All Questions ⁺⁰237321 Questions

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76

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+1930

Algebra

Alice and Bob each have a certain amount of money. If Alice receives $n$ dollars from Bob, then she will have $10$ times as much money as Bob. If, on the other hand, she gives $n$ dollars to Bob, then she will have $4$ times as much money as read more ..

tomtom Jan 22, 2024

-1

70

0

+1930

system

The system of equations
\[\frac{xy}{x + y} = 1, \quad \frac{xz}{x + z} = 1, \quad \frac{yz}{y + z} = 5\]
has exactly one solution. What is $z$ in this solution?

tomtom Jan 22, 2024

0

8

0

+1930

Percent

A magician makes potions by combining maple syrup from a magical maple tree with ordinary water. The magician starts with a large supply of two potions: a red potion, which is $50\%$ magical syrup by volume (and the rest is just water), and blue potion, read more ..

tomtom Jan 22, 2024

0

48

1

+39

help! explanation excluded please!!

The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.
The small squares sides are all 2, i know that the four equilateral triangles sides are also two but i'm really stuc read more ..

rerebas Jan 22, 2024

0

86

0

+400

Series question

Let $r$ be the positive real solution to $x^3 + \frac{2}{5} x - 1 = x^3 - 3x + 7.$ Find the exact numerical value of
r^2 + 2r^5 + 3r^8 + 4r^{11} + \dotsb.

omgitsrne Jan 22, 2024

0

7

0

+400

Series

Find the value of $k$ so that
3 + \frac{3 + k}{4^2} + \frac{3 + 2k}{4^4} + \frac{3 + 4k}{4^6} + \dotsb = 8.

omgitsrne Jan 22, 2024

0

62

0

+400

Exponents

Compute the unique positive integer $n$ such that
2 \cdot 2^2 + 3 \cdot 2^3 + 4 \cdot 2^4 + \dots + n \cdot 2^n = 32.

omgitsrne Jan 22, 2024

Jan 21, 2024

0

6

0

+921

Rate question

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?

booboo44 Jan 21, 2024

0

67

0

+921

Algebra

All members of our painting team paint at the same rate. If $45$ members can paint a specific wall in $60$ minutes, then how long would it take $12$ members to paint the same wall, in minutes?

booboo44 Jan 21, 2024

0

40

0

+921

help with rates

All members of our painting team paint at the same rate. If $40$ members can paint a $100$ square foot wall in $50$ minutes, then how long would it take the $40$ members to paint a $480$ square foot wall, in minutes?

booboo44 Jan 21, 2024

0

75

0

+921

help algebra

All members of our painting team paint at the same rate. If $50$ members can paint a $3600$ square foot wall in $20$ minutes, then how long would it take for $25$ members to paint a $4000$ square foot wall, in minutes?

booboo44 Jan 21, 2024

0

76

0

+921

Proportions

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 ..

booboo44 Jan 21, 2024

0

8

0

+921

Rate question

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $3$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $3$ hours read more ..

booboo44 Jan 21, 2024

0

72

0

+1678

Random Digit

Sam writes down the numbers $1,$ $2,$ $\dots,$ $315,$ $316,$ $317,$ $\dots,$ $248,$ $249,$ $250.$
(a) How many digits did Sam write, in total?
(b) Sam chooses one of the digits written down at random. What is the probability read more ..

wiseowl Jan 21, 2024

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