All Questions ⁺⁰236050 Questions

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Number Theory

How many positive four-digit integers $N$ have the property that the three-digit number obtained by removing the leftmost digit is equal to $\frac{N}{24}?$

AnswerscorrectIy Jul 13, 2024

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14

0

+893

Number Theory

The product of a set of distinct positive integers is $630$. If one of the numbers is 42, what are the other two numbers?

AnswerscorrectIy Jul 13, 2024

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20

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+893

Number Theory

On planet Enigma, the residents use a currency called the confusion. There are only 2 confusion bills on Enigma, one worth 2 confusions and the other worth 3 confusions. There are also some coins of smaller value, but each weighs over 10 read more ..

AnswerscorrectIy Jul 13, 2024

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19

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+893

Number Theory

Find the largest positive integer n such that
\frac{(n + 1)^2}{n + 2}
is an integer.

AnswerscorrectIy Jul 13, 2024

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22

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+893

Number Theory

Let $a$, $b$, $c$, and $n$ be positive integers. If $a + b + c = 19 \cdot 97$ and
a + 3n = b - 2n = \frac{c}{5n},
compute the value of $a$.

AnswerscorrectIy Jul 13, 2024

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6

1

+149

Help

Andrew and Caden had some stamps in the ratio 6:8. Andrew gave a quarter of his stamps to Caden. Caden then had 280 stamps more than Andrew. How many stamps did they have altogether?

sugabreaddoughman Jul 13, 2024

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18

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+149

Help

Mike had 56 more trading cards than Aron. During a game, Mike lost 2/5 of his cards to Aron. Now, Aron has 72 more cards than Mike. How many cards did each of them have at first?

sugabreaddoughman Jul 13, 2024

0

17

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+893

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 ..

AnswerscorrectIy Jul 13, 2024

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32

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+893

Number Theory

You have a total supply of $1000$ pieces of candy, and an empty vat. You also have a machine that can add exactly $52$ pieces of candy per scoop to the vat, and another machine that can remove exactly $39$ pieces of candy with a different scoop from read more ..

AnswerscorrectIy Jul 13, 2024

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27

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+893

Algebra

Find the sum of all positive integers less than 1000 ending in 3 or 4 or 5.

AnswerscorrectIy Jul 13, 2024

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15

0

+893

Algebra

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

AnswerscorrectIy Jul 13, 2024

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31

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+893

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 $k?$

AnswerscorrectIy Jul 13, 2024

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28

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+893

Algebra

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

AnswerscorrectIy Jul 13, 2024

+1

5

2

+36

hints only! DONT GIVE THE ANSWER PLS!

Catherine rolls a standard 6-sided die six times. If the product of her rolls is 600 then how many different sequences of rolls could there have been? (The order of the rolls matters.)

Answerscorrectly Jul 13, 2024

+1

7

2

+36

can some one just give a hint?

in how many ways can the numbers 1 through 5 be entered once each into the five boxes below so that all the given inequalities are true?
also answer wasn't 6 which i got so idk wut it is _:D
it told me this when i wrote 6:Where can the number go?
so read more ..

Answerscorrectly Jul 13, 2024

+1

17

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+36

dude. don't give me answer pls but I'd like some hints or a few things that could help me that I may or may not have overlooked.

question: Franklin the fly starts at the point in the coordinate plane. At each point, Franklin takes a step to the right, left, up, or down. After 12 steps, how many different points could Franklin end up at?
ty for read more ..

Answerscorrectly Jul 13, 2024

Jul 12, 2024

+1

18

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+2653

Algebra

Find all ordered pairs x, y of real numbers such that x+y=10 and x^3+y^3=300.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

LiIIiam0216 Jul 12, 2024

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18

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+2653

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $3$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $3$ hours read more ..

LiIIiam0216 Jul 12, 2024

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17

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+2653

Algebra

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

LiIIiam0216 Jul 12, 2024

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18

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+2653

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $1000$ square foot wall in $10$ minutes, then how long would it take for $5$ members to paint a $1000$ square foot wall, in minutes?

LiIIiam0216 Jul 12, 2024

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24

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+2653

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $100$ square foot wall in $10$ minutes, then how long would it take the $15$ members to paint a $100$ square foot wall, in minutes?

LiIIiam0216 Jul 12, 2024

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23

0

+2653

Algebra

Seven years ago, Grogg's dad was $9$ times as old as Grogg. Four years ago, Grogg's dad was $6$ times as old as Grogg. How old is Grogg's dad currently?

LiIIiam0216 Jul 12, 2024

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28

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+2653

Algebra

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 28/9 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

LiIIiam0216 Jul 12, 2024

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30

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+2653

Algebra

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{8}.

LiIIiam0216 Jul 12, 2024

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