All Questions ⁺⁰232948 Questions

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+719

Number Theory

How many numbers between $1000$ and $2000$ leave a remainder of $3$ when divided by $47?$

bingboy Jun 20, 2024

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3

+719

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 $\phi(2835)$?

NotThatSmart ●●●

bingboy Jun 20, 2024

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+719

Number Theory

Fill in the blanks with three distinct positive integers.
1/___ + 1/___ + 1/___ = \frac{13}{12}

NotThatSmart ●

bingboy Jun 20, 2024

-1

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1

+1262

Geometry

The number of diagonals in a certain regular polygon is equal to $2$ times the number of sides. How many sides does this polygon have?

NotThatSmart ●

ABJeIIy Jun 20, 2024

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2

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+1262

Geometry

Let $IJKLMN$ be a hexagon with side lengths $IJ = LM = 3,$ $JK = MN = 3,$ and $KL = NI = 3$. Also, all the interior angles of the hexagon are equal. Find the area of hexagon $IJKLMN$.

ABJeIIy Jun 20, 2024

-1

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1

+1262

Geometry

In the diagram below, each side of convex quadrilateral $ABCD$ is trisected. (For example, $AP = PQ = QB.$) The area of convex quadrilateral $ABCD$ is $180.$ Find the area of the shaded region. read more ..

NotThatSmart ●

ABJeIIy Jun 20, 2024

-1

1

0

+1262

Polygons

Let $B,$ $A,$ and $D$ be three consecutive vertices of a regular $20$-gon. A regular heptagon is constructed on $\overline{AB},$ with a vertex $C$ next to $A.$ Find $\angle BAD,$ in degrees.

ABJeIIy Jun 20, 2024

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1

+1858

Number Theory

The sum of the reciprocals of three positive integers is $\frac{13}{12}$. What are the three positive integers?

LiIIiam0216 Jun 20, 2024

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2

+1858

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 $\phi(20)$?

LiIIiam0216 Jun 20, 2024

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5

+1858

help me

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?</ read more ..

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LiIIiam0216 Jun 20, 2024

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+136

Counting

A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, read more ..

NotThatSmart ●

BRAlNBOLT Jun 20, 2024

-3

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1

+136

Counting

At a meeting, four scientists, two mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if the mathematicians must sit next to each other? (Two seatings are considered equivalent if read more ..

BRAlNBOLT Jun 20, 2024

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1

1

+136

Counting

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other? (Two seatings are considered the same if read more ..

NotThatSmart ●

BRAlNBOLT Jun 20, 2024

0

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1

+1858

Geometry

Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is $6$, then find the volume of the resulting read more ..

LiIIiam0216 Jun 20, 2024

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1

+1858

Geometry

In square ABCD, P is on BC such that BP = 5 and PC = 2, and Q is on CD such that DQ = 4 and QC = 3. Find sin angle PAQ.

LiIIiam0216 Jun 20, 2024

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3

+603

Algebra

Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2 - 2x^2 + 4x - 1.

NotThatSmart ●●●

Hi6942O Jun 20, 2024

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2

1

+603

Algebra

Find the largest integer $k$ such that the equation
5x^2 - kx + 8 - 20x^2 + 45 = 0
has no real solutions.

Hi6942O Jun 20, 2024

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2

1

+603

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $100$ square foot wall in $10$ minutes, then how long would it take the $15$ members to paint a $100$ square foot wall, in minutes?

Hi6942O Jun 20, 2024

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1

+603

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $1000$ square foot wall in $10$ minutes, then how long would it take for $5$ members to paint a $1000$ square foot wall, in minutes?

Hi6942O Jun 20, 2024

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2

0

+603

Algebra

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

Hi6942O Jun 20, 2024

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1

+603

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $3$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $3$ hours read more ..

Hi6942O Jun 20, 2024

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1

+1858

Number Theory

How many numbers between $1000$ and $2000$ leave a remainder of $3$ when divided by $21?$

Tottenham10 ●

LiIIiam0216 Jun 20, 2024

Jun 19, 2024

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2

1

+603

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).

Hi6942O Jun 19, 2024

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+603

Algebra

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

Tottenham10 ●

Hi6942O Jun 19, 2024

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2

+1858

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 read more ..

LiIIiam0216 Jun 19, 2024

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