All Questions ⁺⁰236302 Questions

0

15

1

+911

Counting

Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends, if every friend gets at least one sticker.

magenta Jun 21, 2024

0

32

0

+911

Counting

Miyu is giving out $8$ identical chocolates to her $5$ friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets exactly $7$ chocolates?

magenta Jun 21, 2024

0

20

1

+911

Counting

How many solutions are there to the equation
u + v + w + x + y + z = 2,
where $u,$ $v,$ $w,$ $x,$ $y,$ and $z$ are nonnegative integers, and $x$ is at most $1?$

magenta Jun 21, 2024

-1

13

1

+1839

Geometry

Trapezoid $HGFE$ is inscribed in a circle, with $\overline{EF} \parallel \overline{GH}$. If arc $GH$ is $66$ degrees, arc $EH$ is $x^2 + 8x$ degrees, and arc $FG$ is $25 + 16x$ degrees, where $x > 0,$ find arc $EPF$, in degrees.

ABJeIIy Jun 21, 2024

-1

26

1

+1839

Geometry

The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.

ABJeIIy Jun 21, 2024

-1

16

0

+1839

Geometry

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

ABJeIIy Jun 21, 2024

-1

24

1

+1839

Geometry

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

NotThatSmart ●

ABJeIIy Jun 21, 2024

Jun 20, 2024

-1

24

1

+1839

Geometry

Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 66^\circ$, then what is $\angle HCA$ in degrees?

NotThatSmart ●

ABJeIIy Jun 20, 2024

0

17

3

+4

Intermediate Alegbra Question

Let be the real-valued function defined for all real except for and and satisfying the functional equation
Find the function satisfying these conditions. Write as a rational function with read more ..

leekord Jun 20, 2024

0

15

1

+868

Geometry

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 8$, $SU = 8$, $TU = 8$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$,
<read more ..

eramsby1O1O Jun 20, 2024

0

18

1

+868

Geometry

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 1$, and $PR =1$, read more ..

eramsby1O1O Jun 20, 2024

0

21

1

+868

Geometry

Find the coordinates of the center of the circle.
The points on the circle are (22,15), (-25,0), (22,-29).

eramsby1O1O Jun 20, 2024

-2

27

1

+219

Number Theory

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

BRAlNBOLT Jun 20, 2024

-2

13

1

+219

Number Theory

Find the smallest positive integer $B$ so that when we express the decimal number $582$ as a base $B$ number, we still get a $2$-digit number.

NotThatSmart ●

BRAlNBOLT Jun 20, 2024

-2

10

1

+219

Number Theory

Fill in each blank with a single digit.
\frac{2}{131} = 0. _ _ _ _ _ _ _ _ _ _

BRAlNBOLT Jun 20, 2024

-2

17

2

+219

Number Theory

Fill in each blank with a single digit. Do not use a calculator.
\frac{13}{29} = 0. _ _ _ _ _ _ _ _ _ _ ...

BRAlNBOLT Jun 20, 2024

-2

18

0

+219

Number Theory

Fill in each blank with a single digit. Do not use a calculator.
\frac{36}{1011} = 0. _ _ _ _ _ _ _ _ _ _ ...

BRAlNBOLT Jun 20, 2024

0

26

1

+22

I don’t understand this question and I need help

Plaintainmountain, a frequent (but disruptive) user on web2.0calc, spams every answer claiming it's AI-generated. After 5 warnings (w), mods decide to ban them if they make at least 3 (min for chaos) AI claims in the next 10 (n) posts. If read more ..

derpmcfearson Jun 20, 2024

-1

19

1

+1839

Counting

In the Olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are 19 skaters, including 2 Americans and 5 Canadians, in how many ways can the medals be awarded to three of the 19 skaters read more ..

ABJeIIy Jun 20, 2024

-1

17

0

+1839

Counting

In a row of five squares, each square 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 five squares, so that at least one square is yellow, and at least one square read more ..

ABJeIIy Jun 20, 2024

0

18

0

+948

In triangle $PQR,$ $M$ is the midpoint of $\overline{PQ}.$ Let $X$ be the point on $\overline{QR}$ such that $\overline{PX}$ bisects $\angle

In triangle $PQR,$ $M$ is the midpoint of $\overline{PQ}.$ Let $X$ be the point on $\overline{QR}$ such that $\overline{PX}$ bisects $\angle QPR,$ and let the perpendicular bisector of $\overline{PQ}$ intersect $\overline{PX}$ at $Y.$ If $PQ = 36$, $PM read more ..

Rangcr897 Jun 20, 2024

0

19

1

+742

Euclidean Algorithm

Use the Euclidean algorithm to find integers $x$ and $y$ such that $164x + 39y = 1,$ with the smallest possible positive value of $x$.

bingboy Jun 20, 2024

0

12

1

+742

Euclidean Algorithm

Use the Euclidean Algorithm to find gcd(972, 1220).

NotThatSmart ●

bingboy Jun 20, 2024

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