All Questions ⁺⁰236336 Questions

0

20

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+948

Number Theory

Jon teaches a fourth grade class at an elementary school where class sizes are always at least $20$ students and at most $60$. One day Jon decides that he wants to arrange the students in their desks in a rectangular grid with no gaps. Unfortunately read more ..

Rangcr897 Jun 23, 2024

-2

25

0

+204

Number Theory

What are the first $5$ digits after the decimal point (technically the hexadecimal point...) when the fraction $\frac{2}{17}$ is written in base $16$?
(Express your answer as a five digit hexadecimal number. You do not need to read more ..

BRAlNBOLT Jun 23, 2024

-3

19

0

+204

Number Theory

Let $N$ be a positive integer. The number $N$ has three digits when expressed in base $7$. When the number $N$ is expressed in base $12$, it has the same three digits, in reverse order. What is $N$? (Express your answer in decim read more ..

BRAlNBOLT Jun 23, 2024

-2

26

0

+204

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 ..

BRAlNBOLT Jun 23, 2024

-2

22

0

+204

Number Theory

Find the smallest positive integer $B$ so that when we express the decimal number $220$ as a base $B$ number, we still get a $2$-digit number.

BRAlNBOLT Jun 23, 2024

0

18

1

+33

Geometry

A circle lies inside a quarter-circle, as shown below. The circle is tangent to side AO and arc AB. Find the radius of the circle.

jumbean Jun 23, 2024

0

25

0

+1379

Algebra

The product $(3-\sqrt{5})(4+\sqrt{5})(1+6\sqrt{5})$ can be expressed in the form $a+b\sqrt{5}$, where $a$ and $b$ are integers. Find $a+b$.

learnmgcat Jun 23, 2024

0

30

0

+1379

Algebra

I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least 600 pounds more than each of her trucks, but no more than 1/2 of the total load her four trucks combined can carry. Based on these read more ..

learnmgcat Jun 23, 2024

0

27

0

+1379

Algebra

Find the minimum value of 9^x - 2 \cdot 3^x + 1 over all real numbers x.

learnmgcat Jun 23, 2024

0

16

0

+1379

Algebra

Find one ordered pair $(x,y)$ of real numbers such that $x + y = 10$ and $x^3 + y^3 = 162 + x^2 + y^2.$

learnmgcat Jun 23, 2024

0

22

1

+2653

Counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

LiIIiam0216 Jun 23, 2024

0

35

0

+2653

Counting

In how many ways can we distribute 13 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving at least four pieces each?

LiIIiam0216 Jun 23, 2024

0

24

0

+1379

Counting

Catherine rolls a standard $3$-sided die six times. If the product of her rolls is $600,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

learnmgcat Jun 23, 2024

0

24

0

+2653

Counting

Catherine rolls a standard $3$-sided die six times. If the product of her rolls is $300,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

LiIIiam0216 Jun 23, 2024

0

20

1

+2653

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?

LiIIiam0216 Jun 23, 2024

0

19

0

+2653

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?

LiIIiam0216 Jun 23, 2024

0

20

1

+2653

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?

LiIIiam0216 Jun 23, 2024

Jun 22, 2024

0

29

0

+1379

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

learnmgcat Jun 22, 2024

0

17

1

+1379

Geometry

Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF which intersect at I. If DI=3, BD=4 and BI=6 then compute the area of triangle BID.

learnmgcat Jun 22, 2024

0

26

1

+1379

Geometry

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

learnmgcat Jun 22, 2024

0

19

0

+1379

Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

learnmgcat Jun 22, 2024

0

12

3

+63

Halp with Polynomials

Find all roots of the polynomial

MeldHunter Jun 22, 2024

0

19

0

+1839

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 ..

ABJeIIy Jun 22, 2024

0

21

1

+1839

Counting

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $480,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

ABJeIIy Jun 22, 2024

0

21

1

+1839

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 ..

ABJeIIy Jun 22, 2024

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