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256 Questions
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help inequality
Jeri finds a pile of money with at least 200. If she puts 60 of the pile in her left pocket, gives away $\frac25$ of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away 200 of the
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1 nov. 2023
0
117
0
+818
Inequality problem
My street hockey team plays three games each week. My team lost all $12$ games in the first four weeks. Then, my team won two games and lost one game in the fifth week, bringing our record to $2$ wins and $13$ losses. Each week after that, my team
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1 nov. 2023
0
82
1
+818
help algebra
One ordered pair $(a,b)$ satisfies the two equations $ab^4 = 48a^2 b$ and $a^2 b^5 = 6a^3 b$. What is the value of $b$ in this ordered pair? (Note: you may have to use the Tab key to get your cursor into the middle answer box.)
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1 nov. 2023
0
90
1
+818
system
Real numbers $a$ and $b$ satisfy
a + ab^2 = 250ab + ab^3
a - ab^2 = 240ab - 50b^2
Enter all possible values of a, separated by commas.
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maximum
1 nov. 2023
0
109
1
+818
help geometry
In traingle ABC, point X is on side BC such that AX=13, BX=10, and CX=6, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.
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1 nov. 2023
0
74
1
+818
geometry problem
Let R be the circle centered at (0,0) with radius 10. The lines x=6 and y=4 divide R into four regions R1, R2, R3 , and R4. Let R_i denote the area of region R_i If R1>R2>R3>R4, then find R1 + R2 + R3 +
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1 nov. 2023
0
62
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+818
counting help
You are given the $4 \times 4$ grid below. Find the number of ways of placing $4$ counters in the squares (at most one counter per square), so that each row contains exactly one counter, and each column contains exactly one counter.
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maximum
29 oct. 2023
0
100
1
+818
help plz
Find the number of positive integers that satisfy both the following conditions:
* Each digit is a $1$ or a $3$ or a $5$
* The sum of the digits is $10$
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29 oct. 2023
0
105
1
+818
need help
A baking club wants to form an executive committee. There are $18$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people?
A baking club wants to form
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29 oct. 2023
0
76
1
+818
help counting
In how many ways can $4$ balls be placed in $8$ boxes if the balls and boxes are both distinguishable?
In how many ways can $4$ balls be placed in $8$ boxes if neither the balls nor the boxes are distinguishable?
In
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29 oct. 2023
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Do not post AoPS homework.
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20 janv. 2025
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