Answer:
The square root of 49 is rational
Step-by-step explanation:
If we take the square root of 49, we get 7, which is a rational number.
Answer:
about 28
Step-by-step explanation:
you have to use the sine rule = side you know * ( sin of angle opposing the side you want to know / sin of angle opposing the side you know)
AB = 19* (sin 75/ sin ( 180 -75-64) )
AB = 19 * ( sin 75 / sin 41) ≈ 27.9739...
.04*7115.68=284.6272
$284.62 or $284.63 (depending on how lenient your teacher is with rounding)
Solution:
we have been asked to explain
How can exponential equations with unequal bases be solved?
So Suppose we have an example of exponential equations with unequal bases as
![a^x=b^{x-3}](https://tex.z-dn.net/?f=%20a%5Ex%3Db%5E%7Bx-3%7D%20)
This can be solved by taking logarithm on both the sides we get
![Loga^x=Logb^{x-3}](https://tex.z-dn.net/?f=%20Loga%5Ex%3DLogb%5E%7Bx-3%7D%20)
Using the Logarithmic exponent property we can write
![xLoga=(x-3)Logb](https://tex.z-dn.net/?f=%20xLoga%3D%28x-3%29Logb%20)
![xLoga=xLogb-3Logb](https://tex.z-dn.net/?f=%20xLoga%3DxLogb-3Logb%20)
![x(Loga-Logb)-=-3Logb](https://tex.z-dn.net/?f=%20x%28Loga-Logb%29-%3D-3Logb%20)
![x=\frac{-3Logb}{Loga-Logb}\\](https://tex.z-dn.net/?f=%20x%3D%5Cfrac%7B-3Logb%7D%7BLoga-Logb%7D%5C%5C%20)
From here either we can simplify it further or we can substitute the values using calculator and on simplification we will get the final answer.
Hence we can solve using Logarithm.
Answer:
(a) 0.9412
(b) 0.9996 ≈ 1
Step-by-step explanation:
Denote the events a follows:
= a person passes the security system
= a person is a security hazard
Given:
![P (H) = 0.04,\ P(P^{c}|H^{c})=0.02\ and\ P(P|H)=0.01](https://tex.z-dn.net/?f=P%20%28H%29%20%3D%200.04%2C%5C%20P%28P%5E%7Bc%7D%7CH%5E%7Bc%7D%29%3D0.02%5C%20and%5C%20P%28P%7CH%29%3D0.01)
Then,
![P(H^{c})=1-P(H)=1-0.04=0.96\\P(P|H^{c})=1-P(P|H)=1-0.02=0.98\\](https://tex.z-dn.net/?f=P%28H%5E%7Bc%7D%29%3D1-P%28H%29%3D1-0.04%3D0.96%5C%5CP%28P%7CH%5E%7Bc%7D%29%3D1-P%28P%7CH%29%3D1-0.02%3D0.98%5C%5C)
(a)
Compute the probability that a person passes the security system using the total probability rule as follows:
The total probability rule states that: ![P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})](https://tex.z-dn.net/?f=P%28A%29%3DP%28A%7CB%29P%28B%29%2BP%28A%7CB%5E%7Bc%7D%29P%28B%5E%7Bc%7D%29)
The value of P (P) is:
![P(P)=P(P|H)P(H)+P(P|H^{c})P(H^{c})\\=(0.01\times0.04)+(0.98\times0.96)\\=0.9412](https://tex.z-dn.net/?f=P%28P%29%3DP%28P%7CH%29P%28H%29%2BP%28P%7CH%5E%7Bc%7D%29P%28H%5E%7Bc%7D%29%5C%5C%3D%280.01%5Ctimes0.04%29%2B%280.98%5Ctimes0.96%29%5C%5C%3D0.9412)
Thus, the probability that a person passes the security system is 0.9412.
(b)
Compute the probability that a person who passes through the system is without any security problems as follows:
![P(H^{c}|P)=\frac{P(P|H^{c})P(H^{c})}{P(P)} \\=\frac{0.98\times0.96}{0.9412} \\=0.9996\\\approx1](https://tex.z-dn.net/?f=P%28H%5E%7Bc%7D%7CP%29%3D%5Cfrac%7BP%28P%7CH%5E%7Bc%7D%29P%28H%5E%7Bc%7D%29%7D%7BP%28P%29%7D%20%5C%5C%3D%5Cfrac%7B0.98%5Ctimes0.96%7D%7B0.9412%7D%20%5C%5C%3D0.9996%5C%5C%5Capprox1)
Thus, the probability that a person who passes through the system is without any security problems is approximately 1.