First you would change the time from minutes to seconds by multiplying 4 by 60 because there are 60 seconds in a minute. After finding that (4*60=240) you would subtract the remaining time (12 seconds) from the total time (240 seconds). You would subtract the remaining time from the total time (228 seconds). Using that you would use the ratio time used/total (228/240). Divide that out and multiply by 100 to get 95%. I hope that helps!
Well, a distance-preserving transformation is called a rigid motion, and the name suggests that it <em>moves the points of the plane around in a rigid fashion.</em>
A transformation is distance-preserving if the distance between the images of any two points and the distance between the two original points are equal.
If that's confusing, I get it; basically if you transform something, the points from the transformation are image points. Take the distance from a pair of image points, and take the distance from a pair of original points, and they should be the same for a <em>rigid </em>motion.
I keep emphasizing this b/c not all transformations preserve distance; a dilation can grow or shrink things. But if you didn't go over dilations, don't say nothin XD
For a standard normally distributed random variable <em>Z</em> (with mean 0 and standard deviation 1), we get a probability of 0.0625 for a <em>z</em>-score of <em>Z</em> ≈ 1.53, since
P(<em>Z</em> ≥ 1.53) ≈ 0.9375
You can transform any normally distributed variable <em>Y</em> to <em>Z</em> using the relation
<em>Z</em> = (<em>Y</em> - <em>µ</em>) / <em>σ</em>
where <em>µ</em> and <em>σ</em> are the mean and standard deviation of <em>Y</em>, respectively.
So if <em>s</em> is the standard deviation of <em>X</em>, then
(250 - 234) / <em>s</em> ≈ 1.53
Solve for <em>s</em> :
16/<em>s</em> ≈ 1.53
<em>s</em> ≈ 10.43
