All Questions ⁺⁰234657 Questions

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+145

Help

There were some jelly beans in a jar. 1/3 of them were purple, 2/9 of them were yellow and the rest were orange. There were 312 orange jelly beans. How many jelly beans are there altogether?

sugabreaddoughman Aug 8, 2024

0

1

2

+24

Let $m$ and $n$ be positive integers. If $m$ has exactly $7$ positive divisors, $n$ has exactly $10$ positive divisors, and $mn$ has exactly

Let $m$ and $n$ be positive integers. If $m$ has exactly $7$ positive divisors, $n$ has exactly $10$ positive divisors, and $mn$ has exactly $22$ positive divisors, then how many divisors does $m^2 n^2$ have?

dogsrule Aug 8, 2024

Aug 7, 2024

0

2

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+310

Algebra

Let z and w be complex numbers such that |z|=1,|w|=1, and |z-2w|=5. Find |z+w| .

cooIcooIcooI17 Aug 7, 2024

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2

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+467

Number Theory

What is 100000_{16} * E21A8_{16} in base 16?

ChiIIBill Aug 7, 2024

0

4

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+467

Number Theory

Let N be a positive integer. The number N has three digits when expressed in base 7. When the number N is expressed in base 18, it has the same three digits, in reverse order. What is N? (Express your answer in decimal read more ..

ChiIIBill Aug 7, 2024

0

4

1

+625

Probability

The following cards are split into three piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?
Ace of spades
Ace of hearts
Ace of diamonds read more ..

AnswerscorrectIy Aug 7, 2024

0

3

1

+625

Probability

Alex chooses a number at random from the set {1, 2, 3, 4, 5}. Winnie also chooses a number at random from the same set. (They can choose the same number.) What is the probability that the product of their numbers is at least 4? read more ..

AnswerscorrectIy Aug 7, 2024

0

6

0

+625

Algebra

Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 100, Shirley runs screaming from the room. What number does Laverne say that sends read more ..

AnswerscorrectIy Aug 7, 2024

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1

+1341

Geometry

In a certain regular polygon, the measure of each interior angle is $2$ times the measure of each exterior angle. Find the number of sides in this regular polygon.

kittykat Aug 7, 2024

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4

1

+1341

Geometry

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $AX = 5,$ and $CX = 5$. What is $BX$?

kittykat Aug 7, 2024

Aug 6, 2024

0

8

0

+1706

Geometry

In triangle $ABC$, $AB = 10$ and $AC = 15$. Let $D$ be the foot of the perpendicular from $A$ to $BC$. If $BD:CD = 1:3$, then find $AD$.

ABJeIIy Aug 6, 2024

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3

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+1706

Geometry

We have a triangle $\triangle ABC$ and a point $K$ on $BC$ such that $AK$ is an altitude to $\triangle ABC$. If $AC = 8,$ $BK = 2$, and $CK = 3,$ then what is $AB$?

ABJeIIy Aug 6, 2024

0

4

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+673

Geometry

Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{AB}$ is $4,$ and the circle has a radius of $5.$ Find the length $AB.$ read more ..

magenta Aug 6, 2024

0

3

1

+673

Geometry

A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point P on the edge of the table (as shown below) has a distance of 6 from one wall, and a distance of 6 from the other wall. Find the radius of the read more ..

magenta Aug 6, 2024

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5

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+2651

Geometry

In trapezoid EFGH, \overline{EF} \parallel \overline{GH}, and P is the point on \overline{EH} such that EP:PH = 1:2. If the area of triangle PEF is 6, and the area of triangle PGH is 6, then find the area of trapezoid EFGH.

LiIIiam0216 Aug 6, 2024

0

5

1

+19

Please Help!

The numbers x1, x2, x3, and x4 are chosen at random in the interval [0,1]. Let I be the interval between x1 and x2, and let J be the interval between x3 and x4. Find the probability that intervals I and J overlap.

helpmeeee Aug 6, 2024

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3

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+328

Counting

How many solutions are there to the equation
u + v + w + x + y + z = 7
where u, v, w, x, y, and z are nonnegative integers, and x is at most 2 or y is at least 3?

onyuIee Aug 6, 2024

0

3

0

+625

Algebra

Let a1, a2, a3, ..., a10 be an arithmetic series. If a1 + a3 = -2 and a2 + a4 + a6 = 1, then find a1.

AnswerscorrectIy Aug 6, 2024

0

2

0

+625

Algebra

Let
f(x) = \frac{2x + 5}{x - 4} + \frac{x^2 + 1}{4x - 3}.
Find the inverse $f^{-1}(x)$.

AnswerscorrectIy Aug 6, 2024

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1

4

+4

Confused

There is a single sequence of integers such that and for Find

DragonsRule Aug 6, 2024

0

1

0

+1475

Geometry

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $4,$ and the area of triangle $PSR$ is $8.$ Find the area of trapezoid read more ..

parmen Aug 6, 2024

0

9

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+2651

Number Theory

If n \equiv 43 \pmod{165}, then what is the residue of $n$ modulo 2?

LiIIiam0216 Aug 6, 2024

0

6

0

+2651

Number Theory

What is the largest positive integer $n$ such that $1457$, $1797$, $709$, $15$, $24$, $197$, $428$ all leave the same remainder when divided by $n$?

LiIIiam0216 Aug 6, 2024

0

4

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+1323

Algebra

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{8}.

blackpanther Aug 6, 2024

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