All Questions ⁺⁰235873 Questions

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Geometry

A rectangle contains a strip of width $1,$ as shown below. Find the area of the strip.

learnmgcat Dec 10, 2024

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Geometry

In triangle PQR, M is the midpoint of PQ .Let X be the point on QR such that PX bisects QPR and let the perpendicular bisector of PQ intersect PX at Y. If PQ=28,PR=16 and MY=5 then find the area of triangle PYR</ read more ..

learnmgcat Dec 10, 2024

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+570

Algebra

For a certain value of k, the system
x + y + 3z = 10 - x + 5y,
4x + 2y + 5z = 7 + 11y + 19z,
kx + z = 3 + 5y
has no solutions. What is this value of k?

cooIcooIcooI17 Dec 10, 2024

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+570

Algebra

Solve the inequality $x(x + 6) > 16 - 5x + 33.$ Write your answer in interval notation.

cooIcooIcooI17 Dec 10, 2024

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+570

Algebra

Solve the inequality $4t^2 \le -9t + 12 - 14t + 36.$ Write your answer in interval notation.

cooIcooIcooI17 Dec 10, 2024

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+267

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 ..

bIueb3rry Dec 10, 2024

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+267

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.

bIueb3rry Dec 10, 2024

Dec 9, 2024

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Counting

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 ..

learnmgcat Dec 9, 2024

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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 ..

learnmgcat Dec 9, 2024

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+267

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 $(A,B,C)$.

bIueb3rry Dec 9, 2024

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+267

Number Theory

Find a six-digit multiple of $64$ that consists only of the digits $2$ and $4$.

bIueb3rry Dec 9, 2024

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+267

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 $a$.

bIueb3rry Dec 9, 2024

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+267

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.

bIueb3rry Dec 9, 2024

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+760

Number Theory

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

booboo44 Dec 9, 2024

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+760

Number Theory

Find the greatest prime divisor of the value of the arithmetic series
1 + 2 + 3 + \dots + 135 + 136 + 137 + 138 + 139 + 140.

booboo44 Dec 9, 2024

Dec 8, 2024

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+760

Number Theory

Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{17}$

NotThatSmart ●

booboo44 Dec 8, 2024

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+313

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

crimefightingvigiI Dec 8, 2024

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Geometry

There are four cities: Capital City, Little Village, Mytown, and Yourtown. The distance from Capital City to Little Village is $5$ miles. The distance from Capital City to Mytown is $2$ miles. The distance from Mytown to Yourtown is $3$ read more ..

crimefightingvigiI Dec 8, 2024

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+294

Algebra

Suppose $a\neq 0$. Compute $\log_{8a} b$ in terms of $a$ and $b$.

MEMEG0D Dec 8, 2024

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Algebra

Find all $c$ such that $|c + 5| - 3|c + 7| = 10 + 2|c - 8|.$ Enter all the solutions, separated by commas.

MEMEG0D Dec 8, 2024

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+46

the bag...

You have a bag which contains only red and green marbles. In this bag with x^2+5 marbles total, x+1 are red. Also, x-3 marbles have a scratch on them. The probability of drawing a red marble from the original bag is equal to that of drawing a marble read more ..

Umeko1.0 Dec 8, 2024

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+219

Counting

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers (1, 2, 3, 4, 5, 6, and 7). Among all the cards of each color, there is exactly one card labeled with each number. read more ..

BRAlNBOLT Dec 8, 2024

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