gnistory

156 Questions
19 Answers

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Algebra

All members of our painting team paint at the same rate. If $15$ members can paint a specific wall in $45$ minutes, then how long would it take $20$ members to paint the same wall, in minutes?

gnistory Oct 21, 2024

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Algebra

A geometric sequence has $400$ terms. The first term is $500$ and the common ratio is $-\frac{1}{20}.$ How many terms of this sequence are greater than $1?$

gnistory Oct 21, 2024

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Counting

Joanna has several beads that she wants to assemble into a bracelet. There are seven beads: five of the beads have the same color, and the other two all have different colors. Using all seven beads, in how many different ways can Joanna assemble read more ..

gnistory Oct 19, 2024

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Counting

Joanna has seven beads that she wants to assemble into a bracelet. Five of the beads have the same color, and the other two all have different colors. In how many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical if read more ..

gnistory Oct 19, 2024

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Counting

Find the number of positive integers that satisfy both the following conditions:
Each digit is a 1, 2, 3, or 4.
The sum of the digits is 11.

gnistory Oct 19, 2024

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Counting

In a series of coin flips, a run is a series of one or more consecutive coin flips that all have the same result. For example, in the sequence
\[TT \textcolor{red}{HHH} TTHHHTH,\]

the red letters form a run of length $3$. (A run read more ..

gnistory Oct 19, 2024

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Algebra

Let $a$ and $b$ be complex numbers. If $a + b = 1$ and $a^2 + b^2 = 2,$ then what is $a^3 + b^3?$

gnistory Oct 15, 2024

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Algebra

What are the coordinates of the points where the graphs of f(x)=x^3 + x^2 - 3x + 5 and g(x) = x^3 + 2x^2 intersect?
Give your answer as a list of points separated by commas, with the points ordered such that their -coordinates read more ..

gnistory Oct 13, 2024

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Algebra

Simplify \dfrac{1}{\sqrt2+sqrt3}+\dfrac{1}{\sqrt2-sqrt3}.

gnistory Oct 13, 2024

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Algebra

Find all ordered pairs x, y of real numbers such that x+y=10 and x^2+y^2=64.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

gnistory Oct 13, 2024

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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 $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $3$ hours read more ..

gnistory Oct 12, 2024

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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 ..

gnistory Oct 12, 2024

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Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $1000$ square foot wall in $10$ minutes, then how long would it take for $5$ members to paint a $1000$ square foot wall, in minutes?

gnistory Oct 12, 2024

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Number Theory

Fill in each blank with a single digit.
\frac{2}{131} = 0. _ _ _ _ _ _ _ _ _ _

gnistory Oct 10, 2024

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Number Theory

Find the smallest positive integer $B$ so that when we express the decimal number $582$ as a base $B$ number, we still get a $2$-digit number.

gnistory Oct 10, 2024

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Number Theory

How many bases $b \ge 2$ are there such that $100_b + 1_b$ is prime?

gnistory Oct 10, 2024