crimefightingvigiI

6 Questions
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Counting

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row?

crimefightingvigiI vor 2 Stunden

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Counting

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

crimefightingvigiI vor 2 Stunden

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Counting

Each square below is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the squares?

crimefightingvigiI vor 2 Stunden

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Algebra

Let
f(x) = \sqrt[3]{x - \sqrt[3]{x}}.
Find the largest three-digit value of $x$ such that $f(x)$ is an integer.

crimefightingvigiI 19.11.2024, 04:58

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Algebra

Evaluate a^3 - \dfrac{1}{a^3} if a - \dfrac{1}{a} = 0.

crimefightingvigiI 19.11.2024, 04:58

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Algebra

Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be a sequence. If
a_n = a_{n - 1} + a_{n - 2}
for all $n \ge 3,$ and $a_{11} = 1$ and $a_{10} = 4,$ then find $a_6.$

crimefightingvigiI 19.11.2024, 04:56