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Post New Question
All Questions
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235783 Questions
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24
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+748
Hard probability
The numbers $x_1,$ $x_2,$ $x_3,$ $x_4$ are chosen at random in the interval $[0,1].$ Let $I$ be the interval between $x_1$ and $x_2,$ and let $J$ be the interval between $x_3$ and $x_4.$ Find the probability that intervals $I$ and $J$ both have
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booboo44
Jan 31, 2024
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30
1
+748
Counting problem
Catherine rolls a standard 6-sided die eight times. If the product of her rolls is 2700, then how many different sequences of rolls could there have been? (The order of the rolls matters.)
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booboo44
Jan 31, 2024
Jan 30, 2024
0
19
1
+748
Help probability
Three cards are randomly drawn from a standard deck of $52$ cards, without replacement. Find the probability that the first card is a king, the second card is hearts, and the third card is red.
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booboo44
Jan 30, 2024
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18
2
+748
Probability
A member of the junior varsity swim team will be elected as President. Each member is equally likely to be elected. The probability that a sophomore is elected is times the probability that a freshman is elected. Everyone on the junior varsity
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booboo44
Jan 30, 2024
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36
1
+748
help 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?
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booboo44
Jan 30, 2024
0
11
8
+0
Geometry problems
1.
Let ABCDE be a right square pyramid, with base ABCD and apex E Find the volume of the pyramid.
2.
Let ABCDEFGH be right rectangular
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Akhaim1
Jan 30, 2024
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21
1
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I'm Confused
The line y=3 intersects the graph of y = 4x2+x-1 at the points A and B. The distance between A and B can be written as , where m and n are positive integers that do not share any factors other than one. Find the value of m-n.</
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mincecrift
Jan 30, 2024
Jan 29, 2024
0
29
1
+1557
System
For certain values of k and m, the system
3a + 2b = 2
a + 2b = k - 8a - mb
has infinitely many solutions (a,b). What are k and m?
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parmen
Jan 29, 2024
-1
24
1
+1557
Complex Numbers
Compute (1 + i)/(2 - i)(3 + i).
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parmen
Jan 29, 2024
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34
1
+1557
Algebra
Simplify the expression
\frac{1}{\sqrt{36}} - \sqrt{27} - \frac{1}{\sqrt{27}} - \sqrt{18} + \frac{1}{\sqrt{18}} - \sqrt{9}
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parmen
Jan 29, 2024
0
27
2
+0
Digits problem
The letters A, B, C, D, E, and F represent digits and ABC,DEF represents a positive six-digit integer. What is the number ABC,DEF if 4(ABC,DEF) = 3(DEF,ABC)?
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ruiruima
Jan 29, 2024
0
34
4
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PLS HELP CPHILL
Given positive integers and such that and , what is the smallest possible value for ?
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daonly39
Jan 29, 2024
Jan 28, 2024
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22
1
+1678
Prism
A rectangular prism has a length of $3$, a width of $5$, and a height of $11$. What is the distance between two opposite corners of the prism?
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wiseowl
Jan 28, 2024
0
31
1
+1678
Cubes
Jessica has one cube with a side length of $1,$ and another cube with a side length of $1.$ She then glues the two cubes together, to form one single solid. What is the smallest possible surface area of the single solid?
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wiseowl
Jan 28, 2024
-1
52
0
+1678
Prism
Let $PQRSTUVW$ be a rectangular prism, as shown. The area of face $TUVW$ is $10,$ the area of face $TUQP$ is $10,$ and the area of face $TPSW$ is $10.$ Find the volume of the rectangular prism.
wiseowl
Jan 28, 2024
0
36
1
+0
Determine the equation of a line parallel to −6x + 3y = −18 with the same x-intercept as the line defined by 14x + 7y − 14 = 0.
Determine the equation of a line parallel to −6x + 3y = −18 with the same x-intercept as the line
defined by 14x + 7y − 14 = 0.
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ljdaskljf
Jan 28, 2024
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45
0
+1678
Pyramid
Let $APQRS$ be a pyramid, where the base $PQRS$ is a square. The total surface area of pyramid $APQRS$ (including the base) is $800$. Let $W$, $X$, $Y$, and $Z$ be the midpoints of $\overline{AP}$, $\overline{AQ}$, $\overline{AR}$, and $\overline{AS}$,
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wiseowl
Jan 28, 2024
-1
27
1
+1678
Pyramid
Let $ABCD$ be a regular tetrahedron. Let $E$, $F$, $G,$ $H$ be the centers of faces $BCD$, $ACD$, $ABD$, $ABC$, respectively. The volume of pyramid $DEFG$ is $18.$ Find the volume of pyramid $EFGH$
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wiseowl
Jan 28, 2024
0
41
0
+1678
Solid geo
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
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wiseowl
Jan 28, 2024
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