All Questions ⁺⁰237637 Questions

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Divisibility Problem. Please Help! TYSM

a) Show that n(2n + 1)(7n + 1) is divisible by 6 for all integers n.
b) Find all integers n such that n(2n + 1)(7n + 1) is divisible by 12.

Explain your answer please!

CPhilFanboy Nov 26, 2020

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560

2

+28

Help

Sou1y Nov 26, 2020

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353

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counting

How many even, three-digit positive integers have the property that exactly two of the integer's digits are even?

Guest Nov 26, 2020

-1

645

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+29

Analytic Geometry question

Just a quick note, this question has been posted already, but the answer wasn't fully explained in detail, so I'm reposting it in hopes that someone can explain one step about how to do the problem.

Let A=(0,0), B=(a,b), and read more ..

ianw11 Nov 26, 2020

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402

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number theory

If a, b, and c are positive integers such that gcd(a,b) = 168 and gcd(a,c) = 88, then what is the smallest possible value of gcd(b,c)?

Guest Nov 26, 2020

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401

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probability

Paul and Jesse each choose a number at random from the first six primes. What is the probability that the sum of the numbers they choose is divisible by 3?

Guest Nov 26, 2020

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686

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circle

Let A, B, and C be points on a circle of radius 18. If angle ACB = 170 degrees, what is the circumference of the minor arc {AB}? Express your answer in terms of pi.

Guest Nov 26, 2020

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542

1

+28

travel word problem

Julia lucked into some tickets last minute for the 2012 Summer
Olympics in London. She certainly can’t pass up her chance at
meeting Prince William and Kate Middleton! Her tickets are so last
minute, though, that she has to rush to the airport read more ..

Sou1y Nov 26, 2020

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611

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+28

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Sou1y Nov 26, 2020

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545

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Joe has exactly enough paint

Joe has exactly enough paint to paint the surface of a cube whose main diagonal is 2. It turns out that this is also exactly enough paint to paint the surface of a sphere. Find the radius of the sphere.

Guest Nov 26, 2020

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594

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A hemisphere-shaped bowl

A hemisphere-shaped bowl with radius 1 foot is filled full with chocolate. All of the chocolate is then evenly distributed between 64 congruent, smaller hemisphere-shaped molds. What is the radius of each of the smaller molds, in feet?

Guest Nov 26, 2020

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601

2

+28

Help

Sou1y Nov 26, 2020

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497

1

probability

A bag contains some sticks with lengths three feet, four feet, five feet, six feet, seven feet, and eight feet. Three sticks are chosen at random.
a) What is the probability that a triangle can be formed with the three chosen sticks?
b) read more ..

Guest Nov 26, 2020

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619

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A circular cylindrical post

A circular cylindrical post with a circumference of 4 feet has a string wrapped around it, spiraling from the bottom of the post to the top of the post. The string evenly loops around the post exactly four full times, starting at the bottom edge and finishing read more ..

Guest Nov 26, 2020

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585

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help

Find a polynomial such that (x+1)^3+x^2*q(x) has degree less than 2.
i dont want the answer can i just have a hint?

Guest Nov 26, 2020

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680

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coordinates

The point (x,y) is first reflected in the x-axis then rotated 90 degrees counterclockwise about the origin, then reflected in the line y = x . What is the image point?

Guest Nov 26, 2020

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420

1

Time

Ben is heading to Tokyo for his winter break. Ben has a direct flight
from Philadelphia leaving at 2PM on Friday and should take 14 hours.
His brother, Matt, is joining him and is leaving New York City at
12PM on the same day. His read more ..

Guest Nov 26, 2020

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631

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+205

Circle

parpar1 Nov 26, 2020

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497

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algebra

Solve the inequality x^3 >= 4x.

Guest Nov 26, 2020

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341

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number theory

In the statement below, the two blanks can be filled by positive single-digit numbers in such a way that the statement is always true:
If 2x = y + 5 (mod 13), then x = __*y + ___ (mod 13).
What is the product of the two digits that go in read more ..

Guest Nov 26, 2020

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410

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50-3=

Guest Nov 26, 2020

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462

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graph

On the graph of y = (x + 2)^4 - 500, how many points are there whose coordinates are both negative integers?

Guest Nov 26, 2020

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