Answer: The system has no solutions because it is inconsistent.
Step-by-step explanation:
This system is an " inconsistent system", this is because each equation:
y = 2 and y = -3
give us a different value for the same variable y (each variable can have only one value at the same time)
So this system is inconsistent, which means that the system has no solutions.
Complete Question
A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 12 % chose chocolate pie, and the margin of error was given as plus or minus 5 percentage points.What values do
, n, E, and p represent? If the confidence level is 90%, what is the value of
?
Answer:
a
is the sample proportion
is the sample size is ![n = 500](https://tex.z-dn.net/?f=n%20%20%3D%20%20500)
is the margin of error is ![E = 0.05](https://tex.z-dn.net/?f=E%20%20%3D%20%200.05)
represents the proportion of those that did not chose chocolate pie i.e ![\r q = 1- \r p](https://tex.z-dn.net/?f=%5Cr%20%20q%20%20%3D%20%201-%20%20%5Cr%20p)
b
![\alpha = 10\%](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%2010%5C%25)
Step-by-step explanation:
Here
is the sample proportion
is the sample size is ![n = 500](https://tex.z-dn.net/?f=n%20%20%3D%20%20500)
represents the proportion of those that did not chose chocolate pie i.e
![\r q = 1- \r p](https://tex.z-dn.net/?f=%5Cr%20%20q%20%20%3D%20%201-%20%20%5Cr%20p)
![\r q = 1- 0.12](https://tex.z-dn.net/?f=%5Cr%20%20q%20%20%3D%20%201-%20%200.12)
![\r q = 0.88](https://tex.z-dn.net/?f=%5Cr%20%20q%20%20%3D%200.88)
is the margin of error is ![E = 0.05](https://tex.z-dn.net/?f=E%20%20%3D%20%200.05)
Generally
is the level of significance and it value is mathematically evaluated as
![\alpha = ( 100 - C )\%](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%28%20100%20-%20%20C%20%20%29%5C%25)
Where
is the confidence level which is given in this question as ![C = 90 \%](https://tex.z-dn.net/?f=C%20%3D%20%2090%20%20%5C%25)
So
![\alpha = ( 100 - 90 )\%](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%28%20100%20-%20%2090%20%20%29%5C%25)
![\alpha = 10\%](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%2010%5C%25)
(a)______________________
| 1 | 2 | 3 | 4 |
-------------------------------------------
Health | 7 | 14 | 21 | 28 |
Fire | 12 | 24 | 36 | 48 |
------------------------------------------
(b) In 84 days, both inspectors will visit on the same day, because the LCM (least common multiple) of 7 and 12 is 84
Answer:
The length of segment QM' = 6
Step-by-step explanation:
Given:
Q is the center of dilation
Pre-image (original image) = segment LM
New image = segment L'M'
The length of LQ = 4
The length of QM = 3
The length of LL' = 4
The original image was dilated with scale factor = 2
QM' = ?
To determine segment QM', first we would draw the diagram obtained from the given information.
Find attached the diagram
When a figure is dilated, we would have similar shape in thus cars similar triangles.
Segment L'M' = scale factor × length of LM
Let LM = x
L'M' = 2x
Using similar triangles theorem, ratio of their corresponding sides are equal.
QM/LM = QM'/L'M'
3/x = QM'/2x
6x = QM' × x
Q'M' = 6
The length of segment QM' = 6
Answer:
Step-by-step explanation:
The unit rate is pages per minute, so divide the pages by the minutes: (5/8)/(2/3) = (5/8)·(3/2) = 15/16 pages per minute