Stanry

118 Questions
12 Answers

0

2

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+380

Counting

We choose a positive divisor of 20^{20} at random (with all divisors equally likely to be chosen). What is the probability that we chose a multiple of 5?

Stanry 8 hours ago

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1

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+380

Counting

How many subsets of \{0, 1, \dots, 9\} have the property that there are at least two elements and the sum of the two largest elements is 4?

Stanry 8 hours ago

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1

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+380

Counting

A permutation of the numbers (1,2,3,\dots,n) is a rearrangement of the numbers in which each number appears exactly once. For example, (2,5,1,4,3) is a permutation of (1,2,3,4,5).
Find the number of permutations (x_1, x_2, \dots, x_8) read more ..

Stanry Apr 13, 2025

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1

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+380

Counting

Find the number of sequences (a_1, a_2, a_3, \dots, a_8) such that:
* a_i \in \{1, 2, 3, 4, 5, 6, 7, 8\} for all 1 \le i \le 8.
* Every number1, 2, 3, 4, 5, 6, 7, 8 appears at least once in the sequence.

Stanry Apr 13, 2025

0

1

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+380

Counting

A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits (spades, hearts, diamonds, and clubs), such that there is exactly one card for any given rank and suit.
You are dealt a hand of read more ..

Stanry Apr 13, 2025

0

1

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+380

Counting

In the array below, in how many different ways can we start with the letter and move from letter to letter (horizontally, vertically, or diagonally), to spell the word "ARCS"?
A read more ..

Stanry Apr 13, 2025

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+380

Counting

How many squares in the plane have at least two points in the lattice below as vertices?

Stanry Apr 13, 2025

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1

+380

Counting

At a meeting, two scientists, two mathematicians, two historians, and two artists are to be seated around a circular table. In how many ways can they be seated so that all four pairs of people from the same discipline are seated together?

Stanry Apr 12, 2025

+1

1

2

+380

Geometry

A and B are two points on a sphere of radius 2. We know the space distance between A and B is 2, What is distance from A to B along the (minor) arc of a great circle?

Stanry Apr 7, 2025

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1

+380

i need help

In the diagram below, \overline{AD} and \overline{BE} are angle bisectors of \angle BAC and \angle ABC, respectively, and they intersect at T. We know that BC = 12, AC = 18 and BF = 3 \cdot AF. Find AB.

Stanry Apr 4, 2025

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+380

help me plz

The left column contains pairs of triangles with different side-length and angle-measure congruences marked. Match each diagram in the left column with a congruence/similarity criterion in the right column that justifies why the two triangles are congruent/similar. read more ..

Stanry Apr 4, 2025

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1

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+380

need help

The left column contains pairs of triangles with different side-length and angle-measure congruences marked. Match each diagram in the left column with a congruence/similarity criterion in the right column that justifies why the two triangles are read more ..

Stanry Apr 4, 2025

0

17

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+380

Number Theory

Which of the residues $0,$ $1,$ $2,$ $3,$ $4$ satisfy the congruence $3x \equiv 0 \pmod{5}?$
Give your answer as a list, separated by commas, in order from least to greatest.

Stanry Oct 29, 2024

0

20

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+380

Number Theory

Which of the residues $0,$ $1,$ $2,$ $3,$ $4,$ $5$ satisfy the congruence $x^2 \equiv 0 \pmod{6}?$
Give your answer as a list, separated by commas, in order from least to greatest.

Stanry Oct 29, 2024

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18

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+380

Number Theory

Let $a$ be an integer such that $a \equiv 5 \pmod{7}$. Find the value of $a + 1 \pmod{7}$. Express your answer as a residue between $0$ and the modulus.

Stanry Oct 29, 2024

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19

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+380

Number Theory

Let $a$ be an integer such that $0 \le a \le 10$ and $a^2 \equiv a \pmod{11}$. If $a \neq 0,$ then find the value of $a$.

Stanry Oct 29, 2024

-1

25

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+380

Number Theory

Let $a$, $b$, $c$, and $n$ be positive integers. If $a + b + c = 19 \cdot 97$ and
a + 3n = b - 2n = \frac{c}{5n},
compute the value of $a$.

Stanry Oct 23, 2024

0

9

1

+380

Number Theory

Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{17}$.

Stanry Oct 23, 2024

+380

0

The number of ways is 10*9 = 90.

StanryOct 1, 2024