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  1. What does it mean when something says (in thousands)

    Oct 31, 2017 · It means "26 million thousands". Essentially just take all those values and multiply them by 1000 1000. So roughly $26 $ 26 billion in sales.

  2. How much zeros has the number $1000!$ at the end?

    May 13, 2014 · If a number ends with n n zeros than it is divisible by 10n 10 n, that is 2n5n 2 n 5 n. A factorial clearly has more 2 2 s than 5 5 s in its factorization so you only need to count …

  3. Creating arithmetic expression equal to 1000 using exactly eight …

    I would like to find all the expressions that can be created using nothing but arithmetic operators, exactly eight $8$'s, and parentheses. Here are the seven solutions I've found (on the Internet)...

  4. Look at the following infinite sequence: 1, 10, 100, 1000, 10000,

    What is the proof that there are 2 numbers in this sequence that differ by a multiple of 12345678987654321?

  5. There are $1000$ people in a hall. One person had their hand …

    Sep 3, 2020 · There are $1000$ people in a hall. One person had their hand painted. Every minute everyone shake their hand with someone else. How much time is needed to paint all …

  6. elementary number theory - Mathematics Stack Exchange

    Oct 8, 2020 · A bit farther on the hint: If you can find the equivalence classes of a1000 (mod) a 1000 (mod) and a1000 (mod) a 1000 (mod), CRT tells us this is enough to find the class of …

  7. algebra precalculus - Partitions using only powers of two on $1000 ...

    How many ways are there to write $1000$ as a sum of powers of $2,$ ($2^0$ counts), where each power of two can be used a maximum of $3$ times. Furthermore, $1+2+4+4$ is the …

  8. combinatorics - Number of ways to invest $\$20,000$ in units of …

    Feb 24, 2023 · Number of ways to invest $20, 000 $ 20, 000 in units of $1000 $ 1000 if not all the money need be spent Ask Question Asked 2 years, 4 months ago Modified 2 years, 4 months …

  9. If the coefficient of $x^{50}$ in the expansion of …

    Problem : If the coefficient of x50 x 50 in the expansion of (1 + x)1000 + 2x(1 + x)999 + 3x2(1 + x)998 + ⋯ + 1001x1000 (1 + x) 1000 + 2 x (1 + x) 999 + 3 x 2 (1 + x) 998 + + 1001 x 1000 is λ …

  10. Find $A^{1000}$ by using Cayley-Hamilton Theorem

    Find A1000 A 1000 by using the Cayley-Hamilton theorem. I find the characteristic polynomial by P(A) = −A3 + 2A2 = 0 P (A) = A 3 + 2 A 2 = 0 (by Cayley-Hamilton) but I don't see how to find …