All Questions ⁺⁰236337 Questions

+1

11

4

+1577

Counting

A baking club wants to form an executive committee. There are $15$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people, including Mark?

CPhill ●●●●

parmen Jun 23, 2024

0

18

1

+1577

Counting

A baking club wants to form an executive committee. There are $15$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people, not including Mark?

parmen Jun 23, 2024

0

11

1

+1577

Counting

A baking club wants to form an executive committee. There are $15$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people?

parmen Jun 23, 2024

0

17

1

+1577

Counting

Joanna has seven beads that she wants to assemble into a bracelet. Three of the beads have the same color, and the other four all have different colors. In how many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical read more ..

parmen Jun 23, 2024

0

13

1

+1560

Counting

At a meeting, $4$ scientists, $3$ mathematicians, and $2$ journalists are to be seated around a circular table. How many different arrangements are possible if every mathematician must sit next to a journalist? (Two seatings are considered read more ..

blackpanther Jun 23, 2024

0

13

1

+1560

Counting

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if all three mathematics textbooks must be together?

blackpanther Jun 23, 2024

+1

21

1

+1560

Counting

Starting with the A moving one letter at a time vertically, horizontally, or diagonally, how many different paths spell ARCH?
A
RRR
CCCCC read more ..

blackpanther Jun 23, 2024

0

14

1

+1560

Counting

I run a book club with $n$ people, not including myself. Every day, for $400$ days, I invite $2$ members in the club to review a book. What is the smallest positive integer $n$ so that I can avoid ever having the exact same group of $2$ read more ..

blackpanther Jun 23, 2024

0

18

1

+1379

Number Theory

A terminal zero is a $0$ that appears at the end of a number. For example, the number $3,800$ has two terminal zeros.
How many terminal zeroes does $40 \cdot 6 \cdot 75 \cdot 12$ have?

learnmgcat Jun 23, 2024

0

22

1

+1379

Number Theory

The number $100$ has four perfect square divisors, namely $1,$ $4,$ $25,$ and $100.$
What is the smallest positive integer that has exactly $2$ perfect square divisors?

NotThatSmart ●

learnmgcat Jun 23, 2024

0

17

1

+1379

Number Theory

A positive integer is called nice if it is a multiple of $6.$
A certain nice positive integer $n$ has exactly $8$ positive divisors. What is the smallest possible value of $n$?

learnmgcat Jun 23, 2024

0

15

1

+1379

Number Theory

A positive integer is called nice if it is a multiple of $6.$
A certain nice positive integer $n$ has exactly $8$ positive divisors. How many prime numbers are divisors of $n?$

NotThatSmart ●

learnmgcat Jun 23, 2024

0

17

1

+976

Number Theory

A positive integer is called terrific if it has exactly 5 positive divisors. What is the smallest terrific positive integer?

Hi6942O Jun 23, 2024

0

16

1

+976

Number Theory

A positive integer is called terrific if it has exactly 5 positive divisors. What is the largest number of primes that could divide a terrific positive integer?

Hi6942O Jun 23, 2024

0

26

0

+976

Number Theory

A positive integer is called terrific if it has exactly 5 positive divisors. What is the smallest number of primes that could divide a terrific positive integer?

Hi6942O Jun 23, 2024

0

22

0

+2653

Number Theory

You have a total supply of $1000$ pieces of candy, and an empty vat. You also have a machine that can add exactly $52$ pieces of candy per scoop to the vat, and another machine that can remove exactly $39$ pieces of candy with a different scoop from read more ..

LiIIiam0216 Jun 23, 2024

0

21

1

+2653

Number Theory

As shown in class, the Euclidean algorithm can be used to find solutions to equations of the form
ax + by = c.
Use the Euclidean algorithm to find integers $x$ and $y$ such that $6x + 3y = 1,$ with the smallest possible positive read more ..

LiIIiam0216 Jun 23, 2024

0

28

1

+2653

Number Theory

Starting at the same time, Bill rings a bell every $36$ seconds, and Wendy blows a whistle every $90$ seconds, and Sam blows a horn every $385$ seconds. How many minutes will it be before both Bill and Wendy and Sam simultaneously make a sound?

LiIIiam0216 Jun 23, 2024

0

12

1

+844

Number Theory

For a positive integer $n$, $\phi(n)$ denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$.
What is $\phi(99)$?

RedDragonl Jun 23, 2024

0

28

0

+844

Number Theory

For a positive integer $n$, $\phi(n)$ denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$.
What is $\phi(25)$?

RedDragonl Jun 23, 2024

0

25

2

+844

Number Theory

How many numbers between $1000$ and $2000$ leave a remainder of $3$ when divided by $65?$

RedDragonl Jun 23, 2024

0

24

0

+844

Number Theory

When fractions are expressed in different bases, they can be terminating or repeating. For example, when $\frac{1}{5}$ is expressed in base $3,$ the result is
0.\overline{0121}_3 = 0.01210121 \dots,
which is repeating.
When read more ..

RedDragonl Jun 23, 2024

0

15

3

+948

Number Theory

Find the greatest prime divisor of the value of the arithmetic series
1 + 2 + 3 + \dots + 200

Rangcr897 Jun 23, 2024

0

15

1

+948

Number Theory

What is the smallest prime divisor of 5^{19} + 7^{13} + 23?

Rangcr897 Jun 23, 2024

0

15

1

+948

Number Theory

How many bases $b \ge 2$ are there such that $100_b + 1_b$ is prime?

Rangcr897 Jun 23, 2024

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