All Questions ⁺⁰232916 Questions

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Counting

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 ..

eramsby1O1O Jun 29, 2024

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+1850

Number Theory

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

LiIIiam0216 Jun 29, 2024

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+1850

Number Theory

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

LiIIiam0216 Jun 29, 2024

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+1850

Number Theory

Express 0.11012 as a base 10 fraction in reduced form.

LiIIiam0216 Jun 29, 2024

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+1850

Number Theory

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

LiIIiam0216 Jun 29, 2024

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+1850

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 ..

LiIIiam0216 Jun 29, 2024

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+1850

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 ..

LiIIiam0216 Jun 29, 2024

0

1

1

+1850

Probability

Alex chooses a number at random from the set $\{1, 2, 3, \dots, 5\}.$ 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 even?
<read more ..

LiIIiam0216 Jun 29, 2024

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+1850

probability

Two different numbers are chosen at random from the set {1, 2, 3, ..., 5}. What is the probability that the product of the numbers is even?

LiIIiam0216 Jun 29, 2024

Jun 28, 2024

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+330

Number Theory

A four-digit hexadecimal integer is written on a napkin such that the units digit is illegible. The first three digits are $7$, $D$, and $3$. If the integer is a multiple of $25_{10}$, what is the units digit?

gnistory Jun 28, 2024

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+330

Number Theory

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

gnistory Jun 28, 2024

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+330

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 $n$?

gnistory Jun 28, 2024

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+330

Number Theory

Express 0.11012 as a base 10 fraction in reduced form.

gnistory Jun 28, 2024

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1

0

+330

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 $12$, it has the same three digits, in reverse order. What is $N$? (Express your answer in decim read more ..

gnistory Jun 28, 2024

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+330

Number Theory

Express 2.\overline{57} as a base 10 fraction in reduced form.

gnistory Jun 28, 2024

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+330

Number Theory

What are the first 5 digits after the decimal point (technically the hexadecimal point...) when the fraction $\frac{2}{7}$ is written in base $16$?

gnistory Jun 28, 2024

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+330

Number Theory

Jon teaches a fourth grade class at an elementary school where class sizes are always at least 10 students and at most 15. One day Jon decides that he wants to arrange the students in their desks in a rectangular grid with no gaps. Unfortunately read more ..

gnistory Jun 28, 2024

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+330

Number Theory

What is the fifth smallest prime number greater than 100?

gnistory Jun 28, 2024

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+330

Counting

Starting with the A and moving one letter at a time vertically, horizontally, or diagonally, how many different paths spell ARCH?
A
RR
CCC read more ..

gnistory Jun 28, 2024

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Geometry

In the diagram, the four points have coordinates $A(0,1)$, $B(1,3)$, $C(5,2)$, and $D(4.5,0)$. What is the area of quadrilateral $ABCD$?

gnistory Jun 28, 2024

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Geometry

Determine the coordinates of the point $P$ on the line $y=-x+6$ such that $P$ is equidistant from the points $A(10,-12)$ and $O(2,8)$ (that is, so that $PA=PO$). Express your answer as an ordered pair $(a,b)$.

gnistory Jun 28, 2024

Jun 27, 2024

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+136

Algebra

Find all real values of $p$ such that
(x+1)(x-2p)
has a minimum value of 0 over all real values of $x$.

BRAlNBOLT Jun 27, 2024

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