All Questions ⁺⁰236009 Questions

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John and Ling start their new jobs on the same day. John's schedule is six workdays followed by one day off. Ling's schedule is seven workdays followed by one day off. On how many days during their first year of work ($365$ days) read more ..

LiIIiam0216 Jul 28, 2024

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7

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+2653

plz help

Brandon spends his afternoon picking apples from an orchard. He notices that if he groups the apples he picked by fives, six, or sevens, then he ends up with $1$ left over. If he groups by eights, he has $1$ left over. If Brandon read more ..

LiIIiam0216 Jul 28, 2024

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help with mods

Find the number of solutions to
N &\equiv 2 \pmod{6}, \\
N &\equiv 2 \pmod{7}, \\
N &\equiv 2 \pmod{8}
in the interval 0 \le N < 1000.

LiIIiam0216 Jul 28, 2024

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need help quick

What are the first 5 digits after the decimal point (technically the hexadecimal point...) when the fraction $\frac{2}{7}$ is written in base $16$?

LiIIiam0216 Jul 28, 2024

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13

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+2653

help me

For a certain positive integer $n$, the number $n^{6873}$ leaves a remainder of $3$ when divided by $23.$ What remainder does $n$ leave when divided by $23$?

LiIIiam0216 Jul 28, 2024

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10

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+2653

really need help

For an integer $n,$ let $f(n)$ be the remainder when $n^8 + n^{16}$ is divided by $5.$ Compute $f(0) + f(1) + f(2) + f(3) + f(4).$

LiIIiam0216 Jul 28, 2024

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11

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+355

Modulo help

Find all integers $n$, $0 \le n < 163$, such that $n$ is its own inverse modulo $163.$

Lilliam0216 Jul 28, 2024

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+2653

help mee

Fill in the coefficients:
n(n - 1)(n + 17)(n - 21)(n - 33) = n^5 + ___ n^4 + ___ n^3 + ___ n^2 + ___n + ___

LiIIiam0216 Jul 28, 2024

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14

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+2653

help me help

The Fibonacci sequence is defined by F_1 = F_2 = 1 and F_{n + 2} = F_{n + 1} + F_n. Find the remainder when F_{1000} is divided by 17.

LiIIiam0216 Jul 28, 2024

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20

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+2653

need help

Let $m$ and $n$ be non-negative integers. If $m = 6n + 2$, then what integer between $0$ and $m$ is the inverse of $5$ modulo $m$? Answer in terms of $n$.

LiIIiam0216 Jul 28, 2024

0

17

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+2653

help help

The number $N$ is a multiple of $7$. The base $2$ representation of $N$ is
10011010011ABC110_2.
Compute the ordered triple of digits $(A,B,C)$.

LiIIiam0216 Jul 28, 2024

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math

Two sides of a square are divided into fourths and another side of the square is trisected, as shown. A triangle is formed by connecting three of these points, as shown. What is the ratio of the area of the shaded triangle to the area of the square? Express read more ..

rudra849 Jul 28, 2024

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11

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+2653

plz help me

What is the largest positive integer $n$ such that $1457$, $1797$, $709$, $15$, $24$, $197$, $428$ all leave the same remainder when divided by $n$?

LiIIiam0216 Jul 28, 2024

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18

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+2653

plz help

Express 0.11012 as a base 10 fraction in reduced form.

LiIIiam0216 Jul 28, 2024

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7

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+2653

help help help

Let $N$ be a positive integer. The number $N$ has three digits when expressed in base $7$. When the number $N$ is expressed in base $12$, it has the same three digits, in reverse order. What is $N$? (Express your answer in decim read more ..

LiIIiam0216 Jul 28, 2024

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14

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+2653

help me help

Express 2.\overline{57} as a base 10 fraction in reduced form.

LiIIiam0216 Jul 28, 2024

Jul 27, 2024

+1

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+5

12 people working together can count a box of votes in 4 hours. how long will it take 30 people to count 10 boxes of votes?

12 people working together can count a box of votes in 4 hours. how long will it take 30 people to count 10 boxes of votes?

Ghyuiiol Jul 27, 2024

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11

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+2653

help me plz

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest terrific positive integer?

LiIIiam0216 Jul 27, 2024

0

10

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+2653

need help

Let $N$ be a positive integer. The number $N$ has three digits when expressed in base $7$. When the number $N$ is expressed in base $12$, it has the same three digits, in reverse order. What is $N$? (Express your answer in decim read more ..

LiIIiam0216 Jul 27, 2024

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14

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+2653

help help

How many bases $b \ge 2$ are there such that $100_b + 1_b$ is prime?

LiIIiam0216 Jul 27, 2024

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7

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+2653

I need help

When expanded as a decimal, the fraction \frac{1}{977} has a repetend (the repeating part of the decimal) that begins right after the decimal point, and is $976$ digits long. Find the first three digits after the decimal point.

LiIIiam0216 Jul 27, 2024

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21

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+2653

help me

Find the largest positive integer $n$ such that $n^3$ divides 15.

LiIIiam0216 Jul 27, 2024

0

5

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+2653

help me quick

Find the unique triple (x,y,z) of positive integers such that and
\frac{1}{x} - \frac{1}{xy} - \frac{1}{xyz} = \frac{1}{3}

LiIIiam0216 Jul 27, 2024

0

18

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+2653

help me help

There is a single sequence of integers $a_2,$ $a_3,$ $a_4,$ $a_5,$ $a_6,$ $a_7$ such that
\frac{a_2}{2!} + \frac{a_3}{3!} + \frac{a_4}{4!} + \frac{a_5}{5!} + \frac{a_6}{6!} + \frac{a_7}{7!} = \frac{3}{128}
and $0 \le a_i < i$ for $i = 2,$ read more ..

LiIIiam0216 Jul 27, 2024

0

10

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+2653

help me plz

In base $b,$ the square of the number $17_b$ is $211_b$. Find the base $b$.

LiIIiam0216 Jul 27, 2024

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