All Questions ⁺⁰234646 Questions

Aug 30, 2024

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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?

onyuIee Aug 30, 2024

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+1341

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?

kittykat Aug 30, 2024

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+673

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.)

magenta Aug 30, 2024

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+116

Geometry

Let $G$ be the center of equilateral triangle $XYZ.$ A dilation centered at $G$ with scale factor $-1$ is applied to triangle $XYZ,$ to obtain triangle $X'Y'Z'.$ Let $A$ be the area of the region that is contained in both triangles $XYZ$ and $X'Y'Z'.$ Find read more ..

MEMEG0D Aug 30, 2024

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+864

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?

Rangcr897 Aug 30, 2024

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+484

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 ..

gnistory Aug 30, 2024

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+96

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 ..

bIueb3rry Aug 30, 2024

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+1694

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.

ABJeIIy Aug 30, 2024

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+73

Please help, functions!

Let
Find the function such that is its own inverse.
Any help is appreciated :D

NotLatePY Aug 30, 2024

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+1055

Number Theory

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

learnmgcat Aug 30, 2024

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+1055

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 ..

learnmgcat Aug 30, 2024

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+92

Algebra

Three runners, Dirk, Edith, and Foley all start at the same time for a $24$ km race, and each of them runs at a constant speed. When Dirk finishes the race, Edith is $10$ km behind, and Foley is $15$ km behind. When Edith finishes the race, how far read more ..

jaekg Aug 30, 2024

Aug 29, 2024

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+523

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 $b$?

siIviajendeukie Aug 29, 2024

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+2651

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 ..

LiIIiam0216 Aug 29, 2024

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+2651

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?

LiIIiam0216 Aug 29, 2024

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+2651

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 ..

LiIIiam0216 Aug 29, 2024

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+312

Number Theory

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

onyuIee Aug 29, 2024

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+312

Number Theory

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

onyuIee Aug 29, 2024

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+92

Algebra

Find all values of $x$ such that $x^2 - 5x + 4 = -x^2 - 25x - 14$. If you find more than one value, then list your solutions, separated by commas.

jaekg Aug 29, 2024

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+92

Algebra

Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 2 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator read more ..

jaekg Aug 29, 2024

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+484

Algebra

Evaluate the infinite geometric series
0.4 + 0.036 + 0.0000324 + ...
Express your answer as a fraction with integer numerator and denominator.

gnistory Aug 29, 2024

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