Answer:
P (−11, 13), Q (−17, −19), R (23, 27)
Step-by-step explanation:
we know that
The reflection of a figure across the x-axis has the following rule
(x,y) -----> (x,-y)
so
P(-11,-13) -----> P(-11,13)
Q(-17,19) -----> Q(-17,-19)
R(23,-27) ----> R(23,27)
Answer:
(A) P (D > 0) = 99.38%
(B) P (D > 15) = 10.56%
Step-by-step explanation:
The random variable D = difference, is defined as the difference between the reading test scores after and before the program.
The random variable <em>D </em>follows a normal distribution with mean,
and standard deviation,
.
(A)
Compute the probability that the children showed any improvement, i.e.
P (D > 0):
![P(D>0)=P(\frac{D-\mu_{D}}{\sigma_{D}} >\frac{0-10}{4} )=P(Z>-2.5)=P(Z](https://tex.z-dn.net/?f=P%28D%3E0%29%3DP%28%5Cfrac%7BD-%5Cmu_%7BD%7D%7D%7B%5Csigma_%7BD%7D%7D%20%3E%5Cfrac%7B0-10%7D%7B4%7D%20%29%3DP%28Z%3E-2.5%29%3DP%28Z%3C2.5%29)
Use the standard normal random variable to determine the probability.
![P(D>0)=P(Z](https://tex.z-dn.net/?f=P%28D%3E0%29%3DP%28Z%3C2.5%29%3D0.9938)
The percentage of children showed any improvement is:
0.9938 × 100 = 99.38%
Thus, 99.38% of children showed improvement.
(B)
Compute the probability that the children improved by more than 15 points, i.e. P (D > 15):
![P(D>15)=P(\frac{D-\mu_{D}}{\sigma_{D}} >\frac{15-10}{4} )=P(Z>1.25)=1-P(Z](https://tex.z-dn.net/?f=P%28D%3E15%29%3DP%28%5Cfrac%7BD-%5Cmu_%7BD%7D%7D%7B%5Csigma_%7BD%7D%7D%20%3E%5Cfrac%7B15-10%7D%7B4%7D%20%29%3DP%28Z%3E1.25%29%3D1-P%28Z%3C1.25%29)
Use the standard normal random variable to determine the probability.
![P(D>0)=1-P(Z](https://tex.z-dn.net/?f=P%28D%3E0%29%3D1-P%28Z%3C1.25%29%3D1-0.8944%3D0.1056)
The percentage of children improved by more than 15 points is:
0.1056 × 100 = 10.56%
Thus, 10.56% of children showed improvement by more than 15 points.
Answer:
Ans 2
Step by step explanation :
2 X 1 = 2
Answer:
Step-by-step explanation:
Given the coordinates E(13,8) and K(7,2), to get the length of the segment EK, we will use the formula for calculating the distance between two points expressed as:
D = √(x2-x1)²+(y2-y1)²
Given
x1 = 13, y1 = 8, x2 = 7, y2 = 2
EK =√(7-13)²+(2-8)²
EK = √(-6)²+(-6)²
EK = √36+36
EK = √72
EK = √36×√2
EK = 6√2
EK = 8.485
EK ≈8.5 (to the nearest tenth)
Hence the length of segment EK is 8.5
For the midpoint, the expression will be used
M(X,Y) = {(x1+x2)/2, (y1+y2)/2}
M(X,Y) = (13+7/2, 8+2/2)
M(X,Y) = (20/2, 10/2)
M(X,Y) = (10,5)
Hence the coordinates of its midpoint is (10,5)
Answer:
56
Step-by-step explanation: