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Recent problems solved by 'mathstutor494'
mathstutor494 answered: 95 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119, >>NextMixture_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
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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
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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 Ans
1 solutions
Answer 450900 by mathstutor494(95) on 2013-04-17 11:46:23 (Show Source):
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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
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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
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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
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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
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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):
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Rectangles/555571: width of a rectangle is 6 kilometers lesss than twice its length.if its area is 56 sqare kilometers
1 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
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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):
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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
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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):
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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
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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,
AR
1 solutions
Answer 359102 by mathstutor494(95) on 2011-12-29 02:49:30 (Show Source):
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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
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