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bIueb3rry
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bIueb3rry
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483
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115
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13
115 Questions
13 Answers
0
31
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+483
Help me
Let $A$, $B$, and $C$ be constants so that
\frac{1}{x^3-2x^2-5x+9}=\frac{A}{x+5}+\frac{B}{x-3} + \frac{C}{(x - 3)^2}
holds for all real numbers $x$ other than $-5$ and $3.$ What is $A$?
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bIueb3rry
16.08.2025
0
2
7
2
+483
Math
In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?
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bIueb3rry
20.07.2025
+1
5
2
1
+483
Algebra
Let x, y, and z be real numbers. If x^2 + y^2 + z^2 = 1, then find the maximum value of
3x + 4y + 5z + x^3 + \frac{4x^2 y}{z} + \frac{z^5}{xy^2}
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bIueb3rry
12.07.2025
0
2
5
1
+483
Algebra
Let x_1, x_2, \dots, x_{100} be real numbers. If
x_1 + 2x_2 + \dots + 100x_{100} = 1,
then find the minimum value of x_1/1 + x_2/2 + \dots + x_{100}/100.
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bIueb3rry
11.07.2025
0
3
28
1
+483
Geometry
Two runners start at vertices A and B simultaneously and run clockwise around the perimeter of square ABCD at the same speed. A drone flies so that it is always at the midpoint of the two runners. What is the minimum distance between the two runners?
mehr ..
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bIueb3rry
27.05.2025
0
12
1
+483
Counting
Find the number of ways of arranging one A, two Bs, three Cs, and four Ds, so that no two Bs are next to each other, no two Cs are next to each other, and no two Ds are next to each other.
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bIueb3rry
19.05.2025
0
1
5
1
+483
Counting
The following cards are split into four piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?
The cards are:
Ace of clubs
Ace of diamonds
mehr ..
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bIueb3rry
10.05.2025
0
5
1
+483
Counting
A bag contains red and blue tiles. Each tile has a number from the set \{-1, 0, 1\} written on it. I want to arrange 7 of these tiles in a row, so that the numbers on any three consecutive tiles sum to 3. In how many ways can this be done, assuming that
mehr ..
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bIueb3rry
10.05.2025
0
2
11
0
+483
Counting
Find the number of subsets of
S = \{1, 3, 8, 17, 30, 36, 47, 58\},
so that the sum of the elements in the subset is less than 20. (Note that for the empty subset, we take the sum of the elements as 0.)
bIueb3rry
19.04.2025
0
1
15
0
+483
Counting
Find the number of subsets of
S = \{1, 3, 8, 17, 30, 36, 47, 58\},
so that the sum of the elements in the subset is a multiple of 5. (Note that for the empty subset, we take the sum of the elements as 0.)
bIueb3rry
19.04.2025
0
3
11
0
+483
Counting
Find the number of paths from A to B in the grid below, so that
* Each step is down or to the right.
* The path cannot pass through any point more than once.
An example path is shown.
The grid is 3 by 3, with
mehr ..
bIueb3rry
17.04.2025
0
1
18
0
+483
Counting
Find the number of ways of filling in the squares of a 3 \times 3 grid so that:
* Each square contains a 0 or a 1.
* The sum of the numbers in each row and each column is at most 1.
An example is shown below.
bIueb3rry
17.04.2025
0
1
16
0
+483
Counting
How many ordered pairs of positive integers (m,n) satisfy \text{lcm}[m,n] = 360 and \gcd(m,n) = 360?
bIueb3rry
17.04.2025
0
3
15
0
+483
Counting
A bag contains red and blue tiles. Each tile has a number from the set \{-1, 0, 1\} written on it. I want to arrange 7 of these tiles in a row, so that the numbers on any three consecutive tiles sum to 3. In how many ways can this be done, assuming that
mehr ..
bIueb3rry
17.04.2025
0
1
11
0
+483
Geometry
Find sin B.
BD = 15, CD = 10, AC = 6
bIueb3rry
04.04.2025
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