All Questions ⁺⁰237738 Questions

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215

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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 31, 2022

0

177

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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 31, 2022

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240

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Counting

How many solutions are there to the equation
u + v + w + x + y + z = 18
where u, v, w, x, y, and z are nonnegative integers, and x is at most 10?

Guest Dec 31, 2022

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177

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counting

In how many ways can you distribute 10 indistinguishable balls among 8 distinguishable boxes, if at least one of the boxes must be empty?

Guest Dec 31, 2022

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241

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Find

Find all values of x such that: x/(x - 5) = 4/(x - 4) + 12/(x^2 - 9x + 20)

Guest Dec 31, 2022

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226

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Trinomial

For what real values of c is 4x^2 + 14x - c - 3x^2 - 12x the square of a binomial?

Guest Dec 31, 2022

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174

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Counting problem

We want to divide 10 dogs (including Fluffy and Nipper) into three groups, one with 3 dogs, one with 5 dogs, and one with 2 dogs. How many ways can we form the groups such that Fluffy is in the 2-dog group and Nipper is in the read more ..

Guest Dec 31, 2022

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188

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Algebra

We are looking to factor 23x^2 + kx - 5 + x^2 - 3. Some values of k allow us to factor it as a product of linear binomials with integer coefficients. what are all such values of k?

Guest Dec 31, 2022

+1

204

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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 ..

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Guest Dec 31, 2022

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220

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Range and Domain Problem

Find the set of values for which the range of the function

is the set of all real numbers.

Guest Dec 31, 2022

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217

2

Fractions

Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 1 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator read more ..

Guest Dec 31, 2022

-1

240

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Circles

The two circles below are externally tangent. A common external tangent intersects line PQ at R. Find QR.

Guest Dec 31, 2022

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184

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counting

Find the number of positive integers that satisfy the following conditions:
* Each digit is a 1 or a 2 or a 3
* The sum of the digits is 10

Guest Dec 31, 2022

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220

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Graphing

What is the smallest distance between the origin and a point on the graph of y = 1/2*(x^2 - 8)?

Guest Dec 31, 2022

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242

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Coefficient

Find the coefficient of y^4 in the expansion of (2y - 5 + y^2)^6.

Guest Dec 31, 2022

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175

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Expand

Expand (sqrt(t) + 3t + 1)^3 + (sqrt(t) - 3t + 1)^3.

Guest Dec 31, 2022

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189

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Complex numbers

Find all the solutions to z^4 = -4 - 5z^2 in complex numbers.
Express all the solutions in the form a + bi, where a and b are real numbers.

Guest Dec 31, 2022

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204

1

i need help

I've been looking at this problem for a long time. Can anyone help?

The equation x^2 - kx - 12 = 5 has only integer solutions for certain positive integers k. What is the sum of all such values of k?

Guest Dec 31, 2022

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203

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Constant term

Find the constant term in the expansion of (2z - 1/(z*sqrt(z)) + 1)^4.

Guest Dec 31, 2022

+1

213

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help needed - algebra 2

Let and be complex numbers such that and . Find the maximum value of

Guest Dec 31, 2022

Dec 30, 2022

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244

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need help

Find the positive integer n such that the expansion of (4x - 7y)^n contains a term of the form cx^2*y.

Guest Dec 30, 2022

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211

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Algebra

For some real number a and some positive integer n, the first few terms in the expansion of (1 + ax)^n are
1 + 10x + 150 x^2 + cx^3 + ...

Find c. read more ..

Guest Dec 30, 2022

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214

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Help binomial

Find the coefficient of u^2 v^9 in the expansion of (2u - 3v + u^2 - v^2)^9.

Guest Dec 30, 2022

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234

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Hard algebra

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and a^3 - 3ab^2 = 673. Find a - b.

Guest Dec 30, 2022

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