 ## Mathmatitions,what would be the odds?

One ticket purchased in the lottery at 171,000,000 to one verses 227 tickets purchased

You don’t need to be a mathematician to take out a calculator and divide 171,000,000 by 227. :

1 out of 753,304 is correct. (Approximately.)

By the way, restated as ODDS you would say, „753,303 to 1 against you winning“, so the first person was, of course, right. ## Periodic and Even-Odd Properties?

If f(x) = sin(x) and f(a) = 1/4, find the exact value of each question below.

(a) f(-a)

(b) f(a) + f(a + 2pi) + f(a – 2pi)

A) For this question, what you must realise is that sine is an odd function. Such functions have the property that f(-x) = -f(x) for all x. Or you could alternatively think of it as being the property that means that when you rotate the graph of the function π radians or 180 degrees around the origin, the graph is in fact identical. Take a look at the graph or plug some numbers into a calculator if you need convincing.

Now that we know that sine is an odd function, then it has the property of f(-x) = -f(x), so, f(-a) is the same as -f(a), and we know that f(a) is 1/4, so f(-a) must be -1/4.

B) For this one, we need to know that sine is a cyclic function. If we look at the graph of y = sinx, we notice that it repeats itself every 2π, so that means that for any real a:
sin(a) = sin(a + 2π) = sin(a + 4π) etc. And equally:
sin(a) = sin(a – 2π) = sin(a – 4π)

So, now we know that f(a + 2π) = 1/4, and so does f(a – 2π), and so does f(a). So we get:
f(a) + f(a + 2π) + f(a – 2π) = 1/4 + 1/4 + 1/4
= 3/4 ## how 598^19 is an odd number?

It was a question asked by someone..

and, most people got „1“ as the last digit for the answer.

but i never figured out, how even that’s possible?
umm, is there any reason, why three people come up with same answer?
thanks, yea.. i almost missed that thing!!!

It’s not an odd number.

The last digit will continue to go in a 4, 2, 6, 8, 4 pattern.

Maybe they tried to do it on a calculator. The number is far too large to be read on a calculator without scientific notation, thus some of the numbers are cut off.

Edit: it is your mistake here. Their question was 19^598, which is not the same as 598^19 😉 ## how do you find the square root of an odd number?

Odd numbers can have perfect square roots — like 9, 25, 49, 81, 121 — in fact, the square of an odd number is always an odd number. So, finding the square root of an odd number is no different from finding it for an even number. If your calculator has the square root function, use it. But if you want to calculate by hand, here’s the brute force method explained:
http://www.personal.psu.edu/faculty/j/x/jxt18/Math4_WEB/Math4%20Math%20Assignments/Square%20Root.htm ## is it worth getting premium bonds…….?

what does the prizes range from?
have you ever won?what ? thx