Let $m$ be the number of integers $n$, $1 \le n \le 2005$, such that the polynomial $x^{2n} + 1 + (x + 1)^{2n}$ is divisible by $x^2 + x + 1$. find the remainder when $m$ is divided by 1000.

Write a polynomial that fits the description: a third-degree polynomial with leading coefficient -4

Which of the following is a function? a.) {(-2, -4/5), (-1,-,,-1)} b.) {(-2,,1/,3/,1)} c.) {(-22)} d.) {(-21)}

Christine wong has asked dave and mike to her move into a new apartment on sunday morning. she has asked them both, in case one of them does not show up. from past experience, christine knows that there is a 40% chance that dave will not show up and a 30% chance that mik a. what is the probability that both dave and mike will show up? (round your answer to 2 decimal places.) b. what is the probability that at least one of them will show up? c. what is the probability that neither dave nor mike will show up? (round your answer to 2 decimal places.)e will not show up. dave and mike do not know each other and their decisions can be assumed to be independent.