The co-ordinate of point B is (4, 1)
<em><u>Solution:</u></em>
Given the coordinate of one endpoint of AB and it’s midpoint M , A(0, 9) M(2, 5)
<em><u>To find: co-ordinate of endpoint B</u></em>
The midpoint m(x, y) of points
is given as:
![m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)](https://tex.z-dn.net/?f=m%28x%2C%20y%29%3D%5Cleft%28%5Cfrac%7Bx_%7B1%7D%2Bx_%7B2%7D%7D%7B2%7D%2C%20%5Cfrac%7By_%7B1%7D%2By_%7B2%7D%7D%7B2%7D%5Cright%29)
Here in this sum,
![m(x, y) = (2, 5)\\\\A(x_1, y_1) = (0, 9)\\\\B(x_2, y_2) = ?](https://tex.z-dn.net/?f=m%28x%2C%20y%29%20%3D%20%282%2C%205%29%5C%5C%5C%5CA%28x_1%2C%20y_1%29%20%3D%20%280%2C%209%29%5C%5C%5C%5CB%28x_2%2C%20y_2%29%20%3D%20%3F)
Substituting in above formula, we get
![\begin{aligned}&(2,5)=\left(\frac{0+x_{2}}{2}, \frac{9+y_{2}}{2}\right)\\\\&(2,5)=\left(\frac{x_{2}}{2}, \frac{9+y_{2}}{2}\right)\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%26%282%2C5%29%3D%5Cleft%28%5Cfrac%7B0%2Bx_%7B2%7D%7D%7B2%7D%2C%20%5Cfrac%7B9%2By_%7B2%7D%7D%7B2%7D%5Cright%29%5C%5C%5C%5C%26%282%2C5%29%3D%5Cleft%28%5Cfrac%7Bx_%7B2%7D%7D%7B2%7D%2C%20%5Cfrac%7B9%2By_%7B2%7D%7D%7B2%7D%5Cright%29%5Cend%7Baligned%7D)
Compare the L.H.S and R.H.S
![2 = \frac{x_2}{2} \text{ and } 5 = \frac{9+y_2}{2}\\\\x_2 = 2 \times 2 \text{ and } 10 = 9 + y_2\\\\x_2 = 4 \text{ and } y_2 = 1](https://tex.z-dn.net/?f=2%20%3D%20%5Cfrac%7Bx_2%7D%7B2%7D%20%20%5Ctext%7B%20and%20%7D%205%20%3D%20%5Cfrac%7B9%2By_2%7D%7B2%7D%5C%5C%5C%5Cx_2%20%3D%202%20%5Ctimes%202%20%5Ctext%7B%20and%20%7D%2010%20%3D%209%20%2B%20y_2%5C%5C%5C%5Cx_2%20%3D%204%20%5Ctext%7B%20and%20%7D%20y_2%20%3D%201)
Thus the co-ordinate of point B is (4, 1)
Ratio 8:2 doubles would be 16:4
hope this helps
The standardized z-score is calculated as (actual score - mean)/(standard deviation).
A. Idonna's z-score would be (670 - 514)/118 = 1.322
Jonathan's z-score would be (26 - 20.9)/5.3 = 0.962
B. This implies that Idonna's score is higher, since it is more standard deviations above the mean.
Answer:
$78.57
Step-by-step explanation:
To find how much money to spend, divide 550 by the number of days, 7.
550/7 = $78.57
Paola should spend $78.57.