Difference between revisions of "2003 AMC 12B Problems"
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== Problem 4 == | == Problem 4 == | ||
+ | Moe uses a mower to cut his rectangular 90-foot by 150-foot lawn. The swath he cuts is 28 inches wide, but he overlaps each cut by 4 inches to make sure that no grass is missed. he walks at the rate of 5000 feet per hour while pushing the mower. Which of the following is closest to the number of hours it will take Moe to mow his lawn? | ||
+ | <math> | ||
+ | \text {(A) } 0.75 \qquad \text {(B) } 0.8 \qquad \text {(C) } 1.35 \qquad \text {(D) } 1.5 \qquad \text {(E) } 3 | ||
+ | </math> | ||
[[2003 AMC 12B Problems/Problem 4|Solution]] | [[2003 AMC 12B Problems/Problem 4|Solution]] | ||
Revision as of 19:30, 1 February 2010
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
Problem 1
Which of the following is the same as
?
Problem 2
Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs 1 dollar more than a pink pill, and Al's pills cost a total of 546 dollars for the two weeks. How much does one green pill cost?
Problem 3
Problem 4
Moe uses a mower to cut his rectangular 90-foot by 150-foot lawn. The swath he cuts is 28 inches wide, but he overlaps each cut by 4 inches to make sure that no grass is missed. he walks at the rate of 5000 feet per hour while pushing the mower. Which of the following is closest to the number of hours it will take Moe to mow his lawn?
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
An ice cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the sphere. If the ice cream melts, it will exactly fill the cone. Assume that the melted ice cream occupies of the volume of the frozen ice cream. What is the ratio of the cone’s height to its radius?
Problem 14
Problem 15
Problem 16
Problem 17
If and
, what is
?
Problem 18
Let be a 5-digit number, and let q and r be the quotient and remainder, respectively, when
is divided by 100. For how many values of
is
divisible by 11?
Problem 19
Let be the set of permutations of the sequence
for which the first term is not
. A permutation is chosen randomly from
. The probability that the second term is
, in lowest terms, is
. What is
?
Problem 20
Part of the graph of is shown. What is
?
Problem 21
An object moves cm in a straight line from
to
, turns at an angle
, measured in radians and chosen at random from the interval
, and moves
cm in a straight line to
. What is the probability that
?
Problem 22
Let be a rhombus with
and
. Let
be a point on
, and let
and
be the feet of the perpendiculars from
to
and
, respectively. Which of the following is closest to the minimum possible value of
?
![[asy] size(200); defaultpen(0.6); pair O = (15*15/17,8*15/17), C = (17,0), D = (0,0), P = (25.6,19.2), Q = (25.6, 18.5); pair A = 2*O-C, B = 2*O-D; pair P = (A+O)/2, Q=(B+O)/2, N=(A+B)/2; draw(A--B--C--D--cycle); draw(A--O--B--O--C--O--D); draw(P--N--Q); label("\(A\)",A,WNW); label("\(B\)",B,ESE); label("\(C\)",C,ESE); label("\(D\)",D,SW); label("\(P\)",P,SSW); label("\(Q\)",Q,SSE); label("\(N\)",N,NNE); [/asy]](http://latex.artofproblemsolving.com/c/2/2/c22d4d20155faaf8bd0cf51f26a5795d14b32322.png)
Problem 23
The number of -intercepts on the graph of
in the interval
is closest to
Problem 24
Positive integers and
are chosen so that
, and the system of equations
![$2x + y = 2003 \quad$](http://latex.artofproblemsolving.com/7/0/6/706aa31c279b4f4744165bfddf5f8bd451518a57.png)
![$\quad y = |x-a| + |x-b| + |x-c|$](http://latex.artofproblemsolving.com/5/7/c/57c363455cd9e9bf8c2dceadb7298327d953e0bc.png)
has exactly one solution. What is the minimum value of ?
Problem 25
Three points are chosen randomly and independently on a circle. What is the probability that all three pairwise distance between the points are less than the radius of the circle?