All Questions ⁺⁰237643 Questions

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225

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Help!

Gizmo can eat $2$ bowls of kibbles in $3$ minutes. Leo can eat one bowl of kibbles in $6$ minutes. Together, how many bowls of kibbles can Gizmo and Leo eat in $10$ minutes?

Guest Jan 16, 2023

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182

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Algebra

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and a^3 - 3ab^2 = 673. Find a - b.

Guest Jan 16, 2023

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198

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Counting question

Find the number of positive integers that satisfy the following conditions:
* Each digit is a 1 or a 2 or a 3
* The sum of the digits is 10

Guest Jan 16, 2023

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190

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Binomials Theorem

Expand (sqrt(t) + 3t + 1)^3 + (sqrt(t) - 3t + 1)^3.

Guest Jan 16, 2023

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165

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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 16, 2023

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151

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khaoula

how much is 5+5

Guest Jan 16, 2023

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211

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sequence

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 Jan 16, 2023

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166

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Coefficient

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

Guest Jan 16, 2023

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156

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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?

Guest Jan 16, 2023

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212

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math problem

In how many ways can you distribute 10 indistinguishable balls among 8 distinguishable boxes, if at least one of the boxes must be empty?

Guest Jan 16, 2023

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147

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counting

We want to divide 10 dogs (including Fluffy and Nipper) into three groups, one with 3 dogs, one with 5 dogs, and one with 2 dogs. How many ways can we form the groups such that Fluffy is in the 2-dog group and Nipper is in the read more ..

Guest Jan 16, 2023

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170

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help geometry

The two circles below are externally tangent. A common external tangent intersects line PQ at R. Find QR.

Guest Jan 16, 2023

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154

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geometry problem

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 16, 2023

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178

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need help quick

A bag contains five white balls and three black balls. Your goal is to draw two white balls.

(a) You simultaneously draw two balls at random. What is the probability that they are both white?
(b) You simultaneously draw two balls read more ..

Guest Jan 16, 2023

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179

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help with Probability

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 16, 2023

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156

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geometry

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 Jan 16, 2023

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165

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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 16, 2023

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156

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Solutions

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 16, 2023

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164

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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. When you buy a ticket, you choose three numbers from 1 to 12, read more ..

Guest Jan 16, 2023

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157

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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 16, 2023

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157

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Probability

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 the probability that the Bears win the tournament. read more ..

Guest Jan 16, 2023

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164

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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 16, 2023

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159

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Digits

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

Guest Jan 16, 2023

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164

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Counting

Syd chooses two different primes, both of which are greater than 10 and multiplies them. The resulting product is less than How many different products could Syd have ended up with?

Guest Jan 16, 2023

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180

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help counting

A fair coin is tossed 12 times. How many different sequences of tosses could there have been, if the number of heads was at least

Guest Jan 16, 2023

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