9514 1404 393
Answer:
B) False
Step-by-step explanation:
Triangles are similar when their angles are the same measures. Because the angles sum to 180°, we only need to show that 2 angles of one triangle are equal to 2 angles of the other triangle.
All three of the angles of the first triangle are given: 20°, 40°, 120°.
One of the angles of the second triangle matches: 40°; but the other angle (80°) doesn't match either of 20° or 120°.
The angles aren't the same, so the triangles are not similar.
__
If we want to go to the trouble, we can figure the third angle of the second triangle. It is 180° -40° -80° = 60°.
Then the angles in the two triangles, listed smallest to largest, are ...
20°, 40°, 120°
40°, 60°, 80°
It is clear the angles of these triangles are not the same.
But what’s the question can you tell me?
Answer:
75 is the l.c.m of 15 and 25
explanation:
<u>multiples</u>:
15 - 15, 30, 45, 60, 75
25 - 25, 50, 75
Therefore, 75 is the l.c.m of 15 and 25 which is divisible by both numbers.
Answer:
A
![P(X = 8 ) = 0.0037](https://tex.z-dn.net/?f=P%28X%20%3D%20%208%20%29%20%3D%20%200.0037)
B
![P(X < 5) = 0.805](https://tex.z-dn.net/?f=P%28X%20%3C%205%29%20%3D%20%200.805)
C
I will not be surprised because the probability that fewer than half covered their mouth when sneezing is less than 0.5
Step-by-step explanation:
From the question we are told that
The probability a randomly selected individual will not cover his or her mouth when sneezing is ![p = 0.267](https://tex.z-dn.net/?f=p%20%3D%20%200.267)
The probability a randomly selected individual will cover his or her mouth when sneezing is
![q = 1 -0.267](https://tex.z-dn.net/?f=q%20%3D%201%20-0.267)
![q = 0.733](https://tex.z-dn.net/?f=q%20%3D%20%200.733)
Generally the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when sneezing is mathematically represented as
![P(X = 8 ) = \left 12 } \atop {}} \right. C_8 * p^8 * q^{12-8}](https://tex.z-dn.net/?f=P%28X%20%3D%20%208%20%29%20%3D%20%20%5Cleft%2012%20%7D%20%5Catop%20%7B%7D%7D%20%5Cright.%20C_8%20%2A%20%20p%5E8%20%2A%20%20q%5E%7B12-8%7D)
![P(X = 8 ) = 495 * (0.267)^8 * (0.733)^{12-8}](https://tex.z-dn.net/?f=P%28X%20%3D%20%208%20%29%20%3D%20495%20%2A%20%20%280.267%29%5E8%20%2A%20%20%280.733%29%5E%7B12-8%7D)
![P(X = 8 ) = 0.0037](https://tex.z-dn.net/?f=P%28X%20%3D%20%208%20%29%20%3D%20%200.0037)
Generally the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when sneezing is mathematically represented as
![P(X < 5 ) = P[ P(X = 0) + \cdots + P(X = 4)]](https://tex.z-dn.net/?f=P%28X%20%3C%20%205%20%29%20%3D%20%20P%5B%20P%28X%20%3D%200%29%20%2B%20%5Ccdots%20%2B%20P%28X%20%3D%20%204%29%5D)
=> ![P(X < 5) = \left 12 } \atop {}} \right. C_0 * (0.267)^0 * (0.733)^{(12- 0) }+\cdots + \left 12 } \atop {}} \right. C_4 * (0.267)^0 * (0.733)^{(12- 4) }](https://tex.z-dn.net/?f=P%28X%20%3C%20%205%29%20%3D%20%5Cleft%2012%20%7D%20%5Catop%20%7B%7D%7D%20%5Cright.%20C_0%20%2A%20%20%280.267%29%5E0%20%2A%20%280.733%29%5E%7B%2812-%200%29%20%7D%2B%5Ccdots%20%2B%20%20%5Cleft%2012%20%7D%20%5Catop%20%7B%7D%7D%20%5Cright.%20C_4%20%2A%20%20%280.267%29%5E0%20%2A%20%280.733%29%5E%7B%2812-%204%29%20%7D)
=> ![P(X < 5) = 0.805](https://tex.z-dn.net/?f=P%28X%20%3C%205%29%20%3D%20%200.805)
Give that half of 12 is 6 then
The probability that fewer than half covered their mouth when sneezing is mathematically represented as
![P(X > 6) = 1 - P( X \le 6 )](https://tex.z-dn.net/?f=P%28X%20%3E%206%29%20%3D%20%201%20-%20%20P%28%20X%20%5Cle%206%20%29)
=> ![P(X > 6) = 1 - [P(X = 0 ) +\cdots+P(X = 6) ]](https://tex.z-dn.net/?f=P%28X%20%3E%206%29%20%20%3D%20%201%20-%20%20%5BP%28X%20%3D%200%20%29%20%2B%5Ccdots%2BP%28X%20%3D%206%29%20%5D)
=> ![P(X > 6) = 1 - [\left 12 } \atop {}} \right. C_0 *(0.267)^0 * (0.733)^{12 - 0 } +\cdots + \left 12 } \atop {}} \right. C_6 * (0.267)^6 * (0.733)^{12-6}]](https://tex.z-dn.net/?f=P%28X%20%3E%206%29%20%3D%201%20-%20%20%5B%5Cleft%2012%20%7D%20%5Catop%20%7B%7D%7D%20%5Cright.%20C_0%20%2A%280.267%29%5E0%20%2A%20%20%280.733%29%5E%7B12%20-%200%20%7D%20%2B%5Ccdots%20%2B%20%5Cleft%2012%20%7D%20%5Catop%20%7B%7D%7D%20%5Cright.%20C_6%20%2A%20%280.267%29%5E6%20%2A%20%20%280.733%29%5E%7B12-6%7D%5D)
=> ![P(X > 6) = 0.0206](https://tex.z-dn.net/?f=P%28X%20%3E%206%29%20%20%20%3D%20%200.0206)