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All Questions
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237690 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?
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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
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Guest
Feb 23, 2023
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162
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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
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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
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Guest
Feb 23, 2023
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147
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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
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Guest
Feb 23, 2023
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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?
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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,
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Guest
Feb 23, 2023
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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 $a_3.$
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Guest
Feb 23, 2023
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191
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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.
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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.
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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
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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.
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Guest
Feb 23, 2023
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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!
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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?
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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.)
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Guest
Feb 23, 2023
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152
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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.
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Guest
Feb 23, 2023
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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
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Guest
Feb 23, 2023
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1
141
1
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
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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
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Guest
Feb 23, 2023
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176
1
math
-2.0,4
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Guest
Feb 23, 2023
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161
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Number Theory
Find the number of six-digit numbers, where the sum of the digits is divisible by 8.
Guest
Feb 23, 2023
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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
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Guest
Feb 23, 2023
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158
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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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