All Questions ⁺⁰237738 Questions

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Equation

Find all real numbers x such that
(3^x - 27)^3 + (27x - 3)^3 = 3x + 27x - 30.

Guest Dec 23, 2022

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221

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How do you show yourr work for finding 5/6 of 18?

How do you show your work for finding 5/6 of 18?

Guest Dec 23, 2022

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help cphill

Enter the letters of the points that satisfy the inequalities
For example, if you think points and make the inequalities true, then enter "B, D, G".

[asy]
unitsize(0.4 cm);
pair read more ..

Guest Dec 23, 2022

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204

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Algebra

Find all solutions of the equation
|x^2 - 30x - 1| + |x^2 - 30x + 29| = 30.

Guest Dec 23, 2022

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216

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Algebra

Arrange the following numbers in increasing order (smallest first, biggest last):

A = 2*1/2*4*1/6
B = 12*128 read more ..

Guest Dec 23, 2022

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176

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Probability

Valeria has three coins, each of which has a probability of 1/2 of coming up heads. On her first turn, she flips all three coins. If all three come up heads, then she stops. Otherwise, for her second turn, she flips any coins that came up tails. read more ..

Guest Dec 23, 2022

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Factoring

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 23, 2022

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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 23, 2022

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186

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Graphing

The graph of y = f(x) is shown below.

For each point (a,b) that is on the graph of y = f(x), the point ((a - 7)/2, (3b + 1)/4) is plotted, forming the graph of another function y = g(x). As an example, the point read more ..

Guest Dec 23, 2022

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Coordinates

A median of a triangle is a line segment joining a vertex of a triangle to the midpoint of the opposite side. The three medians of a triangle are drawn below.

Note that the three medians appear to intersect at the same point! Let's read more ..

Guest Dec 23, 2022

Dec 22, 2022

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189

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Probability question

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 22, 2022

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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 22, 2022

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221

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geometry

In the diagram below, D is a point on segment CE such that segments AD and BE are parellel and point A is not on segment BC. Line segments AD and BC intersect at point P.

If angle CAD = 67 degrees, then what is angle read more ..

Guest Dec 22, 2022

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190

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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 22, 2022

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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 22, 2022

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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 22, 2022

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Counting problem

(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 22, 2022

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help counting

(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 22, 2022

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190

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Fun Challenge Problem

In base b, there are 50 numbers that have their digits all distinct (which means all different).
What is b?

If you can do it, instead of 50, try 100!

Guest Dec 22, 2022

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function

The function f(n) satisfies
binom(2n)n - binom(2n + 1)(2n) = f(n) *binom(2n + 1)(n + 1)
for all positive integers n. Find f(n).

Guest Dec 22, 2022

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240

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help math

Compute
binom{5}{3} + binom{6}{3} + binom{7}{3}

Guest Dec 22, 2022

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