Answer:
y or w
Step-by-step explanation:
Answer: Of course it is possible if you try your hardest and study
Answer:
![c = 14.9cm](https://tex.z-dn.net/?f=c%20%3D%2014.9cm)
Step-by-step explanation:
Given
![b = 10cm](https://tex.z-dn.net/?f=b%20%3D%2010cm)
![B = 12^{\circ}](https://tex.z-dn.net/?f=B%20%3D%2012%5E%7B%5Ccirc%7D)
![A = 150^{\circ}](https://tex.z-dn.net/?f=A%20%3D%20150%5E%7B%5Ccirc%7D)
Required
Determine the length of c
First, we calculate C (the third angle of the triangle).
![C = 180 - A - B](https://tex.z-dn.net/?f=C%20%3D%20180%20-%20A%20-%20B)
![C = 180 - 150 - 12](https://tex.z-dn.net/?f=C%20%3D%20180%20-%20150%20-%2012)
![C = 18^{\circ}](https://tex.z-dn.net/?f=C%20%3D%2018%5E%7B%5Ccirc%7D)
Using Sine's law, we make use of:
![\frac{sin\ B}{b} = \frac{sin C}{c}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%5C%20B%7D%7Bb%7D%20%3D%20%5Cfrac%7Bsin%20C%7D%7Bc%7D)
By substituting values, we have:
![\frac{sin\ 12}{10} = \frac{sin 18}{c}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%5C%2012%7D%7B10%7D%20%3D%20%5Cfrac%7Bsin%2018%7D%7Bc%7D)
Cross multiply
![c* sin\ 12 = 10 * sin\ 18](https://tex.z-dn.net/?f=c%2A%20sin%5C%2012%20%3D%2010%20%2A%20sin%5C%2018)
Make c the subject
![c = \frac{10 * sin\ 18}{sin\ 12}](https://tex.z-dn.net/?f=c%20%3D%20%5Cfrac%7B10%20%2A%20sin%5C%2018%7D%7Bsin%5C%2012%7D)
![c = \frac{10 * 0.3090}{0.2079}](https://tex.z-dn.net/?f=c%20%3D%20%5Cfrac%7B10%20%2A%200.3090%7D%7B0.2079%7D)
approximated
Answer:
a = 0.05
b = 0.028
c =0.014
Step-by-step explanation:
Given that;
inspector A visually inspected 1000 ceramic mugs and found flaws in 36 of them.
Let X represent Inspector A
P(X) = ![\frac{36}{1000}](https://tex.z-dn.net/?f=%5Cfrac%7B36%7D%7B1000%7D)
= 0.036
inspector B visually inspected 1000 ceramic mugs and found flaws in 42 of them.
Let Y represent Inspector B
P(Y) = ![\frac{42}{1000}](https://tex.z-dn.net/?f=%5Cfrac%7B42%7D%7B1000%7D)
= 0.042
A total of 950 mugs were found to be good by both inspectors.
i.e (X∩Y)' = 950
P (X∩Y)' = ![\frac{950}{1000}](https://tex.z-dn.net/?f=%5Cfrac%7B950%7D%7B1000%7D)
= 0.095
We are tasked to find :
a) the probability that a flaw was found in this mug by at least one of the two inspectors [i.e P (X∪Y)]
b) the probability that flaws were found in this mug by both inspectors.
[i.e P ( X∩Y)]
c) the probability that a flaw was found by inspector B but not by inspector A. [i.e P (X) - P ( X∩Y)]
With a);
P (X∪Y) = 1 - P(A∩B)'
P (X∪Y) = 1 - 0.950
P (X∪Y) = 0.05
b)
P(X∩Y) = P(X) + P(Y) - P(X∪Y)
P(X∩Y) = 0.036 + 0.042 + 0.05
P(X∩Y) = 0.028
c)
P (X) - P ( X∩Y) = 0.042 - 0.028
P (X) - P ( X∩Y) = 0.014
Therefore;
the probability that a flaw was found in this mug by at least one of the two inspectors = 0.05
the probability that flaws were found in this mug by both inspectors = 0.028; &
the probability that a flaw was found by inspector B but not by inspector A = 0.014
225, 15^2 (squared) = 225
15 x 15= 225