All Questions ⁺⁰237690 Questions

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155

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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 23, 2023

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162

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System

For a certain value of k, the system
x + y + 3z = 10
-4x + 8y + 5z = 7
kx + z = 3 read more ..

Guest Feb 23, 2023

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162

0

Counting

Help how to count paths

Find the number of paths from A to I, if each step must be in a right-ward direction. (For example, one possible path is A C D E F G H I)

Guest Feb 23, 2023

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186

1

math

What is the completely factored form of this polynomial? x4 − 8x2 + 16

Guest Feb 23, 2023

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154

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Counting

Help I need to use combinations

I run a book club with n people, not including myself. Every day, for 100 days, I invite members in the club to review a book. What is the smallest positive integer n so that I can avoid ever having the read more ..

Guest Feb 23, 2023

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147

0

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 23, 2023

0

185

1

Counting

Sam writes down the numbers 1, 2, 3, ..., 99

(a) How many digits did Sam write, in total?
(b) Sam chooses one of the digits written down, at random. What is the probability that Sam chooses a 0? read more ..

Guest Feb 23, 2023

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150

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Counting

Plz help

A standard six-sided die is rolled 7 times. You are told that among the rolls, there was one 1, two 2's, and three 4's. How many possible sequences of rolls could there have been? (For example, 5, 1, 2, read more ..

Guest Feb 23, 2023

0

153

2

Help please

Given $a_0 = 1$ and $a_1 = 5,$ and the general relation \[a_n^2 - a_{n - 1} a_{n + 1} = (-1)^n\]for $n \ge 1,$ find $a_3.$

Guest Feb 23, 2023

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191

1

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 23, 2023

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201

1

Probability

Four points W, X, Y, and Z are chosen at random on a circle. Find the probabiity that WX > YZ.

Guest Feb 23, 2023

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160

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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 Feb 23, 2023

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182

0

Counting

You are given the 4 x 4 grid below.

(a) Find the number of ways of placing 8 counters in the squares (at most one counter per square), so that each row contains exactly two counters.
read more ..

Guest Feb 23, 2023

+2

203

1

+6

how to expand binomials?

hey everyone stuck in a lesson trying to work out a couple questions. does anyone know how to expand binomials? if so thanks!

bunniesarecute Feb 23, 2023

+2

188

3

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 23, 2023

+1

184

1

Counting

Need help quick

(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 23, 2023

+1

152

0

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 23, 2023

0

187

2

HELPPPPP FAST PLSSSSS

There is a point (x,y) in the first quadrant and on the line 3x-5y=12 for which the x-coordinate is three times the y-coordinate. What is the value of X + Y at that point

Guest Feb 23, 2023

0

1

141

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Counting

When two standard 6-sided dice are rolled, there are 36 possible outcomes for the sum of the two rolls: one sum of 2, two sums of 3, and so on, up to one sum of 12.

Find all possible ways of numbering two 6-sided dice read more ..

Guest Feb 23, 2023

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196

1

Counting

At a meeting, five scientists, two mathematicians, five journalists, two biologists, and three politicians are to be seated around a circular table. How many different arrangements are possible if the scientists must all sit together (in read more ..

Guest Feb 23, 2023

0

176

1

math

Guest Feb 23, 2023

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161

0

Number Theory

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

Guest Feb 23, 2023

0

208

2

HELLLPPPP!!!!! I DONT UNDERSTAND

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 Feb 23, 2023

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158

0

What is an equation of the line that passes through the point (−1,6) and is parallel to the line 2x+y=9?

What is an equation of the line that passes through the point (−1,6) and is parallel to the line 2x+y=9?

Guest Feb 23, 2023

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