All Questions ⁺⁰236009 Questions

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8

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+310

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 $5$ pieces of candy per scoop to the vat, and another machine that can remove exactly $3$ pieces of candy with a different scoop from read more ..

MEMEG0D Oct 14, 2024

0

8

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+219

Number Theory

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest number of primes that could divide a terrific positive integer?

BRAlNBOLT Oct 14, 2024

0

10

0

+219

Number Theory

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the largest number of primes that could divide a terrific positive integer?

BRAlNBOLT Oct 14, 2024

0

10

0

+219

Number Theory

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest terrific positive integer?

BRAlNBOLT Oct 14, 2024

+2

5

4

+6

Precalcus help!

Find the smallest positive solution to

in radians.

California Oct 14, 2024

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6

1

+346

Number Theory

A positive integer is called nice if it is a multiple of $8.$
A certain nice positive integer $n$ has exactly $9$ positive divisors. How many prime numbers are divisors of $n?$

nathanl6656 Oct 14, 2024

0

6

1

+346

Number Theory

A positive integer is called nice if it is a multiple of $8.$
A certain nice positive integer $n$ has exactly $9$ positive divisors. What is the smallest possible value of $n?$

nathanl6656 Oct 14, 2024

0

8

0

+346

Number Theory

Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{17}$.
Be sure to include complete explanations with your answer, using complete sentences. Imagine you were going to show your solution to a classmate, read more ..

nathanl6656 Oct 14, 2024

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8

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+267

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 $\phi(1200)$?

bIueb3rry Oct 14, 2024

0

5

1

+267

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 $\phi(191)$?

bIueb3rry Oct 14, 2024

0

9

2

+267

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?

bIueb3rry Oct 14, 2024

Oct 13, 2024

0

4

3

+13

PLEASE HELP

A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point P on the edge of the table (as shown below) has a distance of 8 from one wall, and read more ..

tomorspain Oct 13, 2024

0

5

1

+868

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?

eramsby1O1O Oct 13, 2024

0

8

0

+868

Counting

Each square below is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the squares?
There is a grid of 4 by 5 squares.

eramsby1O1O Oct 13, 2024

0

9

0

+868

Counting

Find the number of positive integers that satisfy both the following conditions:
Each digit is a 1 or a 3.
The sum of the digits is 5.

eramsby1O1O Oct 13, 2024

0

7

0

+267

Geometry

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $BC = 15,$ and $CX = 5$. What is $BX$?

bIueb3rry Oct 13, 2024

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10

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+267

Geometry

In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.

bIueb3rry Oct 13, 2024

0

9

1

+1234

Algebra

Let
f(x) = \sqrt{x - \sqrt{x}}.
Find the largest three-digit value of $x$ such that $f(x)$ is an integer.

Akhain1 Oct 13, 2024

0

7

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+1234

Algebra

Evaluate $a^3 - \dfrac{1}{a^3}$ if $a - \dfrac{1}{a} = 0$.

Akhain1 Oct 13, 2024

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+1234

Algebra

Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be a sequence. If
\[a_n = a_{n - 1} + a_{n - 2}\]
for all $n \ge 3,$ and $a_{11} = 1$ and $a_{10} = 4,$ then find $a_6.$

Akhain1 Oct 13, 2024

0

8

0

+785

Algebra

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 read more ..

gnistory Oct 13, 2024

+1

4

1

+785

Algebra

Simplify \dfrac{1}{\sqrt2+sqrt3}+\dfrac{1}{\sqrt2-sqrt3}.

gnistory Oct 13, 2024

0

8

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+785

Algebra

Find all ordered pairs x, y of real numbers such that x+y=10 and x^2+y^2=64.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

gnistory Oct 13, 2024

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