Answer:
(22;-3)
Step-by-step explanation:
if to calculate the coordinates of the given midpoint it needed to use:
![x_{midpoint}=\frac{x_{endpoint1}+x_{endpoint2}}{2};](https://tex.z-dn.net/?f=x_%7Bmidpoint%7D%3D%5Cfrac%7Bx_%7Bendpoint1%7D%2Bx_%7Bendpoint2%7D%7D%7B2%7D%3B)
![y_{midpoint}=\frac{y_{endpoint1}+y_{endpoint2}}{2};](https://tex.z-dn.net/?f=y_%7Bmidpoint%7D%3D%5Cfrac%7By_%7Bendpoint1%7D%2By_%7Bendpoint2%7D%7D%7B2%7D%3B)
then to calculate the coordinates of endpoint2, it needed to perform the substitution:
![\frac{-10+x_{endpoint2}}{2}=6,](https://tex.z-dn.net/?f=%5Cfrac%7B-10%2Bx_%7Bendpoint2%7D%7D%7B2%7D%3D6%2C)
![2=\frac{7+y_{endpoint2}}{2},](https://tex.z-dn.net/?f=2%3D%5Cfrac%7B7%2By_%7Bendpoint2%7D%7D%7B2%7D%2C)
finally:
![x_{endpoint2}=22;](https://tex.z-dn.net/?f=x_%7Bendpoint2%7D%3D22%3B)
![y_{endpoint2}=-3.](https://tex.z-dn.net/?f=y_%7Bendpoint2%7D%3D-3.)
Answer:
First, we need to know when the function is increasing, and when is decreasing.
When a function is increasing, it's because to higher <em>x-values </em>belong higher <em>y-values. </em>On the other hand, a function is decreasing when to higher <em>x-values </em>belong lower <em>y-values. </em>The effect in the graph will be a upwards direction of the function when is increasing, and a downwards direction when is decreasing.
So, according to the given graph, we see that between 0 and 4 is increasing, the higher x-values are, higher y-values are. Between 4 and 6 is decreasing, is downwards. Between 6 and 8 is increasing. Between 8 and 10 is decreasing. In finally, between 10 and 14 is neither decreasing or increasing, it remains horizontal.
All these interpretations we can expressed using math language, specifically inequalities:
- 0 < x < 4: increasing.
- 4 < x < 6: decreasing.
- 6 < x < 8: increasing.
- 8 < x < 10: decreasing.
- 10 < x < 14: neither increasing or decreasing.
Solution: We are given:
![\mu=0.33, \sigma =0.7](https://tex.z-dn.net/?f=%5Cmu%3D0.33%2C%20%20%5Csigma%20%3D0.7)
Let
be the weight (oz) of laptop
We have to find ![P(x>32)](https://tex.z-dn.net/?f=P%28x%3E32%29)
To find the this probability, we need to find the z score value.
The z score is given below:
![z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
![=\frac{32-33}{0.7}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B32-33%7D%7B0.7%7D)
![=-1.43](https://tex.z-dn.net/?f=%3D-1.43)
Now, we have to find ![P(z>-1.43)](https://tex.z-dn.net/?f=P%28z%3E-1.43%29)
Using the standard normal table, we have:
![P(z>-1.43)=0.9236](https://tex.z-dn.net/?f=P%28z%3E-1.43%29%3D0.9236)
0.9236 or 92.36% of laptops are overweight
Answer:
8 months
Step-by-step explanation:
Given that:
Amount of money present in the bank account = $2,571.68
Automatic monthly rental payments for car loan = $321.46
Any deposits in the bank account are stopped.
To find:
The number of months taken so that the automatic payments make the value of the account as zero?
Solution:
Let the number of months taken to make the value of the account zero =
months
To find the value of
, we need to divide the total amount initially present in bank account with the monthly rental payment amount.
Therefore, the equation to find the value of
, can be written as:
![m = \dfrac{2571.68}{321.46}](https://tex.z-dn.net/?f=m%20%3D%20%5Cdfrac%7B2571.68%7D%7B321.46%7D)
On solving the above equation, we get the value as following:
months
11+2x=17
Now, lets figure out what x is.
11+2(3)=17
11+6=17