All Questions ⁺⁰238122 Questions

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Find a formula for the sum of the squares of the first n positive odd integers.

Guest Dec 14, 2019

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978

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Anty the ant is on the real number line, and Anty's goal is to get to 0. If Anty is at 1, then on the next step, Anty moves to either 0 or

Anty the ant is on the real number line, and Anty's goal is to get to 0. If Anty is at 1, then on the next step, Anty moves to either 0 or 2 with equal probability. If Anty is at 2, then on the next step, Anty always moves to 1. Let read more ..

Guest Dec 14, 2019

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Two students toss a fair coin. Whenever it lands head up, the first student wins one dollar. If not, the first student loses one dollar. Find the probability that after five coin tosses, the first student's winnings is exactly one dollar. read more ..

Guest Dec 14, 2019

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995

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HELP ASAP

I am stuck on these two problems, can someone help?

There are 20 chairs in a row. Find the number of ways of choosing 5 of these chairs, so that no two chosen chairs are adjacent.
read more ..

Rollingblade Dec 14, 2019

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901

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whoisjoe Dec 14, 2019

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2345

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help last answer was wrong! please ignore dollar signs

Right triangle $XYZ$ has legs of length $XY = 12$ and $YZ = 6$. Point $D$ is chosen at random within the triangle $XYZ$. What is the probability that the area of triangle $XYD$ is at most $12$?

Guest Dec 14, 2019

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843

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Consider a target board that is a square of side 14 cm. If you have a uniform chance of hitting any part of it, what is the probability that your arrow will miss the bull's eye which is a circle of radius 7cm centered at the center of the square? read more ..

ElectricPavlov ●●

Guest Dec 14, 2019

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573

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You roll 2 fair dices with your eye closed, you are told "at least one of the dice is a one", what is the probability that the both dice are a 1?

Guest Dec 14, 2019

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Find n if (1^2 + 2^2 + ... + n^2)/(1 + 2 + .. + n) = 43/3.

Guest Dec 14, 2019

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whoisjoe Dec 14, 2019

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509

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Find all ordered pairs of positive integers (x,y) that satisfy x^2 + y^2 - xy = 49.

Guest Dec 14, 2019

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649

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In triangle ABC, angle A is 45 degrees and angle C is 30 degrees. If altitude BH intersects median AM at P, then AP:PM = 1:k. Find k.

Guest Dec 14, 2019

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609

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The value of t 2-dollar bills and f 5-dollar bills is 87. If all ordered pairs (t,f) are equally likely, then find the probability that both t and f are prime.

Guest Dec 14, 2019

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477

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Find period of the function f(x) = sin(x)^4 + cos(x)^4.

Guest Dec 14, 2019

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761

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The function is defined by f(1) = 1 and f(n) = f(n - 1) + 2n for n >= 2. Find f(n) in terms of n.

Guest Dec 14, 2019

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795

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If a, b, c are positive numbers, find the numerical value of

Guest Dec 14, 2019

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1035

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Geometry

A square is inscribed in a circle forming 4 identical segments. The area of a single segment is 1cm2. What's the area of that square?

Dragan Dec 14, 2019

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485

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help!

Triangle DEF is an equilateral triangle with a side length of 3. A point P is chosen at random within triangle DEF. What is the probability that the length DP is at most 1?

off-topic

Guest Dec 14, 2019

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689

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help!

Triangle DEF is an equilateral triangle with a side length of 3. A point P is chosen at random within triangle DEF. What is the probability that the length DP is at most 1?

off-topic

Guest Dec 14, 2019

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299

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geometry in probability problem need help fast

Right triangle XYZ has legs of length XY=12 and YZ=6. Point D is chosen at random within the triangle XYZ. What is the probability that the area of triangle XYD is at most 12?

Guest Dec 14, 2019

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1658

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Geometry AoPS Help

In rectangle ABCD, AB=3 and BC=9 . The rectangle is folded so that points A and C coincide, forming the pentagon ABEFD. What is the length of segment EF? Express your answer in simplest radical form.

goreisthebest Dec 14, 2019

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Aops Help

A boss plans a business meeting at Starbucks with the two engineers below him. However, he fails to set a time, and all three arrive at Starbucks at a random time between 2:00 and 4:00 p.m. When the boss shows up, if both engineers are not already there, read more ..

goreisthebest Dec 14, 2019

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