All Questions ⁺⁰236048 Questions

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14

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+862

Counting

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. How many ways are there to color the five squares, if there must be at least three yellow squares?

magenta Jun 1, 2024

0

13

1

+862

Counting

The entries in a certain row of Pascal's triangle are
\[1, n, \dots, n, 1.\]
The average of the entries in this row is 2. Find $n$.

magenta Jun 1, 2024

0

12

3

+862

Probability

Triangle XYZ is equilateral, with O as its center. A point P is chosen at random. Find the probability that P is closer to point O than to any of the side lengths.

NotThatSmart ●●●

magenta Jun 1, 2024

+1

16

3

+1938

Crossing the River

Challenge problems annoy me, figuratively and literally, especially when there's a twist in the story as well.
So, I discovered this problem a couple of days ago, and ummm, help?
On one side of a riverbank, read more ..

NotThatSmart Jun 1, 2024

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11

1

+842

Algebra

I drove to the beach at a rate of $40$ miles per hour. If I had driven at a rate of $55$ miles per hour instead, then I would have arrived $25$ minutes earlier. How many miles did I drive?

NotThatSmart ●

RedDragonl Jun 1, 2024

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23

1

+842

Algebra

I have to paint one side of a wall. The wall is $15$ meters tall and $60$ meters long. Each gallon of paint covers $400$ square feet. If a foot is approximately $0.3048$ meters, then what is the smallest whole number of gallons I can buy and read more ..

RedDragonl Jun 1, 2024

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22

1

+842

Algebra

Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. read more ..

RedDragonl Jun 1, 2024

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11

2

+12

Help on question

The system of equations \[\frac{xy}{x + y} = 1, \quad \frac{xz}{x + z} = 2, \quad \frac{yz}{y + z} = 4\] has exactly one solution. What is $z$ in this solution?

Ironwolfyyy Jun 1, 2024

0

33

0

+976

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, find the read more ..

Hi6942O Jun 1, 2024

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13

2

+976

Algebra

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{8}.

NotThatSmart ●●

Hi6942O Jun 1, 2024

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14

2

+976

Algebra

Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$

Hi6942O Jun 1, 2024

0

9

1

+976

Algebra

Fill in the blanks to make a quadratic whose roots are $1$ and $-1.$
x^2 + ___ x + ___

Hi6942O Jun 1, 2024

+2

15

1

+12

A little help? I'm stumped!

Write the equation of the line below in the form Ax+By=C, where A, B, and C are integers with greatest common divisor 1 and A is positive.
FYI: The line passes through the points (-4,2) and (1,-1). The slope, which I read more ..

Algebro Jun 1, 2024

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29

0

+1310

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 ..

learnmgcat Jun 1, 2024

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11

1

+1310

Counting

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 ..

learnmgcat Jun 1, 2024

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19

0

+1310

Counting

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 ..

learnmgcat Jun 1, 2024

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12

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+1310

Geometry

What are the coordinates of the points where the graphs of f(x)=x^3 + x^2 - 3x + 5 and g(x) = x^3 + 2x^2 intersect?
Give your answer as a list of points separated by commas, with the points ordered such that their -coordinates read more ..

learnmgcat Jun 1, 2024

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22

0

+1310

Geometry

In triangle $ABC,$ $AB = 3,$ $AC = 5,$ $BC = 7,$ and $D$ lies on $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC.$ Find $\cos \angle BAD.$

learnmgcat Jun 1, 2024

0

11

1

+842

Geometry

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?

RedDragonl Jun 1, 2024

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14

1

+842

Rectangle problem

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

RedDragonl Jun 1, 2024

+1

16

3

+11

If anyone would like to help me understand these questions, I tried my best, thank you!! (you can give hints)

Can someone please help me to understand these problems! read more ..

daonly39 Jun 1, 2024

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20

1

+1310

Geometry

In triangle $ABC,$ $BC = 32,$ $\tan B = \frac{3}{5},$ and $\tan C = \frac{1}{4}.$ Find the area of the triangle.

learnmgcat Jun 1, 2024

0

13

1

+1310

Geometry

In the diagram below, we have $AB = 24$ and $\angle ADB =90^\circ$. If $\sin A = \frac13$ and $\sin C = \frac12$, then what is $BC$?

learnmgcat Jun 1, 2024

May 31, 2024

0

16

1

+1310

Geometry

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

learnmgcat May 31, 2024

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