All Questions ⁺⁰230590 Questions

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58

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counting

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

Guest Mar 20, 2023

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68

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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 20, 2023

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63

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Probability

What do I do
Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. What is the probability that the area of triangle XYD is at most 20?

Guest Mar 20, 2023

0

64

0

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, 2, read more ..

Guest Mar 20, 2023

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63

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stats

A list of ten distinct, positive integers has a median of 5.5. What is the smallest possible average of the ten positive integers? Explain your ansswer in complete sentences.

Guest Mar 20, 2023

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62

1

Algebra

Need help with these
Select all the correct statements. (For this problem, we assume that an exponential function is of the form ka^x where a > 0)
(A) The following function is exponential: y = 2^x
(B) read more ..

Guest Mar 20, 2023

0

73

1

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 Mar 20, 2023

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68

0

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 Mar 20, 2023

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75

1

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 Mar 20, 2023

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65

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counting problem

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 Mar 20, 2023

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80

1

Analytic geometry

A median of a triangle is a line segment joining a vertex of a triangle to the midpoint of the opposite side. The three medians of a triangle are drawn below.
Note that the three medians appear to intersect at the same point! Let's read more ..

Guest Mar 20, 2023

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80

3

counting

I have to count these for class
There are 18 padded chairs around a circular table, and the chairs are numbered from 1 through 18 . How many ways can five people take their seats, so that no two people are adjacent read more ..

Guest Mar 20, 2023

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82

2

Probability

A stick is broken at two points, chosen at random. If the length of the stick is 6 then what is the probability that all three resulting pieces are shorter than 2 units?

Guest Mar 20, 2023

Mar 19, 2023

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68

1

binomials

Find the positive integer n such that the expansion of (4x - 7y)^n contains a term of the form cx^2*y.

Guest Mar 19, 2023

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62

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geometry

In triangle ABC, the angle bisector of angle BAC meets AC at D. If angle BAC = 60, angle ABC = 60, and AD = 24, then find the area of triangle ABC.

Guest Mar 19, 2023

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71

0

Counting

I don't know how
In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color, and at lest three of the squares are red. How many ways are there to read more ..

Guest Mar 19, 2023

+1

65

4

+38

Mailbox Probability

There are 4 mailboxes and 4 letters, they are randomly placed in mailboxes, what is the probability that one of the mailboxes has exactly 3 letters.

Chickenisyummywith Mar 19, 2023

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60

0

Probability

Can anyone help with this?
Let PQR be an equilateral triangle, centered at O. A point X is chosen at random inside the triangle. Find the probability that X is closer to O than to any of the sides. (In read more ..

Guest Mar 19, 2023

-1

70

6

+275

bases

Xavier writes down a three-digit positive integer. Youssef writes a in front of the digits of Xavier's number, so that the resulting number has four digits. If this four-digit number is times as large as Xavier's original number, what read more ..

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Jasonkiln Mar 19, 2023

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62

4

+275

Bases

How many integers can be expressed in base 5 using exactly three digits and expressed in base 7 using exactly two digits?
I honestly have no idea how to approach this. Any help would be appreciated. Thanks

Jasonkiln Mar 19, 2023

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