All Questions ⁺⁰237643 Questions

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163

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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 17, 2022

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176

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help with 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 17, 2022

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210

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help with modulus

is there any way to solve:

using mod? i tried but im not sure how

Guest Dec 17, 2022

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232

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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 17, 2022

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168

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help with counting

Let n be a positive integer. Let k be a positive integer.

(a) Using a counting argument, show that C(n - 1, k - 1) + C(n - 1, k) = C(n,k).
read more ..

Guest Dec 17, 2022

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167

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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 17, 2022

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181

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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 17, 2022

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188

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triangle

In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect AX at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area read more ..

Guest Dec 17, 2022

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158

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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 17, 2022

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172

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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 17, 2022

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170

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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 17, 2022

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216

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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 17, 2022

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214

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binomials

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

Guest Dec 17, 2022

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184

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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 17, 2022

Dec 16, 2022

+24

239

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+1307

Casework

Let S be the set of points (a,b) in the coordinate plane, where each of a and b may be -1, 0, or 1. How many distinct lines pass through at least two members of S?

dolphinia Dec 16, 2022

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247

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Distributions

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 16, 2022

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239

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Which of the following sets of numbers could not represent the three sides of a triangle?

Which of the following sets of numbers could not represent the three sides of a triangle?

please helpppp

Guest Dec 16, 2022

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180

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6^3x / 36^x^2 = 6^p, express p in terms of x

6^3x / 36^x^2 = 6^p, express p in terms of x

Guest Dec 16, 2022

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165

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counting

Fill in the blanks to make the equation true. (Each blank should contain a 2-digit number)

18/18 + 19/18 + 20/18 + ... + 45/18
read more ..

Guest Dec 16, 2022

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236

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Nathan is going to a carnival that has games and rides.

Nathan is going to a carnival that has games and rides. Each game costs $1 and each ride costs $3.75. Nathan spent $34 altogether at the carnival and the number of rides he went on is twice the number of games he played. Determine the number of games Nathan read more ..

Guest Dec 16, 2022

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176

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distributions

(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 16, 2022

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173

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Graphs

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 16, 2022

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194

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tangent circles

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

Guest Dec 16, 2022

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217

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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 16, 2022

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170

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Algebra

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

Guest Dec 16, 2022

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