All Questions ⁺⁰237119 Questions

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Counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

nathanl6656 Dec 5, 2024

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16

1

+713

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 $n$?

crimefightingvigiI Dec 5, 2024

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12

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+713

Number Theory

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

crimefightingvigiI Dec 5, 2024

Dec 4, 2024

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9

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+1721

Algebra

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

parmen Dec 4, 2024

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11

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+1721

Algebra

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

parmen Dec 4, 2024

Dec 3, 2024

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14

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+1493

Algebra

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

learnmgcat Dec 3, 2024

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8

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+1493

Algebra

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

learnmgcat Dec 3, 2024

+1

15

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+394

Stats Question

An experiment was planned to determine the effect of fertilizer on a measure of leaf area. A number of plots were available for the study, and half were selected at random to be fertilized. In order to assure that the plots to receive the fertilizer and read more ..

hellospeedmind Dec 3, 2024

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Stats Question

A fitness rating was obtained for 9 randomly selected adult women. Each person was also asked her age, weight, and the number of hours she spent exercising each week. The results are summarized in the table below. Identify the regression equation that expresses read more ..

hellospeedmind Dec 3, 2024

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12

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+1493

Algebra

For an integer n, the inequality
x^2 + nx + 15 < -89 - 3x^2
has no real solutions in $x$. Find the number of different possible values of $n$.

learnmgcat Dec 3, 2024

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10

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+1493

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).

learnmgcat Dec 3, 2024

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14

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+1493

Algebra

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.

learnmgcat Dec 3, 2024

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7

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+1721

Counting

The numbers x1, x2, x3, and x4 are chosen at random in the interval [0,1]. Let I be the interval between x1 and x2, and let J be the interval between x3 and x4. Find the probability that intervals I and J contain the number 1/2.

parmen Dec 3, 2024

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15

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+1721

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 ..

parmen Dec 3, 2024

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12

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+1721

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 ..

parmen Dec 3, 2024

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17

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+713

Algebra

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

crimefightingvigiI Dec 3, 2024

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11

1

+713

Algebra

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

crimefightingvigiI Dec 3, 2024

0

16

0

+713

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 - 18x - 25.
What is $k?$

crimefightingvigiI Dec 3, 2024

0

14

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+1493

Geometry

Let $k$ be a positive real number. The line $x + y = 3 + k$ and the circle $x^2 + y^2 = k$ are drawn. Find $k$ so that the line is tangent to the circle.

learnmgcat Dec 3, 2024

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+1493

Geometry

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The line is x = 4, and the equation of the circle is x^2 + y^2 = 25.

learnmgcat Dec 3, 2024

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