onyuIee

145 Questions
11 Answers

0

9

0

+608

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 mehr ..

onyuIee 09.05.2025

0

5

0

+608

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.

onyuIee 09.05.2025

0

5

0

+608

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) mehr ..

onyuIee 09.05.2025

0

7

0

+608

Counting

Adam the ant starts at (0,0). Each minute, he flips a fair coin. If he flips heads, he moves 1 unit up; if he flips tails, he moves 1 unit right.
Betty the beetle starts at (1,1). Each minute, she flips a fair coin. If she flips heads, mehr ..

onyuIee 19.04.2025

0

8

1

+608

Counting

Consider the sequence
1, 5, 6, 25, 26, 30, 31, ...
which consists of every positive integer that can be expressed as a sum of distinct powers of 5.
What is the first term that is greater than 50?

onyuIee 19.04.2025

0

5

0

+608

Counting

Consider the sequence
1, 3, 4, 9, 10, 12, 13, ...
which consists of every positive integer that can be expressed as a sum of distinct powers of 3.
What is the first term that is greater than 20?

onyuIee 19.04.2025

+1

6

1

+608

Counting

Let P be a point chosen uniformly at random inside ABC. Extend ray BP to hit side AC at D. What is the probability that BD < 4?
The sides of triangle ABC are 3, 5, and 7.

onyuIee 10.04.2025

0

10

0

+608

Counting

Given a regular octagon, in how many ways can we color one diagonal red and another diagonal blue so that the two colored diagonals intersect at an endpoint? Consider rotations and reflections distinct.

onyuIee 10.04.2025

0

6

0

+608

Counting

Find the number of ways of placing three As, three Bs, and three Cs in a 3 \times 3 grid, so that every square contains one letter, and each diagonals contains one A, one B, and one C.

onyuIee 10.04.2025

0

18

0

+608

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f(x - 4x^2)
What is the domain of g?

onyuIee 22.02.2025

0

15

0

+608

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = 5 - f(x) + f(5/x).
What is the domain of g?

onyuIee 22.02.2025

0

19

0

+608

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f(2/x + x/2).
What is the domain of g?

onyuIee 22.02.2025

0

15

0

+608

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f((x + 1)(x - 2)).
What is the domain of g?

onyuIee 22.02.2025

0

25

1

+608

Geometry

What are the coordinates of the points where the graphs of f(x)=x^3 + x^2 - 3x + 5 and g(x) = x^3 + 2x^2 intersect?
Give your answer as a list of points separated by commas, with the points ordered such that their -coordinates mehr ..

onyuIee 23.01.2025

0

27

1

+608

Geometry

In triangle $ABC,$ $AB = 3,$ $AC = 5,$ $BC = 7,$ and $D$ lies on $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC.$ Find $\cos \angle BAD.$

onyuIee 23.01.2025

+608

0

The number of ways is 14.

onyuIee09.05.2025