All Questions ⁺⁰237827 Questions

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Right-Triangle Trigonometry

is a regular tetrahedron (right triangular pyramid). If is the midpoint of ,then what is ?

Guest Feb 19, 2023

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162

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Precalc

The position of a particle is given by the parametric equations
x = 3 + 2 sin 2t - cos t
y = 4 + cos 4c + sin 3t
as t ranges over all real numbers. read more ..

Guest Feb 19, 2023

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162

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Coefficient

Help plz help

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

Guest Feb 19, 2023

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219

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Counting

Help how are you supposed to do this

Three adults and three children are to be seated at a circular table. In how many different ways can they be seated if each child must be next to at least one adult? (Two seatings read more ..

Guest Feb 19, 2023

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167

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Binomials

(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?

Guest Feb 19, 2023

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Geometry

Plz help with geometry problem

In the diagram below, PQRS is a parallelogram with a perimeter of 26 and an area of 28. What is the perimeter of rectangle OSTQ? Include an explanation of how you solved the problem. read more ..

Guest Feb 19, 2023

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167

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Counting

Find the number of positive integers that satisfy both the following conditions:
Each digit is a 1 or a 2 or a 3
The sum of the digits is 5

Guest Feb 19, 2023

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160

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Counting

Plz anyone help with 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.)
read more ..

Guest Feb 19, 2023

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161

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Algebra

Let S be the set of all real numbers of the form
a1/3 + a2/3^2 + a3/3^3 + ....
where a_i \in {0, 1, 2} for all i.

(a) Is the number 1/7 in the set S? read more ..

Guest Feb 19, 2023

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158

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Expected value

In a series of coin flips, a run is a series of consecutive coin flips that are all the same. For example, in the sequence
the red letters form a run.
If a fair coin is flipped two times, what is the expected length of the longest run? read more ..

Guest Feb 19, 2023

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165

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Geometry

In triangle ABC, the angle bisector of angle BAC meets AC at D. If angle BAC = 60, angle ABC = 60, and AD = 24, then find the area of triangle ABC.

Guest Feb 19, 2023

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160

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Counting

Plz help with counting need this

In the olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are skaters, including Americans, in how many ways can the medals read more ..

Guest Feb 19, 2023

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165

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Binomials

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

Guest Feb 19, 2023

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156

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Counting

I have to count these for class

There are 18 padded chairs around a circular table, and the chairs are numbered from 1 through 18 . How many ways can five people take their seats, so that no two people are adjacent? read more ..

Guest Feb 19, 2023

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166

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Precalc

The position of a particle is given by the parametric equations
x = sqrt(t^2 + t)
y = t^2 - 1
as t ranges over all real numbers. read more ..

Guest Feb 19, 2023

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170

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Algebra

Factor (ab + ac + bc)^3 - a^3*b^3.

Guest Feb 19, 2023

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163

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Probability

I need the answer to this

Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. What is the probability that the area of triangle XYD is at most 20?

Guest Feb 19, 2023

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203

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HELP

A, B and C are three points on a plane such that AB = BC = 1 and CA = sqrt 3. Draw three circles whose diameters are AB, BC and CA respectively. The area of the region included in all three circles (the grey region below) is (a/b)pi + (sqrt c read more ..

Guest Feb 19, 2023

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147

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Algebra

Let r be a root of x^3 - 2x + 5 = x^3 - x^2 + 9. Show that none of r, r^2, or r^3 is irrational.

Guest Feb 19, 2023

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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 Feb 19, 2023

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Find an equation of the line that satisfies the given conditions.

Find an equation of the line that satisfies the given conditions.
y-intercept 8; parallel to the line 4x + 5y + 6 = 0

Guest Feb 19, 2023

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162

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Inequality

Help with this inequality

(a) Show that if a, b, c, d, e, f are nonnegative real numbers, then (a^2 + b^2)^2 (c^4 + d^4)(e^4 + f^4) >= 32abcdef.
(b) Show that if a, b, c, d, e, f are nonnegative real numbers, read more ..

Guest Feb 19, 2023

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176

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Probability

Need help soon on this

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 of winning each game. Find read more ..

Guest Feb 19, 2023

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Expected value

I need help with this ASAP

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 paths that pass read more ..

Guest Feb 19, 2023

Feb 18, 2023

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i ^ { 0 } +i ^ { 1 } +i ^ { 2 } +i ^ { 3 } +i ^ { 4 } +···+i ^ { 2021 }

i ^ { 0 } +i ^ { 1 } +i ^ { 2 } +i ^ { 3 } +i ^ { 4 } +···+i ^ { 2021 }

Guest Feb 18, 2023

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