According to the college board, sat critical reading scores from the 2014 school year for high school students in the united states were normally distributed with a mean of 497 and a standard deviation of 115. use a standard normal table such as this one to determine the probability that a randomly chosen high school student who took the sat in 2014 will have a critical reading sat score between 450 and 750 points give your answer as a percentage rounded to one decimal placep=%

64.5 %

Step-by-step explanation:

Let's start defining the random variable X.

X : '' SAT critical reading scores from the 2014 school year for high school students in the United States ''

We know that X ~ N (μ,σ)

Where μ is the mean and σ is the standard deviation.

⇒ X ~ N (497,115)

If we want to calculate probabilities related to X we need to standardized the random variable. We do this by subtracting the mean to X and then dividing by the standard deviation. This new random variable will be ''Z'' and Z ~ N (0,1)

We can find the probabilies of ''Z'' in any standard normal table.

The cumulative distribution of ''Z'' is the function Φ where  :

Φ(a)

Now, we need to calculate the following probability :

If we standardized this :

We know that ≅ Z ⇒

⇒

Φ(2.2) - Φ(-0.41) =

⇒ 64.52% ≅ 64.5%

We find that the probability (given as a percentage) is 64.5%

start with a line segment pq that we will copy. mark a point r that will be one endpoint of the new line segment. set the compasses' point on the point p of the line segment to be copied. adjust the compasses' width to the point q. the compasses' width is now equal to the length of the line segment pq.

step-by-step explanation:

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'.