All Questions ⁺⁰236027 Questions

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counting question

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 ..

moneydude242 ●

wiseowl Jan 19, 2024

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53

0

+1678

help 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 ..

wiseowl Jan 19, 2024

0

46

0

+862

Solids

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 ..

magenta Jan 19, 2024

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44

1

+862

Geometry question

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.

magenta Jan 19, 2024

-1

25

1

+1911

Need help

Assume that f(3) = 4. Name a point that must be on the graph of y= (5 + f(2x/3))/11$.

ElectricPavlov ●

tomtom Jan 19, 2024

-1

19

1

+1911

Help with coordinates

Find all points (x,y) that are 5 units away from the point (2,7) and that lie on the line x + y = 13.

tomtom Jan 19, 2024

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28

1

+1911

Coordinates

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

tomtom Jan 19, 2024

-1

55

1

+1911

Coordinates

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 ..

tomtom Jan 19, 2024

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51

1

+1768

Triangle

In triangle $ABC,$ $AB = 3,$ $AC = 5,$ $BC = 7,$ and $D$ lies on $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC.$ Find $\cos \angle BAD.$

bader Jan 19, 2024

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7

1

+1768

Trig

In triangle $ABC,$ $BC = 32,$ $\tan B = \frac{3}{5},$ and $\tan C = \frac{1}{4}.$ Find the area of the triangle.

bader Jan 19, 2024

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32

1

+1768

Triangles

In the diagram below, we have $AB = 24$ and $\angle ADB =90^\circ$. If $\sin A = \frac13$ and $\sin C = \frac12$, then what is $BC$?

bader Jan 19, 2024

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40

1

+1768

Triangle

The sides of a triangle are $2,$ $2,$ and $\sqrt{6} - \sqrt{3}.$ Enter the angles of the triangle in degrees, separated by commas.

bader Jan 19, 2024

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49

1

+0

PLZ HELP I NEED IT NOW

Grogg draws an equiangular polygon with g sides, and Winnie draws an equiangular polygon with w sides. If the interior angle of Winnie's polygon is equal to two times the exterior angle of Grogg's polygon, find the largest possible value of w.
If read more ..

ajdpaifdeffe Jan 19, 2024

0

36

0

+1455

help geometry

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

kittykat Jan 19, 2024

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38

0

+1557

need help

Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends. (Not everyone has to get a sticker.)

parmen Jan 19, 2024

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47

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+1557

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.

parmen Jan 19, 2024

0

56

0

+1557

Help probability

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?

parmen Jan 19, 2024

Jan 18, 2024

0

37

1

+1557

Counting problem

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 $1?$

parmen Jan 18, 2024

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