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Post New Question
All Questions
+0
237293 Questions
0
20
1
+821
Counting
Consider a house with a finite number of rooms. Some of the rooms have an even number of doors, and some of the rooms have an odd number of doors. In the house below, how many doors are there from the house to the outside world?
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cooIcooIcooI17
Sep 26, 2024
0
38
0
+1766
Geometry
In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 12$, find $BC$.
blackpanther
Sep 26, 2024
0
22
0
+1766
Geometry
In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 12$, find $BZ$.
blackpanther
Sep 26, 2024
0
24
0
+1766
Geometry
Triangle ABC is rotated completely around side BC, sweeping out a solid in space. Find the volume of the solid.
AB = 8, AC = 12, CB = 8
blackpanther
Sep 26, 2024
Sep 25, 2024
0
30
0
+413
Geometry
In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?
nathanl6656
Sep 25, 2024
0
29
0
+413
Geometry
In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?
nathanl6656
Sep 25, 2024
0
25
0
+413
Geometry
In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11
nathanl6656
Sep 25, 2024
0
16
1
+972
Geometry
In quadrilateral $PQRS$, $PQ = QR = RS = SP$, $PR = \sqrt{2}$, and $QS = \sqrt{2}$. Find the perimeter of $PQRS$.
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Rangcr897
Sep 25, 2024
0
19
1
+965
Algebra
At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15. Gary orders a bagel and a muffin, which comes out to $3.50. Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.15. How many cents does
read more ..
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magenta
Sep 25, 2024
0
26
1
+949
Counting
Consider a house with a finite number of rooms. Some of the rooms have an even number of doors, and some of the rooms have an odd number of doors. In the house below, how many doors are there from the house to the outside world?
●
gnistory
Sep 25, 2024
0
25
0
+949
Counting
Twelve points are given in the plane, so that no three points lie on the same line.
Five distinct segments joining pairs of these points are chosen at random, with all \binom{12}{2} = 66 such segments equally likely to be chosen. What
read more ..
gnistory
Sep 25, 2024
0
23
0
+949
Counting
A standard 8 times 8 chessboard has 64 unit squares.
Eight rooks are randomly placed on different squares of a chessboard. A rook is said to attack all of the squares in its row and its column.
Compute the probability
read more ..
gnistory
Sep 25, 2024
0
18
1
+290
Geometry
In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $90^\circ.$ Find the area of the rhombus.
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AUnVerifedTaxPayer
Sep 25, 2024
+1
13
1
+290
Geometry
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.
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AUnVerifedTaxPayer
Sep 25, 2024
0
11
1
+290
Geometry
Rectangle $ABCD$ contains a point $X$ such that $AX = 3$, $BX = 3$, and $CX = 3$. Find $DX$.
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AUnVerifedTaxPayer
Sep 25, 2024
0
23
1
+290
Geometry
A rectangle contains a strip of width $1,$ as shown below. Find the area of the strip.
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AUnVerifedTaxPayer
Sep 25, 2024
Sep 24, 2024
0
35
0
+613
Algebra
For some real number a and some positive integer n, the first few terms in the expansion of (1 + ax)^n are 1 - 12x + 54x^2 + cx^3 + ... Find c.
Pythagorearn
Sep 24, 2024
0
18
1
+613
Algebra
Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.
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Pythagorearn
Sep 24, 2024
0
25
1
+949
Algebra
Find the largest real number $c$ such that $1$ is in the range of $f(x)=x^2-5x+c-3x+8$.
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gnistory
Sep 24, 2024
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