All Questions ⁺⁰235702 Questions

Nov 8, 2024

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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 $b$?

blackpanther Nov 8, 2024

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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 ..

blackpanther Nov 8, 2024

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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 ..

blackpanther Nov 8, 2024

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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?

blackpanther Nov 8, 2024

Nov 7, 2024

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Geometry

In triangle PQR, M is the midpoint of \overline{QR}. Find PM.

gnistory Nov 7, 2024

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Geometry

In the diagram below, SR = PQ = 20 and RT:TS = 2:5. Find UV.

gnistory Nov 7, 2024

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Geometry

Trapezoid $ABCD$ is inscribed in the semicircle with diameter $\overline{AB}$, as shown below. Find the radius of the semicircle. Find the area of ABCD.
PQDC is a square.

gnistory Nov 7, 2024

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+253

Counting

There is a group of five children, where two of the children are twins. In how many ways can I distribute $3$ identical pieces of candy to the children, if the twins must get an equal amount of candy?

jaekg Nov 7, 2024

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Counting

In how many ways can you distribute $8$ indistinguishable balls among $2$ distinguishable boxes, if at least one of the boxes must be empty?

jaekg Nov 7, 2024

Nov 6, 2024

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+829

Geometry

In quadrilateral PQRS, PQ = QR = RS = SP, PR = 4, and QS = 16. Find the perimeter of PQRS.

AnswerscorrectIy Nov 6, 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 AMC if [ABC] =180.

AnswerscorrectIy Nov 6, 2024

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