All Questions ⁺⁰237784 Questions

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184

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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 Mar 13, 2023

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174

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Probability

Need help soon on this

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 read more ..

Guest Mar 13, 2023

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172

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Geometry

Let B, A, and D be three consecutive vertices of a regular -gon. A regular heptagon is constructed on AB with a vertex C next to A Find angle BCD in degrees.

Guest Mar 13, 2023

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179

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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.
read more ..

Guest Mar 13, 2023

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171

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Probability

A standard six-sided die is rolled twice. What is the probability that the product of the rolls is 3 or 12?

Guest Mar 13, 2023

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146

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Inequality

Prove that if a, b, and c are positive real numbers, then
sqrt(a^2 + ab + b^2) + sqrt(a^2 + ac + c^2) + sqrt(b^2 + bc + c^2) >= sqrt(3) (sqrt(ab) + sqrt(ac) + sqrt(bc))
When does equality occur?

Guest Mar 13, 2023

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126

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+8

Log questions

1. Let x and b be positive real numbers so that \log_b(x^2) = 10. Find \log_{\sqrt[3]{b}} \left( \frac{1}{x} \right). 2. Let a, b, and c be the roots of 24x^3 - 121x^2 + 87x - 8 = 0. Find \log_3(a)+\log_3(b)+\log_3(c). I'm not really sure how to approach these read more ..

Starziq Mar 13, 2023

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167

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Probability

Help meee hard problems

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, read more ..

Guest Mar 13, 2023

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170

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help asap please

The function , where and . What is the value of ?

Guest Mar 13, 2023

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169

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help plz

I need help with a counting problem.

In how many ways can three points be selected from the grid below so that they form a right isosceles triangle?
read more ..

Guest Mar 13, 2023

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168

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+8

Binomial Theorem question

For some real number a and some positive integer n, the first few terms in the expansion of (1 + ax)^n are \[1 - 20x + 150x^2 + cx^3 + \dotsb.\]Find c.

Starziq Mar 13, 2023

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169

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Help I'm stuck

Can anyone help with this?

Enter (A,B,C) in order below if A, B, and C are the coefficients of the partial fractions expansion of (2x^2 + 3x - 5)/(x(x^2 - 1)) = A/x + B/(x - 1) + C/(x + 1).

Guest Mar 13, 2023

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131

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+34

HELP WITH COUNTING

On my ping-pong team there are four times as many right-handed boys as left-handed boys. Of the students on the team who are left-handed, there are twice as many girls as there are boys. Half of the girls who are on the team are left-handed. If there are read more ..

ChessChris Mar 13, 2023

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179

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binomial theorem stuff

For some real number a and some positive integer n, the first few terms in the expansion of (1 + ax)^n are 1 - 20x + 150x^2 + cx^3 + ...
Find c.

Guest Mar 13, 2023

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171

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Probability

When it rains, every student in Margo's school brings a raincoat, an umbrella, or both. And of the students bring both. The total number of umbrellas brought is equal to twice the number of raincoats.

What percent of the read more ..

Guest Mar 13, 2023

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183

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Fractions

Help this is hard

Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 1 greater than the denominator. He then writes several more fractions. To make each new fraction, he read more ..

Guest Mar 13, 2023

Mar 12, 2023

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149

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geometry

Let ABC be a right triangle, and let H be the point on side AB so that CH is perpendicular to AB. Prove that (x + h)^2*(y + h)^2 = (a + b)^4.

Guest Mar 12, 2023

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147

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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 Mar 12, 2023

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164

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Expected value

Three standard fair 6-sided dice are rolled. What is the expected number of 6's rolled? (For example, if two 6's and a 5 are rolled, then the answer is 2.)

Guest Mar 12, 2023

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165

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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
in nonnegagive integers.

Guest Mar 12, 2023

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165

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Function

For a certain function f(n), the identity
(2n)/n - (2n)/(n + 1) = f(n) (2n)/n
for all nonnegative integers n. Find f(n).

Guest Mar 12, 2023

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138

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Counting

A baking club wants to form an executive committee. There are people in the baking club, including mark. In how many ways can the baking club form an executive committee with people?

Guest Mar 12, 2023

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159

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Alegbra 1 question please help

This is the question

Guest Mar 12, 2023

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