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# Recent problems solved by 'tomlaidlaw'

tomlaidlaw answered: 13 problems
 Rate-of-work-word-problems/681476: Antonio, an experience shipping clerk, can fill a certain order in 5 hours. Brian, a new clerk, needs 9 hours to do the same job. working together, how long would it take them to fill the order..... can someone help me solve this problem please:) 1 solutions Answer 422675 by tomlaidlaw(13)   on 2012-11-15 23:50:46 (Show Source): You can put this solution on YOUR website!You have to think kind of upside down. Antonio can do 1/5 of the job in one hour. Brian can do 1/9 of the job in one hour. Add them together Lowest common denominator is 9 x 5= 45. So 1/5 = 9/45 and 1/9 = 5/45. The total is 14/45 of the job can be done in one hour. Another way to say that is that it will take 45/14 of an hour to get the job done. Divide 45 by 14 and get 3 and 3/14 hours. Multiplying 3/14 by 60 gives 12.86 minutes, so the total job will be done in 3 hours-12.86 minutes. Tom Laidlaw
 Probability-and-statistics/654228: A poker hand consists of 5 cards consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of four hearts and one spade? I have tried nPr and nCr with 26C5 and 26P5 but that hasn't come with my desired answer of 9295. I would like to know to get to the answer because I can't seem to find a way to get to the answer. 1 solutions Answer 408651 by tomlaidlaw(13)   on 2012-09-19 21:46:07 (Show Source): You can put this solution on YOUR website!Combination of 13 cards taken 4 at a time x 13 cards taken 1 at a time. 13C4=715, 13C1 = 13 715x13 = 9295 Tom Laidlaw
 Triangles/616050: If you know only the sides of a triangle, For example, if a triangle had sides of 4 cm, 7 cm, and 12 cm, can you could not identify the three angles of that triangle. and likewise only knowing the three angles of some triangles to determine the other three sides, is that possible1 solutions Answer 390688 by tomlaidlaw(13)   on 2012-06-16 20:26:30 (Show Source): You can put this solution on YOUR website!3 sides, yes 3 angles, no. There could be many triangles with the same angles. You need 3 elements, including at least one side to completely solve a triangle. Look for my solvers in the solvers area. Tom Laidlaw
 Triangles/620263: A ladder is leaning against a house and is forming a 60 degree angle with the ground. If the top of the ladder is 15 from the ground, how long is the ladder to the nearest foot?1 solutions Answer 390685 by tomlaidlaw(13)   on 2012-06-16 19:58:17 (Show Source):
 Triangles/621151: The second angle of a triangle is three times as large as the first. The third angle is 20 degrees less than the sum of the other two angles. Find the measure of the first angle.1 solutions Answer 390684 by tomlaidlaw(13)   on 2012-06-16 19:48:02 (Show Source): You can put this solution on YOUR website!x + 3x + 4x-20 = 180 8x - 20 = 180 8x = 200 x = 25 3x = 75 4x - 20 = 80
 Pythagorean-theorem/618749: Dillon's dad built a small baseball diamond in the field behind their house. The diamond formed by the four bases is a square rotated . This means that each base line meets the next to form a angle. The length of each base line is feet. How far would Dillon need to throw the ball to get it from first base to third base? Round your answer to the nearest foot.1 solutions Answer 390647 by tomlaidlaw(13)   on 2012-06-16 03:58:38 (Show Source): You can put this solution on YOUR website!Since it is a square the simplest answer is side times square root of 2. This is what you will get with the other answer also. You didn't tell us how many feet so I can only give you the general answer. Plug in your own numbers.
Triangles/621181: Find the altitudes of a triangle whose side lengths are 13, 14, and 15
1 solutions

Answer 390627 by tomlaidlaw(13)   on 2012-06-15 20:25:37 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: SSS Triangle Solver 3 sides Use Heron's Formula for Area: First calculate s=(a+b+c)/2, then: Use the Law of Cosines for the angles: side a = 13 side b = 14 side c = 15 AngleA = 53.130 degrees or 0.927 radians AngleB = 59.490 degrees or 1.038 radians AngleC = 67.380 degrees or 1.176 radians Area K = 84.000 Circumcircle Radius = 8.125 __(R = .5a/sinA) incircle radius = 4.000 __(r = 2K/(a+b+c)) height over side a = 12.923 __(ha = csinB) height over side b = 12.000 __(hb = asinC) height over side c = 11.200 __(hc = bsinA) Thanks to hummingbird for the use of his solver. Thanks to Wolfram Math World for the triangle graphic. Tom Laidlaw

 Geometry_Word_Problems/617400: Barb is going to cover a rectangular area 8 feet by 10 feet with rectangular paving blocks that are 4 inches by 8 inches by 2 inches to make a flat patio. What is the minimum number of paving blocks she will need if all the paving blocks will face the same direction? Note: Barb will not cut any of the paving blocks.1 solutions Answer 389536 by tomlaidlaw(13)   on 2012-06-09 19:21:20 (Show Source): You can put this solution on YOUR website!Area of paving block = 8 x 4 = 32 in.^2 patio calcs: 8 ft.*12=96 inches 10 ft.*12=120 inches Area of patio = 120*96 = 11520 in.^2 Number of pavers = 11520/32 = 360 Tom Laidlaw
 Geometry_Word_Problems/617548: a piece of wire 400cm in length is cut into 2 pieces one of the pieces is bent into a rectangal. the rectangle is x cm wide and 3x centimeters long what is the perimeter. give answer in terms of x1 solutions Answer 389534 by tomlaidlaw(13)   on 2012-06-09 19:07:25 (Show Source): You can put this solution on YOUR website!Answer in terms of x: 8x Tom Laidlaw
 Geometry_Word_Problems/40749: A cow is tethered to a ring on the outside of a barn, 4 meters from one of the corners. The barn is 16 meters wide by 34 meters long. The rope is 50 meters in length. Find the cow's grazing area.1 solutions Answer 385196 by tomlaidlaw(13)   on 2012-05-17 02:35:47 (Show Source): You can put this solution on YOUR website!I get: Don't forget the starting place is offset, not directly on the corner. I'll try for a picture when I have more time.The problem did not say if the starting point was on the long side or short side of the barn. This is figured on the long side The principle is still the same. here i'll put the connection on the short side and just give the radius: 1/2 circle at 50 radius +1/4 at 38 + 1/4 at 4 + 1/4 at 46 +1/4 at 12. You'll have to work it out to see which way gives more acreage, and that makes a new puzzle, doen't it. Tom Laidlaw
 Miscellaneous_Word_Problems/40139: THE GRAZING GOAT Zoe the goat is tied by a rope to one corner of a 15 meter by 25 meter barn in the middle of a large, grassy field. Over what area of the field can Zoe graze if the rope is: a) 10 meters long? b) 20 meters long? c) 30 meters long? d) 40 meters long? e) Zoe is happiest when she has at least 400 m2 to graze. What possible lengths of rope could be used? 1 solutions Answer 385161 by tomlaidlaw(13)   on 2012-05-16 19:26:21 (Show Source): You can put this solution on YOUR website!10m rope = 3/4*pi*10^2 20m rope = 3/4*pi*20^2 + 1/4*pi*5^2 30m rope = 3/4*pi*30^2 + 1/4*pi*15^2 + 1/4*pi*5^2 40m rope = 3/4*pi*40^2 + 1/4*pi*25^2 + 1/4*pi*15^2 next: If we have to stick with the prescribed answer choices, then 20 ft. If not, 11.3 m does it. A = 3/4*pi*r^2 A = 3/4*pi*11.3^2 = 401.1509 Tom Laidlaw
 Angles/80367: A man has a barn that is 20 ft by 10 ft. He tethers a cow to one corner of the outside of the barn using a 50-ft rope. What is the total area that the cow is capable of grazing? I'm new to the site so I'l work on making a picture. Thank you and it would be nice if youd show me the steps.1 solutions Answer 384978 by tomlaidlaw(13)   on 2012-05-15 23:53:45 (Show Source): You can put this solution on YOUR website!After the 3/4 circle at every corner the rope shortens by the length of the previous side, so the next portion of circle will not be as large. So you have 3/4 of a 50 radius circle + a sector of a 40 foot circle (blue) + a sector of a 30 foot circle (red) + a triangle with sides of 40, 22.36, and 30. minus half the area of the barn. The triangle is the overlap area of the two arcs, and its area can be figured by Heron's formula: where . I'll leave you to work the numbers. You'll also need the Law of Cosines to get the angles. Tom laidlaw