All Questions ⁺⁰236027 Questions

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Number Theory

Write the following expression as a fraction in lowest terms:
2 + \cfrac{3}{3 + \cfrac{3}{3 + 3}}.

onyuIee Dec 17, 2024

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+510

Number Theory

Find an integer $x$ such that $0 \leq x < 205$ and $x^{89} \equiv 17 \pmod{5}$.

onyuIee Dec 17, 2024

Dec 16, 2024

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4

+667

Geometry

The area of a trapezoid is $80$. The length of one base is $16$ units greater than the other base, and one base of the trapezoid is $12$. Find the length of the median of the trapezoid.

siIviajendeukie Dec 16, 2024

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+667

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.

siIviajendeukie Dec 16, 2024

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+667

Geometry

In trapezoid $ABCD,$ $\overline{AB} \parallel \overline{CD}$. Find the area of the trapezoid.

siIviajendeukie Dec 16, 2024

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+667

Geometry

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid read more ..

siIviajendeukie Dec 16, 2024

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+510

Number Theory

The House of Lilliput is using RSA encryption to receive secret messages from all the realms. They have published their public encoding exponent $e = 8$ and their public modulus $M = pq = 6$.
Break the code: Find their secret decoding read more ..

onyuIee Dec 16, 2024

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+510

Number Theory

Carlos wants to send Cecil a message encrypted with RSA. Cecil has published his public encryption exponent $3$ and his public modulus $3$. When Carlos encrypts the number $3$ with this system, what is the result?

onyuIee Dec 16, 2024

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+510

Number Theory

An eccentric baseball card collector wants to distribute her collection among her descendants. If she divided her cards among her $13$ great-great-grandchildren, there would be $8$ cards left over. If she divided her cards among her $10$ great-grandchildren, read more ..

onyuIee Dec 16, 2024

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+510

Number Theory

When $N$ is divided by $10$, the remainder is $a$. When $N$ is divided by $2$, the remainder is $b$. What is $N$ modulo $20$, in terms of $a$ and $b$?

onyuIee Dec 16, 2024

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+510

Number Theory

When fractions are expressed in different bases, they can be terminating or repeating. For example, when \frac{1}{5} is expressed in base 3, the result is
0.\overline{0121}_3 = 0.01210121 \dots,
which is repeating.
When read more ..

onyuIee Dec 16, 2024

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+510

Number Theory

Find the greatest prime divisor of the value of the arithmetic series
1 + 2 + 3 + \dots + 135 + 136 + 137 + 138 + 139 + 140.

onyuIee Dec 16, 2024

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+1521

Algebra

The sum
6\left( 1\cdot1 + 2\cdot2 + \dots + n(n) \right)
is equal to a polynomial f(n) for all n \ge 1.
Write f(n) as a polynomial with terms in descending order of n.

blackpanther Dec 16, 2024

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+149

Help

Mr Lee bought some food for a party. 1/4 of the food bought were sausages, 7/20 of the food bought were nuggets and the rest were crabsticks. A piece of sausage cost 3 times as much as a piece of nugget and 4 times as much as a piece of crabstick. read more ..

sugabreaddoughman Dec 16, 2024

Dec 15, 2024

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+1521

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 ..

blackpanther Dec 15, 2024

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+1521

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 ..

blackpanther Dec 15, 2024

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+1521

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?

blackpanther Dec 15, 2024

Dec 14, 2024

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3

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+363

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.)

MeIdHunter Dec 14, 2024

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