All Questions ⁺⁰232717 Questions

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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 ..

Hi6942O May 27, 2024

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Counting

At a meeting, four scientists, two mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if the mathematicians must sit next to each other? (Two seatings are considered equivalent if read more ..

Hi6942O May 27, 2024

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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 ..

Hi6942O May 27, 2024

May 26, 2024

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+404

Geometry

A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point $P$ on the edge of the table (as shown below) has a distance of $10$ from one wall, and a distance of $13$ from the other wall. Find the radius read more ..

RedDragonl May 26, 2024

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Geometry

The two circles below are externally tangent. A common external tangent intersects line $PQ$ at $R.$ Find $QR.$

RedDragonl May 26, 2024

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Algebra

Laverne starts counting out loud by 5's. She starts with 1. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 40, Shirley runs screaming from the room. What number does Laverne say that sends Shirley screaming read more ..

RedDragonl May 26, 2024

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Algebra

Let a1, a2, a3, ... be an arithmetic series. Let Sn denote the sum of the first n terms. If S1 = 5 and S2 = 15, then find S15.

RedDragonl May 26, 2024

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Algebra

Let x be a real number such that 625x = 9. Then 125x = ____

RedDragonl May 26, 2024

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Algebra

Find the domain and range of the function f(x) = 2(2 - 3x).

RedDragonl May 26, 2024

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Algebra

The graph of the exponential function f(x) is shown below. Find f(x).
f(0) = 1 and f(1) = 2.

RedDragonl May 26, 2024

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Counting

A baking club wants to form an executive committee. There are $18$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people?
A baking club wants to form read more ..

RedDragonl May 26, 2024

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Geometry

A regular hexagon has a perimeter of p (in length units) and an area of A (in square units). If A=3/2 then find the side length of the hexagon.

RedDragonl May 26, 2024

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Geometry

Let $B,$ $A,$ and $D$ be three consecutive vertices of a regular $20$-gon. A regular heptagon is constructed on $\overline{AB},$ with a vertex $C$ next to $A.$ Find $\angle BAD,$ in degrees.

RedDragonl May 26, 2024

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Geometry

Point $A$ is reflected over the line shown below to point $B$. Find the coordinates of $B$.
Write your answer as an ordered pair $(x,y)$.
Point A is (5,7), and the line is y = x.

Hi6942O May 26, 2024

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Geometry

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$, and $BC read more ..

Hi6942O May 26, 2024

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Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

Hi6942O May 26, 2024

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Algebra

Chuck deposits $2000 into a bank account that compounds weekly at an annual interest rate of 15% Assuming there are no other transactions, what will the balance be after 10 years, in dollars?

Hi6942O May 26, 2024

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Algebra

Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations
a + 2b + 3c + 4d + 5e = 47
2a + 3b + 4c + 5d = 22
3a + 4b + 5c = -17 read more ..

Hi6942O May 26, 2024

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Algebra

Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6 + 2ab,$ then what is $a^3 + b^3?$

Hi6942O May 26, 2024

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+591

Algebra

Find the value of
\cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{2}}}}.

Hi6942O May 26, 2024

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Geometry

Let $\overline{AB}$ be a diameter of a circle, and let $C$ be a point on the circle such that $AC = 4$ and $BC = 4.$ The angle bisector of $\angle ACB$ intersects the circle at point $M.$ Find $CM.$

RedDragonl May 26, 2024

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Geometry

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

RedDragonl May 26, 2024

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Geometry

In triangle ABC, point X is on side BC such that AX = 10, BC = 10, CX = 5, and the circumcircles of traingles ABX and ACX have the same radius. Find the area of triangle ABC.

RedDragonl May 26, 2024

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+641

Trig problem

Let a be a real number such that 0 < a < \frac{\pi}{2}. Show that \left(\sin(a)\right)^7 + \left(\cos ( a)\right)^7< 2 sin(a)^4 cos(a)^4.

eramsby1O1O May 26, 2024

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Geometry

A rectangle contains a strip of width $1,$ as shown below. Find the area of the strip.

Hi6942O May 26, 2024

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