- How much zeros has the number $1000!$ at the end?
yes it depends on $2$ and $5$ Note that there are plenty of even numbers Also note that $25\times 4 = 100$ which gives two zeros Also note that there $125\times 8 = 1000$ gives three zeroes and $5^4 \times 2^4 = 10^4$ Each power of $5$ add one extra zero So, count the multiple of $5$ and it's power less than $1000$
- What does it mean when something says (in thousands)
I'm doing a research report, and I need to determine a companies assets So I found their annual report online, and for the assets, it says (in thousands) One of the rows is: Net sales $ 26,234
- What is the number of triples (a, b, c) of positive integers such that . . .
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- 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 same as $4+2+4+1$ These count as one arrangement, not two separate ones
- Find the number of times - Mathematics Stack Exchange
From $0$ to $999$ there are $1000$ numbers and they have $10\times 1+90\times 2+900\times 3=2890$ digits $190$ are zeros and the other $2700$ are divided equally between the other digits, so there are $300$ fives as $300$ nines etc
- geometry - Calculating size of an object based on distance . . .
Thanks to the intercept theorem this is indeed a simple ratio: $$\frac{x}{3\,\text{feet}}=\frac{10\,\text{feet}}{100\,\text{feet}} \qquad\implies\qquad x=0 3\,\text
- 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?
- Determine the number of odd binomial coefficients in the expansion of
Determine the number of odd binomial coefficients in the expansion of $(x+y)^{1000}$ Hint: The number of odd coefficients in any finite binomial expansion is a power of $2$ Is there a way to prove this without using something like Lucas's theorem or any other non-trivial result?
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