All Questions ⁺⁰237827 Questions

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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. For example, the number 222, 72, 45, and 810 and read more ..

Guest Feb 18, 2023

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Geometry

In tetrahedron ABCO, angle AOB = angle AOC = angle BOC = 90^\circ. A cube is inscribed in the tetrahedron so that one of its vertices is at O, and the opposite vertex lies on face ABC. Let OA = 1, OB = 1, OC = 1. Show that the read more ..

Guest Feb 18, 2023

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Geometry

In triangle PQR, let M be the midpoint of QR, let N be the midpoint of PR, and let O be the intersection of QN and RM, as shown. If QN perp PR, QN = 12, and PR = 14, then find the area of triangle PQR.

Guest Feb 18, 2023

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Algebra

Carissa the chessplayer is a very, very slow walker. In fact, she walks at 100 meters per hour when walking uphill, 180 meters per hour when walking across flat ground, and 250 meters per hour when walking downhill. One day, Carissa walks read more ..

Guest Feb 18, 2023

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161

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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 18, 2023

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169

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Algebra

How do you solve this equation

Find all values of c such that 3*(2c + 1) = 28*(3*c) - 9. If you find more than one value of c, then list your values in increasing order, separated by commas.

Guest Feb 18, 2023

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166

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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 Feb 18, 2023

Feb 17, 2023

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157

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Algebra

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.

(a) Is the number 1/7 in the set S? read more ..

Guest Feb 17, 2023

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166

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Probability

Need help with probability

My sock drawer contains two red socks, two white socks, and two blue socks. For three days in a row, I pull out two socks out of my sock drawer at random. What is the probability that I get matching read more ..

Guest Feb 17, 2023

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163

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Algebra

How do I do this

Find the constant term in the expansion of (2z - 1/(z*sqrt(z)) + 1)^4.

Guest Feb 17, 2023

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190

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+70

math helppp

There are 42 people in pilates class. Today, 36 of them brought yoga mats, 26 of them brought eco-friendly water bottles, and 20 of them remembered to bring both yoga mats and water bottles. How many people had to suffer through class having neither read more ..

sheeshers Feb 17, 2023

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158

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Counting

Plz anyone help with 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.)
read more ..

Guest Feb 17, 2023

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171

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Geometry

Plz help with geometry problem

In the diagram below, PQRS is a parallelogram with a perimeter of 26 and an area of 28. What is the perimeter of rectangle OSTQ? Include an explanation of how you solved the problem. read more ..

Guest Feb 17, 2023

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167

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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?

Guest Feb 17, 2023

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163

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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 Feb 17, 2023

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163

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Algebra

Let r be a root of x^3 - 2x + 5 = x^3 - x^2 + 9. Show that none of r, r^2, or r^3 is irrational.

Guest Feb 17, 2023

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168

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Inequality

Let a, b, and c be nonnegative real numbers. Prove that for all x >= 0,
(x + abc)^3 >= abc(x + a)(x + b)(x + c) >= (x + a + b + c)^3.

Guest Feb 17, 2023

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