Moe uses a mower to cut his rectangular 90-foot by150-foot lawn. The swath he cuts is 28 inches wide,but he overlaps each cut by 4 inches to make surethat no grass is missed. He walks at the rate of 5000feet per hour while pushing the mower. Which of thefollowing is closest to the number of hours it will takeMoe to mow his lawn?(A)0.75(B)0.8(C)1.35(D)1.5(E)32003 AMC 10 B, Problem #5—2003 AMC 12 B, Problem #4—“Moe cuts about two square feet for each foot hepushes the mower forward.”Difficulty:Medium-hardNCTM Standard:Geometry Standard for Grades 9–12: Analyze characteristics and properties oftwo- and three-dimensional geometric shapes and develop mathematical arguments about geometricrelationships.Mathworld.com Classification:Geometry>Plane Geometry>Miscellaneous Plane Geometry>Area
Manytelevisionscreensarerectanglesthataremeasured by the length of their diagonals. The ratioof the horizontal length to the height in a standardtelevision screen is4 : 3.The horizontal length ofa “27-inch” television screen is closest, in inches, towhich of the following?DiagonalHeight(A)20(B)20.5(C)21(D)21.5(E)222003 AMC 10 B, Problem #6—2003 AMC 12 B, Problem #5—“The height, length, and diagonal are in the ratio3 :4 : 5.”SolutionAnswer (D):The height, length, and diagonal are in the ratio3 : 4 : 5.The length of the diagonal is 27, so the horizontal length is45(27) = 21.6inches.Difficulty:Medium-hardNCTMStandard:Geometry Standard for Grades 9–12:Use trigonometric relationships todetermine lengths and angle measures.Mathworld.com Classification:Geometry>Trigonometry>General Trigonometry
The symbolismbxcdenotes the largest integer notexceedingx. For example,b3c= 3, andb9/2c= 4.Computeb√1c+b√2c+b√3c+· · ·+b√16c.(A)35(B)38(C)40(D)42(E)1362003 AMC 10 B, Problem #7—“Let(a+1)2≤x < a2, for some integerxanda.b√xc=a-1.”SolutionAnswer (B):The first three values in the sum are 1, the next five are2, the next seven are 3, and the final one is 4 for a total of3·1 + 5·2 + 7·3 + 1·4 = 38.Difficulty:MediumNCTM Standard:Number and Operations Standard for Grades 9–12: Understand meanings ofoperations and how they relate to one another.Mathworld.com Classification:Number Theory>Rounding>Floor Function
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Natural number, Prime number, Geometric progression