All Questions ⁺⁰232744 Questions

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+1221

Algebra

The sum
6\left( 1\cdot1 + 2\cdot2 + \dots + n(n) \right)
is equal to a polynomial f(n) for all n \ge 1.
Write f(n) as a polynomial with terms in descending order of n.

ABJeIIy Jun 18, 2024

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1

+370

Algebra

Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. read more ..

ChiIIBill Jun 18, 2024

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+370

Algebra

I have to paint one side of a wall. The wall is $15$ meters tall and $60$ meters long. Each gallon of paint covers $400$ square feet. If a foot is approximately $0.3048$ meters, then what is the smallest whole number of gallons I can buy and read more ..

ChiIIBill Jun 18, 2024

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1

+370

Algebra

I drove to the beach at a rate of $40$ miles per hour. If I had driven at a rate of $55$ miles per hour instead, then I would have arrived $25$ minutes earlier. How many miles did I drive?

ChiIIBill Jun 18, 2024

-1

1

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+1221

Algebra

Find polynomial f(n) such that for all integers n \geq 1, we have
6\left( 1\cdot1 + 2\cdot2 + \dots + n(n) \right) = f(n).\]
Write f(n) as a polynomial with terms in descending order of n.

ABJeIIy Jun 18, 2024

Jun 17, 2024

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+500

Geometry

Let $G$ be the center of equilateral triangle $XYZ.$ A dilation centered at $G$ with scale factor $-1$ is applied to triangle $XYZ,$ to obtain triangle $X'Y'Z'.$ Let $A$ be the area of the region that is contained in both triangles $XYZ$ and $X'Y'Z'.$ Find read more ..

booboo44 Jun 17, 2024

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+36

halp asap

Let's take a look at $(x + y)^2$ and $x^2 + y^2$ . While Beeker believes that these two expressions are equal for all real numbers $x$and $y,$Clod believes they are not! Let's get to the bottom of this!
a) read more ..

ghistory Jun 17, 2024

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+497

Counting

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are together? (Two seatings are considered the same if one can be rotated to form the other.)

magenta Jun 17, 2024

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+497

Counting

I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if all the psychology textbooks are together?

magenta Jun 17, 2024

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3

+497

Counting

A speech class has $4$ freshmen and $3$ sophomores. (Everyone is distinguishable.) In how many ways can they stand in line, so that all of the freshmen are standing next to each other?

magenta Jun 17, 2024

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+1180

Algebra

Let $f$ be a cubic polynomial such that $f(0) = 0$, $f(1) = 0$, $f(2) = 0$, and $f(3)=0$. What is the sum of the coefficients of $f$?

blackpanther Jun 17, 2024

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+36

halp asap!

What is the value of $\sqrt[3]{2a^2 b^4} + \dfrac{a - c}{(b+c)^2}$ if $a = 4$,b = 2 c = -5?

NotThatSmart ●

ghistory Jun 17, 2024

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+155

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

BRAlNBOLT Jun 17, 2024

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+1847

Number Theory

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

NotThatSmart ●

tomtom Jun 17, 2024

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+1847

Number Theory

When fractions are expressed in different bases, they can be terminating or repeating. For example, when $\frac{1}{5}$ is expressed in base $3,$ the result is
\[0.\overline{0121}_3 = 0.01210121 \dots,\]
which is repeating.
When read more ..

tomtom Jun 17, 2024

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+641

Counting

North High School has a math club and a science club. There are a students in the math club and b students who are members of both clubs. The total number of students is c. Find an expression for the total number of students who are in the math club or read more ..

eramsby1O1O Jun 17, 2024

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+449

Geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

Rangcr897 Jun 17, 2024

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+449

Geometry

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.

Rangcr897 Jun 17, 2024

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+449

Geometry

Point D is the midpoint of median AM of triangle ABC. Point E is the midpoint of AB, and point T is the intersection of BD and ME. Find the area of triangle BEC if [ABC] = 14.

Rangcr897 Jun 17, 2024

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4

+155

Counting

Miyu is giving out $8$ identical chocolates to her $5$ friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets at least $6$ chocolates?

BRAlNBOLT Jun 17, 2024

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+155

Counting

In how many ways can you distribute $8$ indistinguishable balls among $5$ distinguishable boxes, if at least three of the boxes must be empty?

BRAlNBOLT Jun 17, 2024

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2

+36

halp asap

What is the value of $(a+b)\sqrt{cd}$ if $a = 2$ , $b = 4$, $c = 3$, and $d = 12$?

NotThatSmart ●●

ghistory Jun 17, 2024

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