All Questions ⁺⁰236027 Questions

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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 read more ..

booboo44 Jan 31, 2024

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31

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+773

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.)

booboo44 Jan 31, 2024

Jan 30, 2024

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21

1

+773

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.

booboo44 Jan 30, 2024

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18

2

+773

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 read more ..

booboo44 Jan 30, 2024

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39

1

+773

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?

booboo44 Jan 30, 2024

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13

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 read more ..

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Akhaim1 Jan 30, 2024

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23

1

+0

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.</ read more ..

mincecrift Jan 30, 2024

Jan 29, 2024

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29

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+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? read more ..

parmen Jan 29, 2024

-1

24

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+1557

Complex Numbers

Compute (1 + i)/(2 - i)(3 + i).

parmen Jan 29, 2024

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37

1

+1557

Algebra

Simplify the expression
\frac{1}{\sqrt{36}} - \sqrt{27} - \frac{1}{\sqrt{27}} - \sqrt{18} + \frac{1}{\sqrt{18}} - \sqrt{9}

parmen Jan 29, 2024

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29

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)?

ruiruima Jan 29, 2024

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36

4

+0

PLS HELP CPHILL

Given positive integers and such that and , what is the smallest possible value for ?

daonly39 Jan 29, 2024

Jan 28, 2024

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27

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+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?

wiseowl Jan 28, 2024

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32

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?

wiseowl Jan 28, 2024

-1

57

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

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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.

ljdaskljf Jan 28, 2024

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49

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+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 $\overline{AS}$, read more ..

wiseowl Jan 28, 2024

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31

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 $EFGH$

wiseowl Jan 28, 2024

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45

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+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 read more ..

wiseowl Jan 28, 2024

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