All Questions ⁺⁰237779 Questions

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help

A four by four grid of unit squares contains squares of various sizes (1 by 1 through 4 by 4), each of which are formed entirely from squares in the grid. In each of the 16 unit squares, write the number of squares that contain it. For instance, the middle read more ..

flybirdeee Feb 16, 2025

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20

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Counting

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 ..

learnmgcat Feb 16, 2025

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7

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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 Feb 16, 2025

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12

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+1524

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 Feb 16, 2025

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29

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+381

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 ..

cwimie Feb 16, 2025

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38

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+381

Number Theory

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

cwimie Feb 16, 2025

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27

0

+381

Number Theory

Let $m$ and $n$ be positive integers. If $m$ has exactly $7$ positive divisors, $n$ has exactly $15$ positive divisors, and $mn$ has exactly $14$ positive divisors, then how many divisors does $m^2 n^2$ have?

cwimie Feb 16, 2025

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18

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+823

Algebra

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

crimefightingvigiI Feb 16, 2025

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24

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+823

Algebra

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

crimefightingvigiI Feb 16, 2025

0

40

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+823

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 $k?$

crimefightingvigiI Feb 16, 2025

0

35

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+823

Algebra

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

crimefightingvigiI Feb 16, 2025

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24

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+456

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 $n$.

Jasmo Feb 16, 2025

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32

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+456

Help 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).

Jasmo Feb 16, 2025

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35

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+456

Algebra question

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

Jasmo Feb 16, 2025

Feb 15, 2025

+1

17

2

+31

Trig question, help appreciated! :)

Let be an acute angle. If then what is Please use an exact answer. Thank you!

Jasino Feb 15, 2025

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31

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+456

Algebra

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.

Jasmo Feb 15, 2025

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32

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+456

Algebra

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.

Jasmo Feb 15, 2025

Feb 14, 2025

+1

17

2

+456

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 36 minutes, but when there is a wind blowing from Penthaven to Jackson at 30 miles per hour, the trip takes 3 hours and 45 read more ..

Jasmo Feb 14, 2025

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Algebra

Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6,$ then what is $a^3 + b^3?$

mymilestonecc ●

Jasmo Feb 14, 2025

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29

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+456

Algebra

The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4 read more ..

Jasmo Feb 14, 2025

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23

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+456

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 ..

Jasmo Feb 14, 2025

Feb 13, 2025

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36

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+456

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 $k?$

Jasmo Feb 13, 2025

+1

34

0

+456

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 ..

Jasmo Feb 13, 2025

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31

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+456

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 $a$.

Jasmo Feb 13, 2025

+2

18

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+18

HELP!!!

This histogram shows the numbers of students who received each score on a 20 - point quiz. What was the mean quiz score? Express your answer as a decimal to the nearest tenth.

Chiccen Feb 13, 2025

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