2. Estimating π. Suppose we had forgotten the formula for computing the area of a circle. All is not lost. We can easily use the computer to approximate the circle’s area by simulation. For convenience, we want to determine the area of the unit circle with radius 1. We name this unknown constant Pi (or π). We know that the area covered by a square with the corner points (−1, 1), (1, 1), (1, −1) and (−1, −1) equals 4, as the length of each side is 2. This square completely contains the unit circle. If we had a random point somewhere in the square, we could calculate the probability that the point is also inside the unit circle. A random point Z is determined by two coordinates, say X and Y , which have independent uniform distributions on the interval [−1, 1]. The probability of Z being inside the circle is given by the ratio of the circle’s area and the square’s area or, more mathematically, letting P = probability: P(Z is inside the circle) = (area of the circle)/(area of the rectangle) = Pi/4. Knowing this, we can estimate (the unknown) Pi

answer: 21$

step-by-step explanation:

$42 / $14 = 3   (ratio 3: 1)

$7 x 3 = $21

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

14 ft 7 inches

step-by-step explanation:

since each model inch corresponds to 25 real inches, 7 model inches will correspond to

7×25" = 175"

at 12" per foot, that is 14 feet, 7 inches.