All Questions ⁺⁰237631 Questions

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179

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Math problem

My patio is tiled with square tiles, all the same size. All the tiles are gray, except the tiles along the two diagonals, which are all yellow. (The corners are yellow, the center is yellow, and all the tiles along the diagonal in between are yellow.) If read more ..

Guest Feb 15, 2023

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166

1

Counting

How to solve this

Catherine rolls a 6-sided die five times, and the product of her roll is . How many different sequences of rolls could there have been? (The order of the rolls matters.)

Guest Feb 15, 2023

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145

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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?
(c) What is the sum of all the read more ..

Guest Feb 15, 2023

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173

1

Counting

Need help on this counting

We call a number cozy if every digit in the number is either even or next to an even digit. For example, a number is cozy if every digit in the number is either a 2 or next to a 2. read more ..

Guest Feb 15, 2023

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177

1

Counting

help with counting plz

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 exact read more ..

Guest Feb 15, 2023

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151

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Sequences

Help with sequences

Cai writes down the list of positive integers, excluding squares and cubes and all perfect powers. His sequence starts
2, 3, 5, 6, 7, 10, 11, ...
What is the 100th term in Cai's list?

Guest Feb 15, 2023

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151

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Counting

Need help quick

Find the number of ways of placing 4 balls in 8 boxes if the balls are distinguishable and the boxes are indistinguishable.

Guest Feb 15, 2023

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163

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Probability

Need help with these plz

Valeria has three coins, each of which has a probability of 1/2 of coming up heads. On her first turn, she flips all three coins. If all three come up heads, then she stops. Otherwise, read more ..

Guest Feb 15, 2023

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150

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Algebra

Help how do I get started

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 read more ..

Guest Feb 15, 2023

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146

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complex numbers

Help need help

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

Guest Feb 15, 2023

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186

1

+1348

Problem in Counting

I'm really stuck on this problem. Can anyone help?

You are given the 4 x 4 grid below.
read more ..

sandwich Feb 15, 2023

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158

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Counting

Help needed with 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 read more ..

Guest Feb 15, 2023

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148

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Algebra

Help this is hard

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. read more ..

Guest Feb 15, 2023

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153

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Inequality

Plz help prove 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 read more ..

Guest Feb 15, 2023

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174

1

Algebra

Help I need algebra help

Carissa the chessplayer is a very, very slow walker. In fact, she walks at 100 meters per hour when walking uphill, 120 meters per hour when walking across flat ground, and 180 meters per hour read more ..

Guest Feb 15, 2023

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157

0

Probability

Help I need help plz

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. read more ..

Guest Feb 15, 2023

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142

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Counting

Help how do I count this

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

Guest Feb 15, 2023

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148

0

trig question plz help

From a point 340 meters from the base of the Hoover Dam, the angle of elevation to the top of the dam is 330. Find the height of the dam to the nearest meter.

Guest Feb 15, 2023

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160

1

help

what the greatest common factor or 24 and 40

Guest Feb 15, 2023

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142

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Counting

I don't know how to count

In a regular decagon, the sides are to be colored with five different colors, so that sides are diametrically opposite have the same color. (Not all five colors need to be used.) One possible read more ..

Guest Feb 15, 2023

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160

0

Counting

Plz I need help

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

Guest Feb 15, 2023

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157

0

Counting

Plz help now!

(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 15, 2023

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257

3

Binomial Theorem

How to solve this

For some real number a and some positive integer n, the first few terms in the expansion of (1 + ax)^n are read more ..

Guest Feb 15, 2023

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