All Questions ⁺⁰238008 Questions

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Hi! I'm Struggling. Help is appreciated

1. Compute

[ (1-i)^10(sqrt3 + i)^5 ] / (-1-i*sqrt3)^10
read more ..

Guest Dec 25, 2022

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249

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Algebra

A magician makes potions by combining maple syrup from a magical maple tree with ordinary water. The magician starts with a large supply of two potions: a red potion, which is 75% magical syrup by volume (and the rest is just water), and blue potion, which read more ..

Guest Dec 25, 2022

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246

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Probability

A bag contains five white balls and three black balls. Your goal is to draw two white balls.

(a) You simultaneously draw two balls at random. What is the probability that they are both white?
(b) You simultaneously draw two balls read more ..

Guest Dec 25, 2022

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225

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Expected value

The grid below is made up of line segments, like the line segment in red.
There are a number of paths that go from A to B in the grid, where every step goes to the right or up. If we choose a line segment at random, then what is the expected number of read more ..

Guest Dec 25, 2022

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229

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Probability

In the SuperLottery, three balls are drawn (at random, without replacement) from white balls numbered from 1 to 12, and one SuperBall is drawn (at random) from red balls numbered from 13 to 20. When you buy a ticket, you choose three numbers from 1 to 12, read more ..

Guest Dec 25, 2022

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help counting

(a) Find the number of ways that Magnus can give out 20 identical stickers to 5 of his friends. (Not everyone has to get a sticker.)

(b) Find the number of ways that Magnus can give out 20 identical stickers to 5 of read more ..

Guest Dec 25, 2022

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183

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Counting problem

(a) In how many ways can you distribute 4 distinguishable balls among 3 indistinguishable boxes?

(b) In how many ways can you distribute 4 indistinguishable balls among 5 distinguishable boxes?

Guest Dec 25, 2022

Dec 24, 2022

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190

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help counting

There is a group of five children, where two of the children are twins. How many ways can I distribute 10 identical pieces of candy to the children, if the twins must get an equal amount of candy?

Guest Dec 24, 2022

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247

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Angle bisectors

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 = 8, then find the area of triangle ABC.

Guest Dec 24, 2022

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194

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help counting

Miyu is giving out 9 identical chocolates to her 7 friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets exactly 2 chocolates?

Guest Dec 24, 2022

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211

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Counting

Find the number of solutions to
x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 + x_8 + x_9 + x_10 <= 2
in nonnegagive integers.

Guest Dec 24, 2022

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190

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Probability

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers (1, 2, 3, 4, 5, 6, and 7). Among all the cards of each color, there is exactly one card labeled with each number. The read more ..

Guest Dec 24, 2022

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242

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help counting

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color, and at lest three of the squares are red. How many ways are there to color the five squares?

Guest Dec 24, 2022

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202

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binomials

Fill in the blanks to make the equation true (Each blank should contain a positive integer.)

\binom{n}{k} = \binom{n - 2}{k} + \binom{n - 2}{k - 1} + \binom{n - 1}{k} + \binom{n - 1}{k - 1} + \binom{n}{k - 1} + \binom{n}{k + read more ..

Guest Dec 24, 2022

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213

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+307

Please help just this once prob

For everybody to know the answer is not 2877. Please give me the solution if you can and not just the answer.
Find the least positive four-digit solution to the following system of congruences.

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Imcool Dec 24, 2022

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195

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binomials

For nonnnegative integers a and b, where a >= 2 and b >= 2, simplify
binom{a + b}{2} + binom{2a + b}{2} + binom{a + 2b}{2} - binom{a - b}{2}

Guest Dec 24, 2022

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206

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Function

For a certain function f(n), the identity
(2n)/n - (2n)/(n + 1) = f(n) (2n)/n
for all nonnegative integers n. Find f(n).

Guest Dec 24, 2022

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263

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Probability

The following cards are dealt to three people at random, so that everyone gets the same number of cards. What is the probability that everyone gets a red card?

Guest Dec 24, 2022

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260

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Complex numbers

Describe all solutions to zw - 3w - 2iw + 4z = 7iw + 5w + 11iz - 13 + 15i
where z and w are complex numbers.

Guest Dec 24, 2022

Dec 23, 2022

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231

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Functions

The functions f and h are defined as follows:
f(x) = (x + 5)/(x - 7) and h(x) = (x + 5)(x - 7).

Explain why the functions f and h are not the same function. read more ..

Guest Dec 23, 2022

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