instruction_seed stringlengths 40 2.1k | response_seed stringclasses 1
value |
|---|---|
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the ... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. For example, a graph of $y\equiv x^2\pmod 5$ would consist of the poin... | |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$100_{10}$ in base $b$ has exactly $5$ digits. What is the value of $b$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$12! = 47a001600$, for some digit $a$. What is the value of $a$?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$20!$ has 19 digits, the last 18 of which are 432902008176640000. What is the first digit?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?
# Answer
| |
# Question
$361+2(19)(6)+36=x$. Solve for $x$.
# Answer
| |
# Question
$361+2(19)(6)+36=x$. Solve for $x$.
# Answer
| |
# Question
$361+2(19)(6)+36=x$. Solve for $x$.
# Answer
| |
# Question
$361+2(19)(6)+36=x$. Solve for $x$.
# Answer
|
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 10