All Questions ⁺⁰236050 Questions

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Number Theory

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

RedDragonl Jul 13, 2024

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26

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+842

Number Theory

If n \equiv 43 \pmod{165}, then what is the residue of $n$ modulo 2?

RedDragonl Jul 13, 2024

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27

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+893

Algebra

Let
f(x) = \frac{2x + 5}{x - 4} + \frac{x^2 + 1}{4x - 3}.
Find the inverse $f^{-1}(x)$.

AnswerscorrectIy Jul 13, 2024

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19

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+893

Algebra

Let a1, a2, a3, ... be an arithmetic sequence. Let Sn denote the sum of the first n terms. If S_5 = 1/5 and S_10 = 1/10, then find S_15.

AnswerscorrectIy Jul 13, 2024

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18

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+893

Algebra

Let a1, a2, a3, ..., a10 be an arithmetic series. If a1 + a3 = -2 and a2 + a4 + a6 = 1, then find a1.

AnswerscorrectIy Jul 13, 2024

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27

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+893

Algebra

Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 100, Shirley runs screaming from the room. What number does Laverne say that sends read more ..

AnswerscorrectIy Jul 13, 2024

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14

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+842

Probability

Alex chooses a number at random from the set {1, 2, 3, 4, 5}. Winnie also chooses a number at random from the same set. (They can choose the same number.) What is the probability that the product of their numbers is at least 4? read more ..

RedDragonl Jul 13, 2024

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22

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+842

Probability

The following cards are split into three piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?
Ace of spades
Ace of hearts
Ace of diamonds read more ..

RedDragonl Jul 13, 2024

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20

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+842

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 ..

RedDragonl Jul 13, 2024

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13

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+842

Number Theory

What is 100000_{16} * E21A8_{16} in base 16?

RedDragonl Jul 13, 2024

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27

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+842

Number Theory

Express 0.11012 as a base 10 fraction in reduced form.

RedDragonl Jul 13, 2024

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21

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+842

Number Theory

Express 0.\overline{2123} as a base 10 fraction in reduced form.

RedDragonl Jul 13, 2024

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24

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+842

Number Theory

Compute A710B_{16} * 5_{16} in base 16.

RedDragonl Jul 13, 2024

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26

1

+54

Help with Magnitude

Let z and w be complex numbers such that |z|=1,|w|=7, and |5z-2w|=11. Find |3z+4w|

RedDragon1 Jul 13, 2024

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17

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Number Theory

Find the units digit of $13*287$.

AnswerscorrectIy Jul 13, 2024

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27

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+893

Number Theory

Find the last three digits of $35*{781}$.

AnswerscorrectIy Jul 13, 2024

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19

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+893

Number Theory

How many of the $1000$ smallest positive integers are congruent to $5$ modulo $171?$

AnswerscorrectIy Jul 13, 2024

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18

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+893

Number Theory

How many positive integers $n$ satisfy $127 \equiv 18 \pmod{n}$? ($n = 1$ is allowed.)

AnswerscorrectIy Jul 13, 2024

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9

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+893

Algebra

Find the ordered pair (s,t) that satisfies the system
s/2 + 5t = 3 - 7s + 10t
3t - 6s = 9 + 2t + 7s

AnswerscorrectIy Jul 13, 2024

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14

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+893

Algebra

Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2 - 2x^2 + 4x - 1.

AnswerscorrectIy Jul 13, 2024

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11

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+893

Algebra

The equation of the line below can be expressed in the form
\frac{x}{a} + \frac{y}{b} = 1.
Find a.
The lines passes through (5,8) and (-4,17).

AnswerscorrectIy Jul 13, 2024

0

12

1

+893

Number Theory

On planet Enigma, the residents use a currency called the confusion. There are only two confusion bills on Enigma, one worth $7$ confusions and the other worth $12$ confusions. There are also some coins of smaller value, but each weighs over read more ..

AnswerscorrectIy Jul 13, 2024

0

13

1

+893

Algebra

Evaluate the infinite geometric series
0.4 + 0.036 + 0.0000324 + ...
Express your answer as a fraction with integer numerator and denominator.

AnswerscorrectIy Jul 13, 2024

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31

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+893

Algebra

Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 2 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator read more ..

AnswerscorrectIy Jul 13, 2024

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