All Questions ⁺⁰230633 Questions

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help counting

Joanna has six beads that she wants to assemble into a bracelet. Four of the beads have the same color, and the other two all have different colors. In how many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical read more ..

cooIcooIcooI17 Mar 28, 2024

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+41

Help

Solarblade Mar 28, 2024

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Counting

Franklin the fly starts at the point $(0,0)$ in the coordinate plane. At each point, Franklin takes a step to the right, left, up, or down. After $2$ steps, how many different points could Franklin end up at?

cooIcooIcooI17 Mar 28, 2024

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help plz

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

cooIcooIcooI17 Mar 28, 2024

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+84

help counting

Catherine rolls a standard $6$-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.)

cooIcooIcooI17 Mar 28, 2024

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counting

My square patio is tiled with square tiles, all the same size. All the tiles are gray, except the tiles along the two diagonals, which are all yellow. (The corners are yellow, the center is yellow, and all the tiles along the diagonal in between read more ..

cooIcooIcooI17 Mar 28, 2024

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+28

seating wars

At a meeting, 4 mathematicians, 3 scientists, and 2 journalists are to be seated around a circular table. How many different arrangements are possible if the mathematicians must all sit together (in 4 consecutive seats) and the 3 scientists must read more ..

coolcoolcool17 Mar 28, 2024

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Ms. Q's deck of cards...

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers (1, 2, 3, 4, 5, 6, and 7). Among all the cards of each color, there is exactly one card labeled with each number. read more ..

coolcoolcool17 Mar 28, 2024

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a child has to sit next to two adults

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if each child must be next to two adults? (Two seatings are considered the same if one can be rotated to form the other.)

coolcoolcool17 Mar 28, 2024

Mar 27, 2024

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+1032

help algebra

Let $x$, $y$, and $z$ be nonzero real numbers. Find all possible values of
\frac{x}{|x|} + \frac{y}{|y|} + \frac{z}{|z|} + \frac{x + y + z}{|x + y + z|}

kittykat Mar 27, 2024

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Absolute value

Find all $c$ such that $|c + 5| - 3|c + 7| = 10 + 2|c - 8|.$ Enter all the solutions, separated by commas.

kittykat Mar 27, 2024

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+1032

Logarithm

Find $x$ if $\log_2 (\log_3 x) = \log_3 (\log_2 x).$

kittykat Mar 27, 2024

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+1032

Logarithms

Suppose $a\neq 0$. Compute $\log_{8a} b$ in terms of $a$ and $b$.

kittykat Mar 27, 2024

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7

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+910

help geometry

Let $G$ be the center of equilateral triangle $XYZ.$ A dilation centered at $G$ with scale factor $-\frac{4}{3}$ is applied to triangle $XYZ,$ to obtain triangle $X'Y'Z'.$ Let $A$ be the area of the region that is contained inside both triangles read more ..

Akhain1 Mar 27, 2024

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+910

Laser

Let $ABCD$ be a square with side length $1.$ A laser is located at vertex $A,$ which fires a laser beam at point $X$ on side $\overline{BC},$ such that $BX = \frac{1}{2}.$ The beam reflects off the sides of the square, until it ends up at another read more ..

Akhain1 Mar 27, 2024

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Rotation

Let A1 A2 A3 ... A15 be a regular polygon. A rotation centered at $A_4$ with an angle of $\alpha$ takes $A_3$ to $A_5$. Given that $\alpha < 180^\circ$, find $\alpha,$ in degrees.

Akhain1 Mar 27, 2024

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Dilation

Point $B$ is the image of point $A$ under a dilation with center $O$. If $OB = 30$, and the scale factor of the dilation is $5$, then what is $OA$?

Akhain1 Mar 27, 2024

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+357

Rectangle

The perimeter of a rectangle is $40,$ and the length of one of its diagonals is $10 \sqrt{2}.$ Find the area of the rectangle.

falafronk Mar 27, 2024

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+357

Parallelogram

Find the area of parallelogram ABCD.

falafronk Mar 27, 2024

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+357

Rhombus

In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $20^\circ.$ Find the area of the rhombus.

falafronk Mar 27, 2024

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+357

help trapezoid

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.

falafronk Mar 27, 2024

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+1509

Counting question

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 ..

bader Mar 27, 2024

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+1509

help counting

Determine the number of ways of choosing three points from the grid below, so that they form an isosceles right triangle.

bader Mar 27, 2024

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+1509

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?

bader Mar 27, 2024

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+1509

Counting

In how many ways can I arrange $3$ different math books and $4$ different history books on my bookshelf, if at least three history textbooks are next to each other?

bader Mar 27, 2024

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