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# Recent problems solved by 'Greenfinch'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389, >>Next

 Trigonometry-basics/298471: please help me answer my question find all solutions of the equation 4cos^2x-4cosx+1=01 solutions Answer 214682 by Greenfinch(383)   on 2010-04-29 17:42:23 (Show Source): You can put this solution on YOUR website!Treat as a quadratic. Factorize it into (2cosx -1)^2 = 0 cos x = 1/2 x = 60 or 300 degrees
 Probability-and-statistics/294594: A bag contains 3 quarters and 5 dimes. Another bag contains 12 pennies and 8 nickels. One coin is chosen from each bag without looking. Find P [dime and penny].1 solutions Answer 212509 by Greenfinch(383)   on 2010-04-21 07:40:29 (Show Source): You can put this solution on YOUR website!P (dine) = 5/8 P(penny) = 12/20 = 3/5 P(penny and dime)= (5x3)/(5x8) = 3/8
 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 x1 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
 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): You can put this solution on YOUR website!126800 x 1.15 = 145820 145820 x 0.80 = 116656 Answer is C
 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)
 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
 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
 Graphs/291033: Find the y-intercept and the x-intercept for the equation 2x+3y=12 1 solutions Answer 210567 by Greenfinch(383)   on 2010-04-12 04:48:45 (Show Source): You can put this solution on YOUR website!When x = 0, 3y = 12, so y = 4 when y = 0, 2x = 12, so x = 6 y-intercept is thus at (0,4) x - intercept is at (6,0)
 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
 Triangles/291034: find the area of a triangle with sides of length 7 and 9 and included angle of 72 degress1 solutions Answer 210564 by Greenfinch(383)   on 2010-04-12 04:23:05 (Show Source): You can put this solution on YOUR website!Area of triangle is =( a x b sin C)/2 In this case = 7 x 9 x sin 72 /2 = 29.958
 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
 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
 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
 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
 Miscellaneous_Word_Problems/290808: if emma pays one-fourth of her salary for taxes,one-eigth for a car loan,one-fifth for savings. how muh of her retirement is left? write the 100 percent as a fraction?1 solutions Answer 210433 by Greenfinch(383)   on 2010-04-11 16:31:25 (Show Source): You can put this solution on YOUR website!1/4 + 1/8 + 1/5 = (10 + 5 + 8)/40 = 23/40 used so 17/40 left. or 42.5%
 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): You can put this solution on YOUR website!Area is x^2 + 50x, width is x, so length is area/width (x^2 + 50x)/x = x + 50
 Polygons/290837: if each interior angle of a regular polygon measures 135 degrees, the polygon must be?1 solutions Answer 210429 by Greenfinch(383)   on 2010-04-11 16:24:25 (Show Source): You can put this solution on YOUR website!If interior angle is 135 degrees, the exterior angle is 45 degrees. The total exterior angles is always 360 degrees. so there are 8 sides
 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
 Volume/290832: find the radius of a ball with a volume of 41 cubic inches1 solutions Answer 210425 by Greenfinch(383)   on 2010-04-11 15:57:10 (Show Source): You can put this solution on YOUR website!V= 4(pi x radius^3)/3 = 41 So radius^3 = 41 x 3/(4 x pi)= 9.788 So radius = 2.139 inches
 Polygons/290826: If each exterior angle of a regular polygon measures 90 degrees how many sides does the polygon have?1 solutions Answer 210422 by Greenfinch(383)   on 2010-04-11 15:49:49 (Show Source): You can put this solution on YOUR website!Sum of exterior angles is 360 degrees. if each angle is 90 there must be 4 sides.
 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
 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) 351 solutions Answer 206944 by Greenfinch(383)   on 2010-03-26 06:10:13 (Show Source): You can put this solution on YOUR website!Total games for season are 90. 70% of 90 is 63. Have already won 40, so need to win another 23. Answer is (B)
 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): You can put this solution on YOUR website!Highest number is 9, lowest number is 1. Range is therefore 9 - 1 = 8
 Miscellaneous_Word_Problems/285522: If 200 ≤ a ≤ 400 and 600 ≤ b ≤ 1200 then the largest value of the quotient b/a is a) 3/2 (B) 3 (C) 6 (D) 300 (E) 600 1 solutions Answer 206942 by Greenfinch(383)   on 2010-03-26 05:49:04 (Show Source): You can put this solution on YOUR website!The highest value of b/a is with highest b over lowest a Highest b is 1200, lowest a is 200 1200/200 = 6 So (C) is right
 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)
 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
 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.
 Angles/285520: if the sum of the interior angle of a polygon is 22 right angles find the number of its sides1 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
 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
 Exponential-and-logarithmic-functions/283117: A 5000g sample of Iodine-131 decayed into 312.5 grams in 2.025 days. What is the half-life of Iodine-131?1 solutions Answer 205551 by Greenfinch(383)   on 2010-03-20 12:58:03 (Show Source): You can put this solution on YOUR website!5000/312.5 = 16 so it has decayed to 1/16 of the original. 16 is 2^4, so 4 half-lives. 2.025 days = 2916 minutes. So 1 half-life is 729 minutes or 12 hours 9 minutes
 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!! Nathalie1 solutions Answer 205550 by Greenfinch(383)   on 2010-03-20 12:52:27 (Show Source): You can put this solution on YOUR website!I think you are overcomplicating this. All they are asking for is the log to the base e of 68.5 ln(68.5) = 4.226833745