Answer:
2/8 and the simplified version is 1/4 
Step-by-step explanation:
 
        
                    
             
        
        
        
Just take both sides multiply by 2 then divide 3
        
             
        
        
        
Well plug 0 in for x and solve for y and that is the vertex of your expression
        
             
        
        
        
Answer:
36.88% probability that her pulse rate is between 69 beats per minute and 81 beats per minute.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean  and standard deviation
 and standard deviation  , the zscore of a measure X is given by:
, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:

Find the probability that her pulse rate is between 69 beats per minute and 81 beats per minute.
This is the pvalue of Z when X = 81 subtracted by the pvalue of Z when X = 69.
X = 81



 has a pvalue of 0.6844
 has a pvalue of 0.6844
X = 69



 has a pvalue of 0.3156
 has a pvalue of 0.3156
0.6844 - 0.3156 = 0.3688
36.88% probability that her pulse rate is between 69 beats per minute and 81 beats per minute.
 
        
                    
             
        
        
        
Answer:
a) SPAZ is equilateral.
b) Diagonals SA and PZ are perpendicular to each other. 
c) Diagonals SA and PZ bisect each other.
Step-by-step explanation:
At first we form the triangle with the help of a graphing tool and whose result is attached below. It seems to be a paralellogram.
a) If figure is equilateral, then SP = PA = AZ = ZS:
![SP = \sqrt{[4-(-4)]^{2}+[(-2)-(-4)]^{2}}](https://tex.z-dn.net/?f=SP%20%3D%20%5Csqrt%7B%5B4-%28-4%29%5D%5E%7B2%7D%2B%5B%28-2%29-%28-4%29%5D%5E%7B2%7D%7D)

![PA = \sqrt{(6-4)^{2}+[6-(-2)]^{2}}](https://tex.z-dn.net/?f=PA%20%3D%20%5Csqrt%7B%286-4%29%5E%7B2%7D%2B%5B6-%28-2%29%5D%5E%7B2%7D%7D)



![ZS = \sqrt{[-4-(-2)]^{2}+(-4-4)^{2}}](https://tex.z-dn.net/?f=ZS%20%3D%20%5Csqrt%7B%5B-4-%28-2%29%5D%5E%7B2%7D%2B%28-4-4%29%5E%7B2%7D%7D)

Therefore, SPAZ is equilateral.
b) We use the slope formula to determine the inclination of diagonals SA and PZ:




Since  , diagonals SA and PZ are perpendicular to each other.
, diagonals SA and PZ are perpendicular to each other. 
c) The diagonals bisect each other if and only if both have the same midpoint. Now we proceed to determine the midpoints of each diagonal:








Then, the diagonals SA and PZ bisect each other.