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Recent problems solved by 'mathstutor494'

 Mixture_Word_Problems/738729: How much of a 7% alcohol solution should be mixed with how much of a 15% alcohol solution so that you get 20 gallons of a 12% alcohol solution?1 solutions Answer 450910 by mathstutor494(95)   on 2013-04-17 13:20:21 (Show Source): You can put this solution on YOUR website!Let x be the number of gallons of 15% alcohol Therefore number of gallons of 7% alcohol = 20-x x*0.15+(20-x)*0.07=20*0.12 0.15x+1.4-0.07x = 2.4 0.15x-0.07x = 2.4 - 1.4 0.08x = 1 x = 1/0.08 = 12.8 Gallons Ans : 12.8 Gallons of 15% alcohol 7.2 Gallons of 7% alcohol
 Geometry_Word_Problems/738731: the area of a rectangular slab of sidewalk is 45 square feet. its length is 3 feet more than four times the width.find the length and the width. Let width be x feet Then length = 4x+3 Area = x*(4x+3) which is equal to 45 (given) Therefore x*(4x+3)= 45 4x^2+3x = 45 4x^2 + 3x -45=0 4x^2 + 15x -12x -45=0 x*(4x+15) -3*(4x+15)=0 (x-3)(4x+15)=0 so x=3 or 15/4 Ans : Length = 15ft and width=3ft 1 solutions Answer 450903 by mathstutor494(95)   on 2013-04-17 11:58:18 (Show Source): You can put this solution on YOUR website!Let width be x feet Then length = 4x+3 Area = x*(4x+3)which is equal to 45 (given) Therefore x*(4x+3)= 45 4x^2+3x = 45 4x^2 + 3x -45=0 4x^2 + 15x -12x -45=0 x*(4x+15) -3*(4x+15)=0 (x-3)(4x+15)=0 so x=3 or 15/4 Ans : Length = 15ft and width=3ft
 Percentage-and-ratio-word-problems/738732: Joe has 450.00 to spend on company party. he spends 1/2 on food and 1/3 on decorations. What fraction represents portion he spent on food and decorations? Total spent = (1/2 + 1/3 ) = 5/6 Fraction spent on food and decorations > 5/6 Ans1 solutions Answer 450900 by mathstutor494(95)   on 2013-04-17 11:46:23 (Show Source):
 Numbers_Word_Problems/556785: The average of three numbers is 10 more than the least of the numbers and 15 more than the greatest. The median of the numbers is 5. What is their sum?1 solutions Answer 362237 by mathstutor494(95)   on 2012-01-13 01:24:43 (Show Source): You can put this solution on YOUR website!The question seems to be incorrect.
 Geometry_Word_Problems/556786: The angle theta is formed by the positive x axis and a ray through the point (5, -12). Find the value of sin(theta), cos(theta), and tan(theta)1 solutions Answer 362236 by mathstutor494(95)   on 2012-01-13 01:05:19 (Show Source): You can put this solution on YOUR website!Ans : sin(theta)= -5/13 cos(theta)= 12/13 tan(theta)= -5/12 If you need more help, email me at mathstutor494@gmail.com
 Linear_Equations_And_Systems_Word_Problems/556779: Mario has P5000 to invest and decides to invest part of it at 4% and the rest of it at 6 1/2 %. If the total interest for the year is P245, how much does Mario have invested at each rate?1 solutions Answer 362235 by mathstutor494(95)   on 2012-01-13 00:57:45 (Show Source): You can put this solution on YOUR website!Mario has P5000 to invest and decides to invest part of it at 4% and the rest of it at 6 1/2 %. If the total interest for the year is P245, how much does Mario have invested at each rate? Ans : Mario invested P3,200 @4% and P1,800 @6.5% rate If you need more help, email me at mathstutor494@gmail.com
 Linear_Equations_And_Systems_Word_Problems/556781: Will is 4 years older than Phil. Three years from now, Will will be twice as old as Phil was last year. Find their present ages.1 solutions Answer 362234 by mathstutor494(95)   on 2012-01-13 00:45:13 (Show Source): You can put this solution on YOUR website!Ans : Will 7 years, Phil 3yrs f you need more help, email me at mathstutor494@gmail.com
 Parallelograms/556782: ABCD is a quadrilateral with AB = 8, BC = 13 and DC = 15. What is the maximum possible integral value of AD?1 solutions Answer 362233 by mathstutor494(95)   on 2012-01-13 00:41:27 (Show Source): You can put this solution on YOUR website!Ans = 35 If you need more help, email me at mathstutor494@gmail.com
 Linear_Equations_And_Systems_Word_Problems/556777: If 5 is subtracted from two thirds of a number, the result is 5 more than one-fourth of the number.What is the number? 1 solutions Answer 362232 by mathstutor494(95)   on 2012-01-13 00:20:38 (Show Source): You can put this solution on YOUR website!Ans : Number is 24 If you need more help, email me at mathstutor494@gmail.com
 Complex_Numbers/556549: solve quadratic equation by completing the square -x^2-2x=5 1 solutions Answer 362231 by mathstutor494(95)   on 2012-01-13 00:05:22 (Show Source): You can put this solution on YOUR website!-x^2-2x=5 > x^2+2x+5=0 > x^2+2x+1+4=0 > (x+1)^2=-4 >(x+1)^2=4i^2 So x+1 = +-2i x= -1+-2i
 absolute-value/555812: Can you please solve this for me? 2|x-3|+5=31 solutions Answer 362039 by mathstutor494(95)   on 2012-01-11 23:35:34 (Show Source): You can put this solution on YOUR website!2|x-3|+5=3 2|x-3|=3-5 2|x-3|=-2 |x-3|=-2/2 |x-3|=-1 Therefore x-3= -1 or -(x-3)=-1 x=-1+3 or -x=-1-3 x=2 or x=4
 Surface-area/555620: A hemispherical dome holds a volume of 486 pie ft^3. Find the surface area. (omit the area of the circle) * please help me!!!***1 solutions Answer 361868 by mathstutor494(95)   on 2012-01-11 09:17:54 (Show Source): You can put this solution on YOUR website!A hemispherical dome holds a volume of 486 pie ft^3. Find the surface area. Volume of Semisphere = 2/3 pi r^3 > 486 = 2/3 pi r^3 > r^3 = (486*3)/(2*pi) Hence r = 9/ 1.46 > 6.16 Surface Area of a Semisphere = 2 pi r^2 Area of a circle = pi r^2 So Surface Area of a Semisphere less Area of a circle > 2 pi r^2 - pi r^2 > pi r^2 Substituting values of pi & r from above > 3.14* (6.16)^2 > 119.15 ft^2
 Geometry_Word_Problems/555619: i have a wall 11ft x 8ft.how much wall paper will i need to cover this wall.need in answer to be in M2. 1 solutions Answer 361861 by mathstutor494(95)   on 2012-01-11 08:49:33 (Show Source): You can put this solution on YOUR website!What is M2?
 Money_Word_Problems/555618: Jill Roger borrowed \$16,000 to buy a new boat. Assuming an interest charge of \$2,900 what will be her monthly payment if she takes 30 months to repay the loan (+interest). Assume the loan is repaid in equal payments.1 solutions Answer 361860 by mathstutor494(95)   on 2012-01-11 08:48:45 (Show Source): You can put this solution on YOUR website!Amount to be repaid including interest = 16,000+2,900 i.e. 18,900 Time/months to repay the loan (+interest) = 30 Hence equally monthly installment = 18,900/30 Ans = \$ 630
 Mixture_Word_Problems/555567: the area of a rectangular filed is 450m^2and the difference between the lengths of two adjacent sides is 7m. find the of the perimeter of the rectangle. 1 solutions Answer 361847 by mathstutor494(95)   on 2012-01-11 03:24:22 (Show Source): You can put this solution on YOUR website!Let width be "x" So length = x+7 Hence area = x*(x+7) which is equal to 450 > x^2 + 7x = 450 > x^2 + 7x -450=0 > x^2 + 25x - 18x -450=0 > x(x+25) -18(x+25)=0 > (x-18) (x+25) > x = 18 or -25 Ans = length of the shorter side 18m
 Polygons/555570: If I have a 4 sided polygon and one side is 68 degrees and 100 degrees and a 90 degree angles, how do I find what a is? 1 solutions Answer 361845 by mathstutor494(95)   on 2012-01-11 03:07:00 (Show Source): You can put this solution on YOUR website!Sum of interior angles of 4 sided polygon = 360 degree Hence fourth angle is = 360-100-90-68 102 Degree
 Rectangles/555571: width of a rectangle is 6 kilometers lesss than twice its length.if its area is 56 sqare kilometers1 solutions Answer 361844 by mathstutor494(95)   on 2012-01-11 03:02:33 (Show Source): You can put this solution on YOUR website!Let Length be "x" Then width = 2x-6 Area = x*(2x-6) which is equal to 56 Sq Km so the eqn is x*(2x-6)=56 >2x^2 - 6x = 56 > 2x^2 - 6x - 56=0 > x^2 - 3x-28=0 (dividing by 2) > x^2 -7x + 4x -28 = 0 > x(x-7) +4(x-7) = 0 > (x+4) (x-7) = 0 So x = -4, 7 As length can't be negative, so the answer is Length =7km, Breadth = 8km
 Coordinate-system/555572: (π,0),(π/2,1) finding the distance between two points. I don't understand how the pi can be simplified to use in the distance formula.1 solutions Answer 361842 by mathstutor494(95)   on 2012-01-11 02:53:36 (Show Source): You can put this solution on YOUR website!Substitute pi by its numeric value i.e. 3.14 So the 2 points are (3.14,0), ( 1.57,1) Now apply Distance Formula
 test/555574: 12b+6+12=6b+2-141 solutions Answer 361841 by mathstutor494(95)   on 2012-01-11 02:48:20 (Show Source): You can put this solution on YOUR website!12b+6+12=6b+2-14 > 12b+18=6b-12 Rearranging similar terms >12b-6b = -12-18 >6b = -30 > b= -30/6 b= -5 Ans
 Rate-of-work-word-problems/555575: three taps together can fill a tank in 10 minutes. the first tap alone can fill it in 30 minutes nad the second tap alone in 25 minutes . in how much time will the third tap alone fill the tank?1 solutions Answer 361840 by mathstutor494(95)   on 2012-01-11 02:45:07 (Show Source): You can put this solution on YOUR website!1/10 - (1/30 + 1/25) > 37.5 minutes
 Percentage-and-ratio-word-problems/555576: If 1 US Dollar = 0.68 Sterling pounds, then how many US Dollars is 1 Sterling pound?1 solutions Answer 361839 by mathstutor494(95)   on 2012-01-11 02:40:52 (Show Source): You can put this solution on YOUR website!1/0.68> 1.47
 test/555573: 1 solutions Answer 361837 by mathstutor494(95)   on 2012-01-11 02:18:08 (Show Source): You can put this solution on YOUR website!What is the problem?
 Average/553465: A number is multiplied by 3. If 3 is subtracted from the product you get 24? 1 solutions Answer 360865 by mathstutor494(95)   on 2012-01-06 10:19:17 (Show Source): You can put this solution on YOUR website!Let the number be "x". Given that when x is multiplied by 3 and 3 is from the product you get 24 3x-3=24. Adding 3 to both sides, we get 3x=27 So x=9 Ans
 Complex_Numbers/553467: Simplify 4- squareroot3/ 2-squareroot3 rationalize the denominator 1 solutions Answer 360861 by mathstutor494(95)   on 2012-01-06 09:42:23 (Show Source): You can put this solution on YOUR website!4- squareroot3/2-squareroot3 Rationalize the denominator by multiplying above term by (2+squareroot3), we get > {(4- squareroot3)*(2+squareroot3)}/{(2-squareroot3)*(2+squareroot3)} > {(8-(2squareroot3)+(4squareroot3)-3}/(2-3) Rearranging similar terms, we get > (5+2squareroot3)/-1 > -(5+2*1.73) > -8.46 Ans
 Mixture_Word_Problems/551049: A goat is tied to one of the corners of a rectangular barn on a rope that is 50 feet long. The dimensions of the barn are 40 feet by 30 feet. Assuming that the goat can graze wherever its rope allows it to reach, what is the square footage of the grazing area for the goat?1 solutions Answer 359319 by mathstutor494(95)   on 2011-12-30 07:24:24 (Show Source): You can put this solution on YOUR website!As the rope covers entire area of the barn, goat will 40*30= 1200 Sq Ft
 Proportions/550797: Divide Rs 1,870 into three parts in such a way that half of the first part,one-third of the second part and one-sixth of the third part are equal.1 solutions Answer 359103 by mathstutor494(95)   on 2011-12-29 03:13:05 (Show Source): You can put this solution on YOUR website!Let equal part be "x" > first part = 2x > second part = 3x > third part = 6x As sum total of all parts = 1870 Therefore 2x+3x+6x = 1870 > 11x = 1870 So x = 1870/11 > 170 Ans
 logarithm/550794: Can you pls. help me solve this log prob. (Have a few others: would be happy to donate if this is the kind of problem you can solve.) When I convert logs to exponents, I have perfect squares, some things cancel, and--of course--I have reciprocals, so some things become -1. However, I'm still not getting the "clean" answer I expect. Solve for X: 2 log bx = 2 log b(1-a) + 2 log b(1 + a) - log b (1/a - a)^2 Thanks very much, AR1 solutions Answer 359102 by mathstutor494(95)   on 2011-12-29 02:49:30 (Show Source): You can put this solution on YOUR website!The eqn seems erroneous. Pls check and revert by email.
 expressions/550795: kindly evaluate (-8)5(1)81 solutions Answer 359100 by mathstutor494(95)   on 2011-12-29 02:42:24 (Show Source): You can put this solution on YOUR website!(-8)5(1)8 > (-8)*5*(1)*8 > -320
 Linear-equations/550796: How to solve this in linear equation:49.6*x-207.8=0?1 solutions Answer 359099 by mathstutor494(95)   on 2011-12-29 02:35:17 (Show Source): You can put this solution on YOUR website!49.6*x-207.8=0 >49.6*x=207.8 >x = 207.8/49.6 > x = 4.18
 Equations/550544: find x+1/x if x-1/x= square root of 51 solutions Answer 358921 by mathstutor494(95)   on 2011-12-28 10:43:55 (Show Source): You can put this solution on YOUR website!x-1/x = square root of 5 Squaring both sides >x^2+(1/x^2)-2=5 >x^2+(1/x^2)=5+2 >x^2+(1/x^2)=7 Adding 2 to both sides >x^2+(1/x^2)+2=7+2 >(x+1/x)^2= 3^2 Square root of above eqn... Ans x+1/x=3
 Geometry_Word_Problems/550579: Find the angles of a triangle if one angle exceeds a second angle by 45 degrees and is three times as large as the third angle. A woman is 5 times as old as her youngest daughter. How old is each now if the sum of their ages is 50? A motor boat travels at the rate of 50kph down the river. If the current of the river is 5kph, how far can it travel up the river in 2 hours? The age of a man is 10 years more than three times his brother's age. Find the age of each if 5 years from now he will be 4 years more than twice his brother's age. A reservoir can be filled by one pipe in 6 hrs and by another pipe in 8 hrs. It can be emptied by a third pipe in 10 hrs. Starting empty, how long will it take to fill the reservoir if all pipes are open?1 solutions Answer 358877 by mathstutor494(95)   on 2011-12-28 04:43:48 (Show Source): You can put this solution on YOUR website!Let one angle be x So second angle = x-45 and third angle = x/3 As sum of all the 3 angles add up to 180 deg Therefore x+(x-45)+(x/3) = 180 > x = 96.42 Ans : Angle of the triangles are 96.42, 51.42 and 32.14