All Questions ⁺⁰235290 Questions

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+60

help me pls with counting and probability

Find the number of ways of choosing three circles below, so that no two circles are next to each other.
[asy]
unitsize(1 cm);
int i;
for (i = 0; i <= 11; ++i) {<#> draw(Circle(2*dir(360/12*i),0.3));<#> label(string(i + 1), read more ..

ghistory Oct 13, 2024

Oct 12, 2024

0

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1

+645

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $3$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $3$ hours read more ..

gnistory Oct 12, 2024

0

2

0

+645

Algebra

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

gnistory Oct 12, 2024

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1

+645

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $1000$ square foot wall in $10$ minutes, then how long would it take for $5$ members to paint a $1000$ square foot wall, in minutes?

gnistory Oct 12, 2024

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+120

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $100$ square foot wall in $10$ minutes, then how long would it take the $15$ members to paint a $100$ square foot wall, in minutes?

AUnVerifedTaxPayer Oct 12, 2024

0

1

0

+120

Algebra

Find the largest integer $k$ such that the equation
5x^2 - kx + 8 - 20x^2 + 45 = 0
has no real solutions.

AUnVerifedTaxPayer Oct 12, 2024

0

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1

+120

Algebra

Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2 - 2x^2 + 4x - 1.

AUnVerifedTaxPayer Oct 12, 2024

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+77

Could I get some help on this rly hard Alg Problem :D

Define Compute
thanks a lot!

NotLatePY Oct 12, 2024

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0

+1796

Geometry

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.

ABJeIIy Oct 12, 2024

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1

0

+1796

Geometry

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 ..

ABJeIIy Oct 12, 2024

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+4

Floor Question System of Equations

Find all possible values of b, where (a,b,c) satisfies and a, b, and c are positive. Enter all values, separated by commas.

SirFizzbone.Official Oct 12, 2024

Oct 11, 2024

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+1405

Counting

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 ..

kittykat Oct 11, 2024

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1

+1405

Counting

At a meeting, four scientists, two mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if the mathematicians must sit next to each other? (Two seatings are considered equivalent if read more ..

kittykat Oct 11, 2024

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+1405

Counting

A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, read more ..

kittykat Oct 11, 2024

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+802

Geometry

Let $B,$ $A,$ and $D$ be three consecutive vertices of a regular $20$-gon. A regular heptagon is constructed on $\overline{AB},$ with a vertex $C$ next to $A.$ Find $\angle BAD,$ in degrees.

RedDragonl Oct 11, 2024

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+802

Geometry

In the diagram below, each side of convex quadrilateral $ABCD$ is trisected. (For example, $AP = PQ = QB.$) The area of convex quadrilateral $ABCD$ is $180.$ Find the area of the shaded region.

RedDragonl Oct 11, 2024

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+802

Geometry

Let $IJKLMN$ be a hexagon with side lengths $IJ = LM = 3,$ $JK = MN = 3,$ and $KL = NI = 3$. Also, all the interior angles of the hexagon are equal. Find the area of hexagon $IJKLMN$.

RedDragonl Oct 11, 2024

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+802

Geometry

The number of diagonals in a certain regular polygon is equal to $2$ times the number of sides. How many sides does this polygon have?

RedDragonl Oct 11, 2024

+1

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3

+760

Number Theory

Fill in the blanks with three distinct positive integers.
1/___ + 1/___ + 1/___ = \frac{13}{12}

AnswerscorrectIy Oct 11, 2024

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1

4

+760

Number Theory

For a positive integer n, \phi(n) denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$. What is $\phi(2835)$?

AnswerscorrectIy Oct 11, 2024

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2

+760

Number Theory

How many numbers between $1000$ and $2000$ leave a remainder of $3$ when divided by $47?$

AnswerscorrectIy Oct 11, 2024

Oct 10, 2024

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1

+1796

Number Theory

Use the Euclidean Algorithm to find gcd(972, 1220).

ABJeIIy Oct 10, 2024

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