All Questions ⁺⁰236048 Questions

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Number Theory

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

gnistory Oct 29, 2024

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6

2

+38

Is this hard?

Janie can stuff 30 envelopes in one min. Find an expression for the number of envelopes she can stuff in n hours

SuckAtMathPleaseHelp Oct 29, 2024

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6

2

+38

Travel? Harder than you think

I'm visiting Germany, but forgot to exchange dollors for euros. My meal costs 17 euros. I gave the cahier 40 dollars. If 1 euro is worth $1.32, then how much change in euros should I receive?

SuckAtMathPleaseHelp Oct 29, 2024

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4

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+862

Number Theory

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.

magenta Oct 29, 2024

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4

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+862

Number Theory

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

magenta Oct 29, 2024

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5

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+862

Number Theory

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

magenta Oct 29, 2024

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5

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+862

Number Theory

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 $23$?

magenta Oct 29, 2024

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5

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+281

Number Theory

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 18, it has the same three digits, in reverse order. What is N? (Express your answer in decimal read more ..

jaekg Oct 29, 2024

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+281

Number Theory

Which of the residues $0,$ $1,$ $2,$ $\dots,$ $11$ satisfy the congruence $3x \equiv 8 \pmod{5}?$
Give your answer as a list, separated by commas, in order from least to greatest.

jaekg Oct 29, 2024

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4

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+330

Number Theory

Which of the residues $0,$ $1,$ $2,$ $3,$ $4$ satisfy the congruence $3x \equiv 0 \pmod{5}?$
Give your answer as a list, separated by commas, in order from least to greatest.

Stanry Oct 29, 2024

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6

0

+330

Number Theory

Which of the residues $0,$ $1,$ $2,$ $3,$ $4,$ $5$ satisfy the congruence $x^2 \equiv 0 \pmod{6}?$
Give your answer as a list, separated by commas, in order from least to greatest.

Stanry Oct 29, 2024

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5

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+330

Number Theory

Let $a$ be an integer such that $a \equiv 5 \pmod{7}$. Find the value of $a + 1 \pmod{7}$. Express your answer as a residue between $0$ and the modulus.

Stanry Oct 29, 2024

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7

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+330

Number Theory

Let $a$ be an integer such that $0 \le a \le 10$ and $a^2 \equiv a \pmod{11}$. If $a \neq 0,$ then find the value of $a$.

Stanry Oct 29, 2024

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4

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+510

Number Theory

Let $a$ be an integer such that $0 \le a \le 7$ and $a^2 \equiv a \pmod{8}$. If $a \neq 0,$ then find the value of $a$.

onyuIee Oct 29, 2024

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4

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+510

Number Theory

Find the last two digits of $16*{37}$.
(Compute the remainder when $16*{37}$ is divided by 100.)

onyuIee Oct 29, 2024

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7

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+510

Number Theory

Find the remainder when $100^{100}$ is divided by $18$.

onyuIee Oct 29, 2024

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6

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+510

Number Theory

Given
a &\equiv 1 \pmod{7} \\
b &\equiv 2 \pmod{7} \\
c &\equiv 6 \pmod{7} read more ..

onyuIee Oct 29, 2024

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4

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+606

Algebra

Let
$$f(x) = \frac{1}{1+\frac{2}{1+\frac 3x}}.$$
There are three real numbers $x$ that are not in the domain of $f(x)$. What is the sum of those three numbers?

cooIcooIcooI17 Oct 29, 2024

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+606

Algebra

The function $f(x)$ is defined only on domain $[-1,2]$, and is defined on this domain by the formula
$$f(x) = 2x^2-8x+1.$$
What is the range of $f(x)$? Express your answer as an interval or as a union of intervals.

cooIcooIcooI17 Oct 29, 2024

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6

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+606

Algebra

For certain values of k and m, the system
3a + 2b = 2
a + 2b = k - 8a - mb
has infinitely many solutions (a,b). What are k and m? read more ..

cooIcooIcooI17 Oct 29, 2024

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7

0

+606

Algebra

Let $x$ and $y$ be nonnegative real numbers. If $x + y = 25$, then find the minimum value of $6x + 3y.$

cooIcooIcooI17 Oct 29, 2024

0

6

3

+36

Number Theory

A regular a-gon, a regular b-gon, and a regular c-gon fit perfectly around a point. What is the largest possible value of c?
a-6, b-20, c-42, d-50, e-100

So far, I plugged in possible values read more ..

HelpIneedHelp Oct 29, 2024

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7

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+1310

Algebra

Find $t$ if the expansion of the product of $x^3$ and $x^2 + tx$ has no $x^2$ term.

learnmgcat Oct 29, 2024

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8

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+1310

Algebra

There exists a polynomial $f(x)$ and a constant $k$ such that
(x^2 - 2x - 5) f(x) = 2x^4 + 19x^3 + kx^2 - 15x - 1.
What is $k?$

learnmgcat Oct 29, 2024

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6

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+1310

Algebra

What is the coefficient of $x$ in $(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)$?

learnmgcat Oct 29, 2024

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