maximum

256 Questions
65 Answers

0

2

1

+819

Algebra

Let a and b be the solutions to 7x^2 + x - 5 = 6x^2 - 11x - 2. Compute (a - 4) + (b - 4).

maximum Apr 11, 2024

0

2

1

+819

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{PQ}.$ Let $X$ be the point on $\overline{QR}$ such that $\overline{PX}$ bisects $\angle QPR,$ and let the perpendicular bisector of $\overline{PQ}$ intersect $\overline{PX}$ at $Y.$ If PQ = 36, PM = 22, read more ..

maximum Apr 7, 2024

0

5

1

+819

Hexagon

Let $IJKLMN$ be a hexagon with side lengths $IJ = LM = 3,$ $JK = MN = 3,$ and $KL = NI = 3$. Also, all the interior angles of the hexagon are equal. Find the area of hexagon $IJKLMN$.

maximum Jan 28, 2024

0

9

1

+819

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 times the probability that a freshman is elected. Everyone on the junior varsity read more ..

maximum Jan 16, 2024

0

10

1

+819

Counting

Find the number of positive integers that satisfy both the following conditions:
- Each digit is a 1 or a 2 or a 3
- The sum of the digits is 5

maximum Jan 16, 2024

0

8

0

+819

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 ..

maximum Dec 18, 2023

0

12

0

+819

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 ..

maximum Dec 18, 2023

0

8

1

+819

help counting

Six children are each offered a single scoop of any of $3$ flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that some flavor of ice cream is selected by exactly five c read more ..

maximum Dec 14, 2023

0

6

1

+819

Counting

A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, read more ..

maximum Dec 14, 2023

0

7

1

+819

Counting problem

How many ways can you write two different letters chosen from
A B C D E F G H I J K L M N O P
so that they are in alphabetical order, and the first letter is a vowel? For example, AF and EN count, but DE and KC do not.

maximum Dec 14, 2023

0

11

0

+819

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 ..

maximum Dec 14, 2023

0

16

0

+819

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 ..

maximum Dec 14, 2023

0

9

0

+819

Counting

At a meeting, $5$ scientists, $2$ mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if each scientist must sit next to a mathematician? (Two seatings are considered equivalent read more ..

maximum Dec 14, 2023

0

8

1

+819

help plz

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other? (Two seatings are considered the same if read more ..

maximum Dec 14, 2023

0

10

1

+819

need help

I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if there must be a mathematics textbook exactly in the middle, and all the psychology textbooks are read more ..

maximum Dec 14, 2023

0

4

1

+819

Counting

A speech class has $4$ freshmen and $3$ sophomores. (Everyone is distinguishable.) In how many ways can they stand in line, so that all the freshmen are standing together?

maximum Dec 14, 2023

+819

+1

This is AoPS homework. Do not post AoPS homework.

maximumFeb 6, 2024

+819

0

This is AoPS homework. Do not post AoPS homework.

maximumJan 20, 2024