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Post New Question
All Questions
+0
235873 Questions
0
3
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+769
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
0
4
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
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SuckAtMathPleaseHelp
Oct 29, 2024
0
5
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?
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SuckAtMathPleaseHelp
Oct 29, 2024
0
3
0
+842
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
0
3
0
+842
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
0
5
0
+842
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
0
5
0
+842
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
0
4
0
+241
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
0
4
0
+241
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
0
3
0
+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
0
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
0
5
0
+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
0
6
0
+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
0
3
0
+434
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
0
3
0
+434
Number Theory
Find the last two digits of $16*{37}$.
(Compute the remainder when $16*{37}$ is divided by 100.)
onyuIee
Oct 29, 2024
0
6
0
+434
Number Theory
Find the remainder when $100^{100}$ is divided by $18$.
onyuIee
Oct 29, 2024
0
4
0
+434
Number Theory
Given
a &\equiv 1 \pmod{7} \\
b &\equiv 2 \pmod{7} \\
c &\equiv 6 \pmod{7}
read more ..
onyuIee
Oct 29, 2024
0
4
0
+570
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
0
3
0
+570
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
0
4
0
+570
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
0
5
0
+570
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
4
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 ..
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HelpIneedHelp
Oct 29, 2024
0
6
0
+1286
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
0
5
0
+1286
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
0
5
0
+1286
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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