All Questions ⁺⁰237643 Questions

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181

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Constant term

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

Guest Jan 11, 2023

Jan 10, 2023

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169

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Binomials

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 Jan 10, 2023

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178

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Probability question

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 Jan 10, 2023

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194

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help counting

In how many ways can the numbers 1 through 5 be entered once each into the five boxes below so that all the given inequalities are true?

Guest Jan 10, 2023

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201

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plz help

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 Jan 10, 2023

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197

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Binomial Theorem

(a) Simplify (n/k)/(n/(k - 1))

(b) For some positive integer n, the expansion of (1 + x)^n has three consecutive coefficients a, b, c that satisfy 1:8:28. What must n be?
read more ..

Guest Jan 10, 2023

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159

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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 Jan 10, 2023

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186

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Hard counting

Each unit square of the 4 x 4 grid below is to be filled in with the number 1, 2, 3 or 4 so that
* each row contains the numbers 1, 2, 3, and 4 in some order
* each column contains the numbers 1, 2, 3 and 4 in some order
* each 2 read more ..

Guest Jan 10, 2023

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154

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Graphing question

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

Guest Jan 10, 2023

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174

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Counting question

Sam wants to color the three sides of an equilateral triangle. He has two different colors to choose from. In how many different ways can Sam color the sides of the triangle? (Two colorings are considered the same if one coloring can be read more ..

Guest Jan 10, 2023

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229

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need help with proabability

The Boomtown Bears are playing against the Tipton Toros in a baseball tournament. The winner of the tournament is the first team that wins three games. The Bears have a probability of 1/5 of winning each game. Find the probability that the Bears win read more ..

Guest Jan 10, 2023

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159

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Arrangements

Find the number of ways of arranging the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 in a row so that the product of any two adjacent numbers is even or a mutliple of 3

Guest Jan 10, 2023

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154

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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 Jan 10, 2023

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205

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help digits

Find the number of six-digit numbers, where the sum of the digits is divisible by 8.

Guest Jan 10, 2023

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168

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Analytic geometry

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 Jan 10, 2023

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157

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plz help ASAP

find the equation of the tangent to the curve y=ln(lnx) at the point (e,0)

Guest Jan 10, 2023

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157

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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 Jan 10, 2023

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162

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binomials

Simplify (binom{200}{50} binom{200}{51})/(binom{200}{49} binom{48})

Guest Jan 10, 2023

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159

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help 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 Jan 10, 2023

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168

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algerbra 2

what is the factored form of this polynomial
x^3 + 3x^2 - 13x -15

Guest Jan 10, 2023

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162

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Binomials

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 Jan 10, 2023

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216

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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 50% magical syrup by volume (and the rest is just water), and blue potion, which read more ..

Guest Jan 10, 2023

+1

246

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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 Jan 10, 2023

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168

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help complex numbers

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

Guest Jan 10, 2023

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166

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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 Jan 10, 2023

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