Absolute Value
Absolute Value
means ...
... only how far a number is from zero:
<span>
<span><span>
</span>
<span>
<span>
"6" is 6 away from zero,
and "−6" is also 6 away from zero.
So the absolute value of 6 is 6,
and the absolute value of −6 is also 6 </span>
</span>
</span></span>
More Examples:
<span><span>The absolute value of −9 is 9</span><span>The absolute value of 3 is 3</span><span>The absolute value of 0 is 0</span><span>The absolute value of −156 is 156</span></span>
No Negatives!
So in practice "absolute value" means to remove any negative
sign in front of a number, and to think of all numbers as positive (or
zero).
Absolute Value Symbol
To show that we want the absolute value of something, we put
"|" marks either side (they are called "bars" and are found on the right
side of a keyboard), like these examples:
<span>
<span><span>
|−5| = 5
|7| = 7
</span>
</span></span>
Sometimes absolute value is also written as "abs()", so abs(−1) = 1 is the same as <span>|−1| = 1</span>
The midpoint of a line can be represented by the point that is in the very center of the line. A line segment such as AT also represents half of the line. The symbol of the tilde with the equal sign underneath represents congruence meaning the two segments are the same. Therefore each equation shows the same true statement in a different form
Answer:
see below
Step-by-step explanation:
d = t^2
t =0
d = 0^2 = 0
t =3
d = 3^2 = 9
t =5
d = 5^2 = 25
Answer:
8.20=0.1s+5 <- equation
32 songs
Step-by-step explanation:
I have an expression
![\sigma = \sqrt{p(1-p)/n}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7Bp%281-p%29%2Fn%7D)
floating around in my head; let's see if it makes sense.
The variance of binary valued random variable b that comes up 1 with probability p (so has mean p) is
![E( (b-p)^2 ) = (-p)^2(1-p) + (1-p)^2p = p(1-p)](https://tex.z-dn.net/?f=E%28%20%28b-p%29%5E2%20%29%20%3D%20%20%28-p%29%5E2%281-p%29%20%2B%20%281-p%29%5E2p%20%3D%20p%281-p%29)
That's for an individual sample. For the observed average we divide by n, and for the standard deviation we take the square root:
![\sigma = \sqrt{p(1-p)/n}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7Bp%281-p%29%2Fn%7D)
Plugging in the numbers,
![\sigma = \sqrt{.24(1-.24)/490} = 0.019 = 1.9\%](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B.24%281-.24%29%2F490%7D%20%3D%200.019%20%3D%201.9%5C%25)
One standard deviation of the average is almost 2% so a 27% outcome was 3/1.9 = 1.6 standard deviations from the mean, corresponding to a two sided probability of a bit bigger than 10% of happening by chance.
So this is borderline suspect; most surveys will include a two sigma margin of error, say plus or minus 4 percent here, and the results were within those bounds.