All Questions ⁺⁰237643 Questions

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Distributions

(a) In how many ways can you distribute 4 distinguishable balls among 3 indistinguishable boxes?

(b) In how many ways can you distribute 4 indistinguishable balls among 5 distinguishable boxes?

Guest Jan 5, 2023

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163

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help counting

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 5, 2023

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168

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help factoring

We are looking to factor 23x^2 + kx - 5 + x^2 - 3. Some values of k allow us to factor it as a product of linear binomials with integer coefficients. what are all such values of k?

Guest Jan 5, 2023

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194

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Counting problems

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

(a) Using a counting argument, show that C(n - 1, k - 1) + C(n - 1, k) = C(n,k).
read more ..

Guest Jan 5, 2023

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185

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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?
read more ..

Guest Jan 5, 2023

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169

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help with trig

In the diagram below, what are AC and BC?

Guest Jan 5, 2023

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169

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help

A restaurant has 11.5 litres of juice. It sells juice by the glass. Each glass will hold 275 ml of juice. How many full glasses of juice could the restaurant sell?

Guest Jan 5, 2023

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166

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algebra

Based on the Census, state A has
16
fewer electoral votes for president than state B. If the total number of electoral votes for these two states is
84, read more ..

Guest Jan 5, 2023

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163

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geometry

Triangle ABC is a right triangle with angle BAC= 90 degrees and angle B > angle . Suppose AP is an altitude of the triangle, AQ is an angle bisector of the triangle, and AR is a median of the triangle, and angle PAQ = 18 degrees. If P read more ..

Guest Jan 5, 2023

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789

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How to make digits 1-100 with 2, 0, 2, 3

How to make digits 1-100 with 2, 0, 2, 3

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Guest Jan 5, 2023

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176

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help needed

Arrange the following numbers in increasing order (smallest first, biggest last):

A = 2*1/2*4*1/6
B = 12*128 read more ..

Guest Jan 5, 2023

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161

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Algebra

Fill in the blanks:
(3 + sqrt(5) + sqrt(2) - 1)^4 = __ + __ sqrt(5) + __ sqrt(2)

Guest Jan 5, 2023

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208

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Counting

There is a group of five children, where two of the children are twins. How many ways can I distribute 10 identical pieces of candy to the children, if the twins must get an equal amount of candy?

Guest Jan 5, 2023

Jan 4, 2023

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187

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Inequality

(a) Prove 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) Prove that if a, b, c, d, e, f are nonnegative real numbers, then (a^2 + b^2)(c^2 + d^2)(e^2 + read more ..

Guest Jan 4, 2023

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161

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Probability

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, for her second turn, she flips any coins that came up tails. read more ..

Guest Jan 4, 2023

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158

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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.)

(b) Find the number of ways that Magnus can give out 20 identical stickers to 5 of read more ..

Guest Jan 4, 2023

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164

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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 4, 2023

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230

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help

Latita had 12 marbles she gave billy 2 she has 10/12 of her marbles left what fraction of the marbles did latita give away? Write in simplest form

Guest Jan 4, 2023

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204

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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 4, 2023

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155

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Algebra

For some real number a and some positive integer n, the first few terms in the expansion of (1 + ax)^n are
1 + 10x + 150 x^2 + cx^3 + ...

Find c. read more ..

Guest Jan 4, 2023

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161

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Function

Let F(x) be the real-valued function defined for all real x except for x = 1 and x = 2 and satisfying the functional equation
F(x) + F((2x - 3)/x) = x.
Find the function F(x) satisfying these conditions. Write F(x) as read more ..

Guest Jan 4, 2023

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178

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Pythagorean theorem

Belmont is 7 miles due north of the airport, and Newton is 6 miles due east of the airport. How far apart are Belmont and Newton? If necessary, round to the nearest tenth.

Guest Jan 4, 2023

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153

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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 Jan 4, 2023

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