All Questions ⁺⁰236027 Questions

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15

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+868

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 $n$.

eramsby1O1O May 21, 2024

0

23

1

+868

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.

eramsby1O1O May 21, 2024

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22

1

+868

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?

eramsby1O1O May 21, 2024

0

24

0

+868

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 ..

eramsby1O1O May 21, 2024

0

16

0

+868

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 ..

eramsby1O1O May 21, 2024

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18

0

+1234

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 $WXYZ$?

Akhain1 May 21, 2024

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25

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+1234

Geometry

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 $AB$.

Akhain1 May 21, 2024

0

29

0

+1234

Geometry

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

Akhain1 May 21, 2024

0

26

0

+1234

Geometry

In triangle ABC, point X is on side BC such that AX=5, BX=5, CX=4, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

Akhain1 May 21, 2024

0

13

1

+118

HELP ASAP

In quadrilateral BCDE, sides $\overline{BD}$ and $\overline{CE}$ are extended past B and C, respectively, to meet at point A. If BD = 18, BC = 8, CE = 2, AC = 7 and AB = 3, then what is DE? read more ..

SilviaJendeukie May 21, 2024

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26

0

+976

Counting

In how many ways can I arrange $3$ different math books and $4$ different history books on my bookshelf, if at least three of the history books are next to each other?

Hi6942O May 21, 2024

0

22

0

+976

Counting

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row?

Hi6942O May 21, 2024

0

20

0

+1310

Counting

North High School has a math club and a science club. There are a students in the math club and b students who are members of both clubs. The total number of students is c. Find an expression for the total number of students read more ..

learnmgcat May 21, 2024

0

20

0

+1310

Counting

North High School has a math club and a science club. There are a students in the math club and b students who are members of both clubs. The total number of students is c. Find an expression for the total number of students read more ..

learnmgcat May 21, 2024

0

24

0

+1310

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 of the freshmen are standing next to each other?

learnmgcat May 21, 2024

0

29

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 all the psychology textbooks are together?

learnmgcat May 21, 2024

0

27

0

+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 together? (Two seatings are considered the same if one can be rotated to form the other.)

learnmgcat May 21, 2024

0

13

1

+68

Let matrix A and the vectors v_1 and v_2 be defined below: A= \begin{bmatrix} -1 && -6 \\ 2 && -6 \end{bmatrix}

Let matrix A and the vectors v_1 and v_2 be defined below: A=\begin{bmatrix} -1 && -6 \\ 2 && -6 \end{bmatrix}, v_1=(2;-1) and v_2=(3;-2).
Show that A sends vectors v_1 and v_2 to scalar multiples of themselves read more ..

LearningCat May 21, 2024

0

16

0

+976

Algebra

Let
f(x) = \left\lfloor\frac{3x - 5}{3x + 4}\right\rfloor.
Evaluate f(1)+f(2) + f(3) + \dots + f(999)+f(1000). (This sum has $1000$ terms, one for the result when we input each integer from $1$ to $1000$ into $f$.)

Hi6942O May 21, 2024

0

19

0

+976

Algebra

Find the minimum value of \frac{x^2}{x - 1 + x^3} for x > 1

Hi6942O May 21, 2024

May 20, 2024

0

25

0

+1234

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

Akhain1 May 20, 2024

0

19

0

+1234

Geometry

In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $20^\circ.$ Find the area of the rhombus.

Akhain1 May 20, 2024

0

32

1

+1234

Geometry

Find the area of parallelogram ABCD.

Akhain1 May 20, 2024

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