Answer:
The p value would be given by:
For this case since th p value is lower than the significance level of0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly different from 46.7 MPG
Step-by-step explanation:
Information given
represent the mean
represent the population standard deviation
sample size
represent the value to verify
represent the significance level for the hypothesis test.
z would represent the statistic
represent the p value
Hypothesis to test
We want to test if the true mean for this case is 46.7, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation the statistic is given by:
(1)
Replacing we got:
The p value would be given by:
For this case since th p value is lower than the significance level of0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly different from 46.7 MPG
It is 30-88 degrees I think
Answer:
easy
Step-by-step explanation:
The radius of the circle is 3 cm.
<u>Step-by-step explanation:</u>
Refer the attached diagram, the circle with centre O. In that given, AB is tangent given as 4 cm and distance of point from the circle, OA = 5 cm
As AB is tangent, OB (radius of circle) is perpendicular to AB (tangent at any point of circle). Therefore the angle of OBA is 90 degree.
Also, triangle OAB is a right angled triangle (refer attached diagram). By using Pythagoras theorem in right angled triangle,
![(\text {Hypotenuse})^{2}=(\text {Height})^{2}+(\text {Base})^{2}](https://tex.z-dn.net/?f=%28%5Ctext%20%7BHypotenuse%7D%29%5E%7B2%7D%3D%28%5Ctext%20%7BHeight%7D%29%5E%7B2%7D%2B%28%5Ctext%20%7BBase%7D%29%5E%7B2%7D)
![(O A)^{2}=(O B)^{2}+(A B)^{2}](https://tex.z-dn.net/?f=%28O%20A%29%5E%7B2%7D%3D%28O%20B%29%5E%7B2%7D%2B%28A%20B%29%5E%7B2%7D)
Substitute the given values in the above expression, we get
![(5)^{2}=(O B)^{2}+(4)^{2}](https://tex.z-dn.net/?f=%285%29%5E%7B2%7D%3D%28O%20B%29%5E%7B2%7D%2B%284%29%5E%7B2%7D)
![(O B)^{2}=25-16=9](https://tex.z-dn.net/?f=%28O%20B%29%5E%7B2%7D%3D25-16%3D9)
Taking square root on both side, we get
Radius of the circle, OB = 3 cm