Answer: C
ABCD may or may not be a parellolgram. Line BD bisects line AC, however we cant figure out if line AC bisects line BD.
Answer:
Slope = 2 Y-Intercept = (0, 3)
Step-by-step explanation:
Slope :
which is
from two points: point1 (x1 , y1) and point2 (x2, y2).
For the purpose of getting the slope I will be using point (0, 3) as point 1
and point (-3, -3) as point 2.
If you plug in 0 as x1, 3 as y2, -3 for x2, and -3 for y2:
=
= 2
Y-Intercept: The y intercept is the point where the line is touching the y axis. Which in this graph, there is only point (0,3).
Answer:
Does this sample provide convincing evidence that the machine is working properly?
Yes.
Step-by-step explanation:
<u>Normal distribution test:</u>
![$z=\frac{x- \mu }{ \frac{\sigma}{\sqrt{n}} }=\frac{ (x-\mu)\sqrt{n}}{\sigma} $](https://tex.z-dn.net/?f=%24z%3D%5Cfrac%7Bx-%20%5Cmu%20%7D%7B%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%20%7D%3D%5Cfrac%7B%20%28x-%5Cmu%29%5Csqrt%7Bn%7D%7D%7B%5Csigma%7D%20%20%24)
Where,
![x: \text{ sample mean}](https://tex.z-dn.net/?f=x%3A%20%5Ctext%7B%20sample%20mean%7D)
![\sigma: \text{ standard deviation}](https://tex.z-dn.net/?f=%5Csigma%3A%20%5Ctext%7B%20standard%20deviation%7D)
![n: \text{ sample size determination}](https://tex.z-dn.net/?f=n%3A%20%5Ctext%7B%20sample%20size%20determination%7D)
![\mu: \text{ hypothesized size of the screw}](https://tex.z-dn.net/?f=%5Cmu%3A%20%5Ctext%7B%20hypothesized%20size%20of%20the%20screw%7D)
![$z=\frac{(1.476-1.5)\sqrt{200} }{0.203 } $](https://tex.z-dn.net/?f=%24z%3D%5Cfrac%7B%281.476-1.5%29%5Csqrt%7B200%7D%20%7D%7B0.203%20%7D%20%24)
![$z=\frac{(-0.024)10\sqrt{2} }{0.203 } $](https://tex.z-dn.net/?f=%24z%3D%5Cfrac%7B%28-0.024%2910%5Csqrt%7B2%7D%20%7D%7B0.203%20%7D%20%24)
![z \approx -1.672](https://tex.z-dn.net/?f=z%20%5Capprox%20-1.672)
Once the significance level was not given, It is usually taken an assumption of a 5% significance level.
Taking the significance level of 5%, which means a confidence level of 95%, we have a z-value of ![\pm 1.96](https://tex.z-dn.net/?f=%5Cpm%201.96)
Therefore, we <u>fail to reject the null</u>. It means that the hypothesis test is not statistically significant: the average length is not different from 1.5!
Answer:
![\sqrt{68}](https://tex.z-dn.net/?f=%5Csqrt%7B68%7D)
Step-by-step explanation:
(7 , -1) = (x1 , y1)
(9 , -9) = (x2 , y2)
distance formula = ![\sqrt{(x2 - x1)^2 + (y2 - y1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x2%20-%20x1%29%5E2%20%2B%20%28y2%20-%20y1%29%5E2%7D)
=![\sqrt{(9 - 7)^2 + (-9 - (-1))^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%289%20-%207%29%5E2%20%2B%20%28-9%20-%20%28-1%29%29%5E2%7D)
=![\sqrt{2^2 + (-9 + 1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B2%5E2%20%2B%20%28-9%20%2B%201%29%5E2%7D)
=![\sqrt{4 + (-8)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B4%20%2B%20%28-8%29%5E2%7D)
=![\sqrt{4 + 64}](https://tex.z-dn.net/?f=%5Csqrt%7B4%20%2B%2064%7D)
=![\sqrt{68}](https://tex.z-dn.net/?f=%5Csqrt%7B68%7D)