All Questions ⁺⁰234977 Questions

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Algebra

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 ..

siIviajendeukie Oct 7, 2024

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+559

Algebra

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

siIviajendeukie Oct 7, 2024

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+559

Algebra

Let a1, a2, a3, ... be an arithmetic sequence. Let Sn denote the sum of the first n terms. If S_5 = 1/5 and S_10 = 1/10, then find S_15.

siIviajendeukie Oct 7, 2024

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+260

Geometry

In square ABCD, P is on BC such that BP = 5 and PC = 2, and Q is on CD such that DQ = 4 and QC = 3. Find sin angle PAQ.

nathanl6656 Oct 7, 2024

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+260

Geometry

Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is $6$, then find the volume of the resulting read more ..

nathanl6656 Oct 7, 2024

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+165

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 next to each other, and all the adults are next to each other? (Two seatings are considered the same if read more ..

MEMEG0D Oct 7, 2024

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+165

Counting

At a meeting, four scientists, two mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if the mathematicians must sit next to each other? (Two seatings are considered equivalent if read more ..

MEMEG0D Oct 7, 2024

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+165

Counting

A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, read more ..

MEMEG0D Oct 7, 2024

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+46

Please Help

On a True/False test, Amy answered the first three questions wrong but answered the rest of the questions correctly. On the same test, Scott answered exactly two questions wrong. He answered the last question wrong, the questions before it correctly, read more ..

greenplanet2050 Oct 7, 2024

Oct 6, 2024

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+786

Number Theory

Starting at the same time, Bill rings a bell every $36$ seconds, and Wendy blows a whistle every $90$ seconds, and Sam blows a horn every $385$ seconds. How many minutes will it be before both Bill and Wendy and Sam simultaneously make a sound?</ read more ..

RedDragonl Oct 6, 2024

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+786

Number Theory

For a positive integer n, \phi(n) denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$. What is $\phi(20)$?

RedDragonl Oct 6, 2024

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+362

Number Theory

Fill in the blanks with three distinct positive integers.
1/___ + 1/___ + 1/___ = \frac{13}{12}

onyuIee Oct 6, 2024

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+362

Number Theory

For a positive integer n, \phi(n) denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$. What is $\phi(2835)$?

onyuIee Oct 6, 2024

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+362

Number Theory

How many numbers between $1000$ and $2000$ leave a remainder of $3$ when divided by $1999$?

onyuIee Oct 6, 2024

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+47

Really hard math puzzles that you'll probably find on an SAT

Fun math puzzles, I'll try my best to do them weekly or something like that.
1. C=59(F−32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. read more ..

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AUnVerifiedTaxPayer Oct 6, 2024

Oct 5, 2024

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+1095

Geometry

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

learnmgcat Oct 5, 2024

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+1095

Geometry

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

learnmgcat Oct 5, 2024

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