveled at 15mph for 6 hours .. how far is that?\n\n[modified below with details for additional answers]\n2. Basically \n4mph x SomeTime = SomeDistance\n5mph x (Sometime-1 hour) = SomeDistance\n\nor, \nif 4x=y and 5(x-1)=y\nthen,\n4x=5x-5\n4x-5x=-5\n-x=-5\nx=5  (this is the SomeTime)\n\ngoing back to the first equation\n4mph x SomeTime = SomeDistance\n4mph x 5hours = 20 Miles\n\ndoublecheck with the second equation,\n5mph x (Sometime-1hour) = SomeDistance\n5mph x (5hours-1hour) = 5mph x 4hours = 20 miles\n\n\n3. If the fast freight was going 60mph for 6 hours (noon to 6pm), then the whole trip is how far? .. 360 miles.  If the slow freight takes 8 hours to go 360 miles, then what is the speed of the slow freight?  360mph/8m = 45 mph