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Recent problems solved by 'Greenfinch'
Greenfinch answered: 383 problems
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Triangles/294613: in a right triangle the measures of the legs are 8 and x+6, and the measure of the hypotenuse is x+8. solve for x
1 solutions
Answer 212508 by Greenfinch(383)   on 2010-04-21 07:36:16 (Show Source):
You can put this solution on YOUR website!Using Pythagoras
8^2 + (X + 6)^2 = (X + 8)^2
64 + X^2 + 12X + 36 = X^2 + 16X + 64
12X +36 = 16X
4X = 36
X = 9
Check sides are 8, 15, 17 which is a right-angled triangle
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Miscellaneous_Word_Problems/292879: The population of a town is 126800. It increases by 15% in the 1st year and decreases by 20% in the 2nd year. What is the population of the town at the end of two years?
(1) 174984 (2) 135996 (3) 116656 (4) 145820 (5) None of these
1 solutions
Answer 211438 by Greenfinch(383) on 2010-04-16 05:51:24 (Show Source):
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Rectangles/290954: If the length of a rectangle is 3 feet longer than the width and
the diagonal is 15 feet, then what are the length and width?
1 solutions
Answer 210638 by Greenfinch(383) on 2010-04-12 15:53:01 (Show Source):
You can put this solution on YOUR website!width is x, length is x + 3, diagonal is 15
using Pythagoras x^2 +(x + 3)^2 = 225
2x^2 + 6x + 9 = 225
2x^2 + 6x -216 = 0
x^2 + 3x - 108 = 0
(x + 12 )(x - 9)= 0
x = -12, or +9
width is 9, length is 12, diagonal is 15 (a 3,4,5 triangle)
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Word_Problems_With_Coins/291019: A box contains $6.25 in nickels, dimes, and quarters. There are 85 coins in all, with three times as many nickels as dimes. How many quarters are there.
1 solutions
Answer 210569 by Greenfinch(383) on 2010-04-12 05:00:37 (Show Source):
You can put this solution on YOUR website!no of dimes is X, no of nickels is 3X, no of quarters is 85 - 4X
so 10X + (3Xx5) + (85 - 4x)x25 = 625 (do it all in cents)
10X + 15X + 2125 -100X = 625
-75X = -1500
X = 20,
so 20 dimes, 60 nickels and 5 quarters
To check 20 x 10 = 200
60 x 5 = 300
5 x 25 = 125
total = 625 or $6.25
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Geometry_Word_Problems/291021: The perimeter of a triangle is 81 cm. The smallest side is 7cm.shorter than the medium side. The medium side is 4 cm.shorter than the longest side. Find the lengths of the three sides.
1 solutions
Answer 210568 by Greenfinch(383) on 2010-04-12 04:54:24 (Show Source):
You can put this solution on YOUR website!Shortest side is X, medium side is X + 7, longest side is X + 11
perimeter is X + (X + 7) + ( X + 11) =3X + 18 = 81
So 3X= 63
X = 21, other sides are 28 and 32
perimeter is 21 + 28 + 32 = 81 so it checks
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Geometry_Word_Problems/291025: The side of a square is 5 cm. shorter than the side of an equilateral triangle. The perimeter of the square is 7 cm. less than the perimeter of the triangle. Find the lengths of a side of the square and of a side of the triangle.
1 solutions
Answer 210565 by Greenfinch(383) on 2010-04-12 04:28:13 (Show Source):
You can put this solution on YOUR website!Side of square is X, side of triangle is X+8
perimeter of square is 4X, perimeter of triangle is 3X + 24
We are told that 4X + 7 = 3X + 24
or X = 17
So side of square is 17, side of triangle is 25
perimeter of square is 68, perimeter of triangle is 75
It checks
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Functions/291039: Train A and B are traveling in the same direction on parallel tracks.
Train A is traveling at 60 miles per hour and train B is traveling at 80 miles per hour. Train A passes a station at 8:25AM. If train B passes the same station at 8:40AM at what time will train B catch up to train A? _____:______
1 solutions
Answer 210563 by Greenfinch(383) on 2010-04-12 04:19:31 (Show Source):
You can put this solution on YOUR website!At 8:40, train A is 15 miles down the track. the difference is speeds of the two trains is 20 miles/hour, so the question reduces to how long will it take train B, at 20 miles /hour to cover 15 miles? Answer 45 minutes.
so they pass at 9:25 am
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Coordinate-system/291043: a rectangular corral has a perimeter of 64 yards. Its lenth is 8 yards more than its width. What are the dimensions of the corral?
1 solutions
Answer 210562 by Greenfinch(383) on 2010-04-12 04:14:38 (Show Source):
You can put this solution on YOUR website!Call the width X and thus the length is X + 8
Perimeter is 2X + 2(X+8) = 64
4X + 16 = 64
4X = 48
X = 12, so length should be 20
2x width = 24, 2 x length is 40 total perimeter is 64, it checks
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Coordinate-system/291045: audrey has 35 dimes and quarters in her piggy bank with a total value of 6.95. How many of the coins are dimes and how many are quarters?
1 solutions
Answer 210561 by Greenfinch(383) on 2010-04-12 04:10:32 (Show Source):
You can put this solution on YOUR website!Not being American, i assume a dimes is 10 cents and a quarter is 25 cents.
There are 35 coins, so call the number of quarters X and the number of dimes 35 -X
The equation is then 25X + 10(35 - X) = 695 (Do it all in cents)
25X + 350 - 10X = 695
15X = 345
X= 23
So there should be 23 quarters and 12 dimes
Check 23 x 25 + 12 x 10 = 575 + 120 = 695
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Rate-of-work-word-problems/291044: Q.1 If a:m=5:8 and m:d=7:14 then a:d will be....?
Q.2 A pipe fill tank in 5 mins, B fill in 6 mins. Both will fill in mins...?(by working at same time)
1 solutions
Answer 210560 by Greenfinch(383) on 2010-04-12 04:04:25 (Show Source):
You can put this solution on YOUR website!a:m = 5:8, m:d = 7:14 = 1:2
a:d is thus 5:8:(8x2) or 5:16
A fills 1/5 per min, B fills 1/6 per min. Together, they fill at 1/5 + 1/6
So 6 + 5 over 30 = 11/30ths per min. Time is thus 30/11 = 2 8/11 mins
Roughly 2 mins 44 secs
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Surface-area/290838: A rectangular painting with a width of x centimeters has an area of x2 + 50x square centimeters. Find a binomial that represents the length. See the figure below.
1 solutions
Answer 210431 by Greenfinch(383) on 2010-04-11 16:27:24 (Show Source):
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Linear-equations/290776: Find an equation of the line that passes through (2,2) and is perpendicular to y=2x-6. need help thanks.
1 solutions
Answer 210427 by Greenfinch(383) on 2010-04-11 16:16:58 (Show Source):
You can put this solution on YOUR website!Gradient of y = 2x - 6 is 2, so gradient of the perpendicular is -1/2
So equation is 2y + x = c
To go through (2,2) 2x2 + 2 = c, so c = 6
Equation is thus 2y = x = 6
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Rectangles/290798: The length of a rectangle is twice the width of the rectangle. The length of a diagonal of the rectangle is 25cm. How do I find out the are of the rectangle?
1 solutions
Answer 210421 by Greenfinch(383) on 2010-04-11 15:43:39 (Show Source):
You can put this solution on YOUR website!If the width is X, the length is 2X and the diagonal is sqrt ((X^2) + (2X)^2)
So sqrt(5X^2) = 25 or 5X^2 = 625
X^2 = 125
Area is X x 2X = 2X^2 = 250
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Miscellaneous_Word_Problems/285526: A team won 40 of its first 50 games. How many of the remaining 40 games must this team win so it will have won exactly 70% of its games for the season?
(A) 20 (B) 23 (C) 28 (D) 30 (E) 35
1 solutions
Answer 206944 by Greenfinch(383) on 2010-03-26 06:10:13 (Show Source):
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Number-Line/285506: The range describes the variability of the data (that is, how much do the numbers vary). Find the range of each set of numbers
7,7,5,4,1,9,8,8,8,5,2
1 solutions
Answer 206943 by Greenfinch(383) on 2010-03-26 05:53:31 (Show Source):
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Travel_Word_Problems/285512: The horizontal distance of a kite from the boy flying it is 30 m and 50 m of cord is out from the roll. If the wind
moves the kite horizontally at the rate of 5 km per hour directly away from the boy, how fast is the cord being
released?
1 solutions
Answer 206941 by Greenfinch(383) on 2010-03-26 05:44:42 (Show Source):
You can put this solution on YOUR website!If the horizontal distance is 30m and the string is 50m, the vertical distance is 40m (3,4,5 triangle).
Kite is moving away at 5000/3600 horizontally (in m/s)
Ratio of string extension to horizontal distance is 5 to 3
So 5000/3600 = 1.39 m/s
String released at (5/3)x 1.39 = 2.32 m/s (Roughly 2 1/3 m/s)
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Miscellaneous_Word_Problems/285514: 2 cars are 400 miles apart. both start at the same time and travel toward one another. they meet 4 hours later. the speed of one car is 20mph faster than the other. what is the speed of each car.?
1 solutions
Answer 206940 by Greenfinch(383) on 2010-03-26 05:26:09 (Show Source):
You can put this solution on YOUR website!If they are 400 miles apart and meet after 4 hours, they are moving towards each other at 100 miles / hour
The speed of one is X and the speed of the other is X + 20
So 2X + 20 = 100
X= 40 and the other is 60 miles/hour
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Money_Word_Problems/285517: Hello! I'd greatly appreciate it if anyone can help me on this deceptively hard (for me, at least) word problem. It is as follows:
A storeowner's average day sales is $500, realizing a profit of 20% of the selling price. To increase the volume of his sale, he advertised his goods by spending an average of $20 a day for advertising. If his average daily sales rose to $700 with the rate of the profit still remaining the same, how much additional profit did the advertising bring?
Thank you very much for the time and help! Godspeed! :)
1 solutions
Answer 206938 by Greenfinch(383) on 2010-03-26 05:23:13 (Show Source):
You can put this solution on YOUR website!The wording is what makes it hard. Why cannot Mathematicians consider learning English!
Initially, the sales are $500 from which there is a profit of $100
Afterwards there are sales of $700, from which there is a profit of $140.
Assuming that the advertising is an extra cost of $20, the extra profit is $20 less than the $140 - $100 difference, or $20.
If however, the rate of profit stays the same, this might be construed to mean that the advertising is now included in the costs of sales and does not have to be considered seperately. In that case the profit increase is $40 per day.
Either interpretation is possible when the question is written in this way.
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Angles/285520: if the sum of the interior angle of a polygon is 22 right angles find the number of its sides
1 solutions
Answer 206936 by Greenfinch(383) on 2010-03-26 05:15:09 (Show Source):
You can put this solution on YOUR website!Interior angles are (n - 2)180
If that equals 22 rt angles, (n - 2) x 2 = 22
So n - 2 = 22/2 = 11
So n = 13
Check 13 - 2 = 11. 11 x 2 = 22
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Probability-and-statistics/283109: A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail? Please show all steps so i can understand
1 solutions
Answer 205554 by Greenfinch(383) on 2010-03-20 13:04:51 (Show Source):
You can put this solution on YOUR website!Probability of failure is .02, so probability of non-failure is .98
For two independent events use the binomial process.
Chance of 2 non failures is .98^2 = 0.9604
Chance of 2 failures is 0.02^2 = 0.0004
Chance of 1 failure is 2 x 0.02 x 0.98 = 0.0392
Total = 1.00000
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logarithm/283139: Hi,
I thought I was finally getting the hang of this?
I was hit with
Find the natural logarithm of the given number, 68.5
I finally understand how to solve equations with the logs, etc..
But I have never just dealt with one number.
Is someone able to tell me how i go about this, do I find a way to put in an equation form?
Thanks!!
Nathalie
1 solutions
Answer 205550 by Greenfinch(383) on 2010-03-20 12:52:27 (Show Source):
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