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Post New Question
All Questions
+0
237263 Questions
0
14
1
+448
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 ..
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MEMEG0D
Oct 14, 2024
-1
16
0
+216
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
-1
20
0
+216
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
-1
25
0
+216
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
+3
11
4
+7
Precalcus help!
Find the smallest positive solution to
in radians.
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California
Oct 14, 2024
0
21
1
+413
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 $n?$
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nathanl6656
Oct 14, 2024
0
15
1
+413
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 $n?$
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nathanl6656
Oct 14, 2024
0
29
0
+413
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
0
20
0
+414
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
21
1
+414
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 $\phi(191)$?
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bIueb3rry
Oct 14, 2024
0
22
2
+414
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?
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bIueb3rry
Oct 14, 2024
Oct 13, 2024
0
13
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
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tomorspain
Oct 13, 2024
0
16
1
+900
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?
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eramsby1O1O
Oct 13, 2024
0
25
0
+900
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
23
0
+900
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
21
0
+414
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
0
21
0
+414
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
21
1
+1266
Algebra
Let
f(x) = \sqrt{x - \sqrt{x}}.
Find the largest three-digit value of $x$ such that $f(x)$ is an integer.
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Akhain1
Oct 13, 2024
0
17
1
+1266
Algebra
Evaluate $a^3 - \dfrac{1}{a^3}$ if $a - \dfrac{1}{a} = 0$.
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Akhain1
Oct 13, 2024
0
18
0
+1266
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
22
0
+921
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
11
1
+921
Algebra
Simplify \dfrac{1}{\sqrt2+sqrt3}+\dfrac{1}{\sqrt2-sqrt3}.
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gnistory
Oct 13, 2024
0
21
0
+921
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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