All Questions ⁺⁰235722 Questions

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Geometry

What is the radius of the sphere whose volume is 33 times its surface area?

nerdboy Oct 1, 2024

0

5

0

+448

Counting

Find the number of positive integers that satisfy both the following conditions:
- Each digit is a 1 or a 2 or a 3
- The sum of the digits is 5

onyuIee Oct 1, 2024

0

9

0

+448

Counting

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 ..

onyuIee Oct 1, 2024

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7

0

+448

Counting

The six faces of a cube are painted black. The cube is then cut into 6^3 smaller cubes, all the same size. One of the small cubes is chosen at random, and rolled. What is the probability that when it lands, the face on the top is black?

onyuIee Oct 1, 2024

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5

1

+77

Bases

What is the value of ? Express your answer in base 10.

nerdboy Oct 1, 2024

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5

3

+77

Prime numbers

How many prime numbers are there from 200-400

nerdboy Oct 1, 2024

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7

1

+77

Prime numbers

What is the value of the sum of all prime numbers up to fifty?

nerdboy Oct 1, 2024

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10

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+834

Geometry

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$,
<read more ..

gnistory Oct 1, 2024

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7

0

+834

Geometry

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$, read more ..

gnistory Oct 1, 2024

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6

2

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number theory

what is the smallest integer n that n^2-17 is a prime number squared?

nerdboy Oct 1, 2024

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5

1

+77

In how many ways can you choose 2 people out of a group of 10 people?

In how many ways can you choose 2 people out of a group of 10 people?

nerdboy Oct 1, 2024

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7

1

+77

Number theory

Let n be a positive integer such that n= ABC_7 and n=CBA_11. Find the largest possible value of n in base 10.

nerdboy Oct 1, 2024

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7

0

+85

Solving Linear Inequalities

A charity organization is holding a food drive with a goal to collect at least 1,000 cans of food by the end of the month. It currently has 565 cans from donations and is having an event where 87 guests will attend and bring cans. Which solution set represents read more ..

Alyssiaca Oct 1, 2024

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5

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+85

Solving Linear Inequalities

Elizabeth is selling jam at a farmers market, and she earns $5.00 for each jar of jam that she sells. Her goal for the weekend is to earn at least $450.00, and she has already made $95.00 from jam sales as well as $24.00 from leading a demonstration. What read more ..

Alyssiaca Oct 1, 2024

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10

0

+829

Algebra

Let a and b be positive real numbers such that a + b = 1. Find the set of all possible values of a/b.

AnswerscorrectIy Oct 1, 2024

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7

1

+829

Algebra

A right triangle with integer leg lengths is called cool if the number of square units in its area is equal to five times the number of units in the sum of the lengths of its legs. What is the sum of all the different possible areas of cool right read more ..

AnswerscorrectIy Oct 1, 2024

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9

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+829

Algebra

The graphs of x = y^4 and x + y^2 = 1 + x^2 - y^3 intersect at two points. The distance between these points is of the form sqrt(u + v*sqrt(5)), where u and v are integers. Find the ordered pair (u,v).

AnswerscorrectIy Oct 1, 2024

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7

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+279

Algebra

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 28/5 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

bIueb3rry Oct 1, 2024

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9

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+829

Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

AnswerscorrectIy Oct 1, 2024

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11

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+829

Geometry

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

AnswerscorrectIy Oct 1, 2024

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8

0

+829

Geometry

Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF which intersect at I. If DI=3, BD=4 and BI=6 then compute the area of triangle BID.

AnswerscorrectIy Oct 1, 2024

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7

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+253

Counting

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

jaekg Oct 1, 2024

0

8

0

+637

Geometry

Let \alpha and \beta be acute angles whose sum is also acute, such that $\angle BAC = \alpha,$ $\angle DAB = \beta,$ and $AB = 1$. Let $E$ be the foot of the perpendicular from $A$ to $BC$, and $F$ be the foot of the perpendicular from $E$ to $AB$, as shown read more ..

siIviajendeukie Oct 1, 2024

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