All Questions ⁺⁰237784 Questions

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151

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Probability

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 Apr 15, 2023

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152

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Let n be a positive integer. (a) There are n^2 ordered pairs (a, b) of positive integers, where Using a counting argument, show that this

Let n be a positive integer.
(a) There are n^2 ordered pairs (a, b) of positive integers, where Using a counting argument, show that this number is also equal to

(b) There are n^3 ordered triples (a, b, c) of positive integers, read more ..

Guest Apr 15, 2023

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79

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Difficult 3D Geometry: Cube Inscribed in Tetrahedron

In tetrahedron A cube is inscribed in the tetrahedron so that one of its vertices is at , and the opposite vertex lies on face . Let and Show that the side length of the cube is

Hints read more ..

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Guest Apr 15, 2023

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145

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geometry help

In triangle PQR, let X be the intersection of the angle bisector of angle P with side QR, and let Y be the foot of the perpendicular from X to line PR. If PQ = 9, QR = 9, and PR = 9, then compute the length of XY. read more ..

Guest Apr 15, 2023

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140

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help plz with geometry

I am stuck on this:
In square ABCD, P is on BC such that BP = and PC = , and Q is on CD such that BQ = and QC = . Find sin angle PAQ.

Guest Apr 15, 2023

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142

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plz help

I need help with this problem:
Let G be the centroid of triangle ABC. If triangle ABG is an equilateral triangle with a side length of 2, then find the area of triangle ABC.

Guest Apr 15, 2023

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139

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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 Apr 15, 2023

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153

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word problem

A company produces x units of a product per month, where C(x) represents the total cost and R(x) represents the total revenue for the month. The functions are modeled by C(x)=300x+250 and R(x)=-0.5x^2+800-100. The profits is the difference between revenue read more ..

Guest Apr 15, 2023

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154

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Counting

Help I need to use combinations

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 read more ..

Guest Apr 15, 2023

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162

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Please help! Thanks!

In trapezoid ABCD, AB is parallel to CD, and AB < CD. The base CD has a length of 8. The legs AD and BC have lengths of 7, and the diagonal BD has a length of 9. Find the area of the trapezoid.

Guest Apr 15, 2023

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140

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counting

When two standard 6-sided dice are rolled, there are 36 possible outcomes for the sum of the two rolls: one sum of 2, two sums of 3, and so on, up to one sum of 12.
Find all possible ways of numbering two 6-sided dice read more ..

Guest Apr 15, 2023

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153

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Janice has been saving part of her allowance in a bag every month.

Janice has been saving part of her allowance in a bag every month. The bag containing $2 and $10 notes had a total value of $1344. 8 pieces of $10 notes were exchanged for $2 notes of the same value. In the end, the number of $10 notes was the same as the read more ..

Guest Apr 15, 2023

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165

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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 Apr 15, 2023

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161

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counting

Joanna has six beads that she wants to assemble into a bracelet. Two of the beads have the same color, and the other four all have the same color. How many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical if one can read more ..

Guest Apr 15, 2023

Apr 14, 2023

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154

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Probability

I need to compute probability
A member of the junior varsity swim team will be elected as President. Each member is equally likely to be elected. The probability that a sophomore is elected is the probability read more ..

Guest Apr 14, 2023

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175

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counting

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

Guest Apr 14, 2023

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177

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Help pls!

A spinner has 10 equally sized sections, 8 of which are gray and 2 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on blue and the second spin lands on gray ?
Write your answer as a fraction in simplest read more ..

Guest Apr 14, 2023

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152

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A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. Find the height h o

A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. Find the height h of the roof.

Guest Apr 14, 2023

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187

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counting

At a meeting, five scientists, two mathematicians, five journalists, two biologists, and three politicians are to be seated around a circular table. How many different arrangements are possible if the scientists must all sit together (in read more ..

Guest Apr 14, 2023

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