Two is subtracted from a number, and then the difference is multiplied by 5. The result is 30
2 answers:
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Answer:
Step-by-step explanation:
From the given information:
a.
Compute :
b.
Compute P(A ∩ B)
P(A ∩ B) = P(A) +P(B) - P(A∪B)
P(A ∩ B) = 0.32 + 0.46 - 0.57
P(A ∩ B) = 0.21
Thus, since P(A ∩ B) ≠ 0, we can say that they are not mutually exclusive.
c.
P(A ∩ C) = P(A) +P(C) - P(A∪C)
P(A ∩ C) = 0.32 + 0.23 -0.55
P(A ∩ C) = 0
Thus, since P(A ∩ C) = 0, we can say that they are both mutually exclusive.
d. To determine P[(A ∪ B ∪ C)′]
i.e. none of the events occurring
Then :
P(B ∩ C) = 0.46 +0.23 -0.49
P(B ∩ C) = 0.20
Therefore:
P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B ) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)
P(A ∪ B ∪ C) = 0.32 + 0.46 + 0.23 - 0.21 - 0 - 0.20 + 0
P(A ∪ B ∪ C) = 0.60
Part A:
The general form of the equation of a transverse wave is given by:
![y(x,t)=A\cos\left[2\pi\left( \frac{x}{\lambda} - \frac{t}{T} \right)\right]](https://tex.z-dn.net/?f=y%28x%2Ct%29%3DA%5Ccos%5Cleft%5B2%5Cpi%5Cleft%28%20%5Cfrac%7Bx%7D%7B%5Clambda%7D%20-%20%5Cfrac%7Bt%7D%7BT%7D%20%5Cright%29%5Cright%5D)
where A is the amplitude,
is the wavelength, and T is the period.
Given that a certain transverse wave is described by:
![y(x,t)=bcos[2\pi(xl-t\tau)]](https://tex.z-dn.net/?f=y%28x%2Ct%29%3Dbcos%5B2%5Cpi%28xl-t%5Ctau%29%5D)
, where b = 5.90 mm , l = 29.0 cm , and \tau = 3.90\times10^{-2} s
Thus, the amplitude is b = 5.90 mm = 5.9\times10^{-3} \ m
Part B:
The general form of the equation of a transverse wave is given by:
where A is the amplitude, is the wavelength, and T is the period.
Given that a certain transverse wave is described by:
![y(x,t)=bcos[2\pi\left(\frac{x}{l}-\frac{t}{tau}\right)\right]](https://tex.z-dn.net/?f=y%28x%2Ct%29%3Dbcos%5B2%5Cpi%5Cleft%28%5Cfrac%7Bx%7D%7Bl%7D-%5Cfrac%7Bt%7D%7Btau%7D%5Cright%29%5Cright%5D)
, where b = 5.90 mm , l = 29.0 cm , and \tau = 3.90\times10^{-2} s
<span>Thus,
Part C:
</span><span>The general form of the equation of a transverse wave is given by:
where A is the amplitude, is the wavelength, and T is the period.
</span><span>Given that a certain transverse wave is described by:
,
where b = 5.90 mm , l = 29.0 cm , and \tau = 3.90\times10^{-2} s
</span>
<span>The wave's frequency, f, is given by:
</span>
Part D:
Given that the <span>the wavelength is
</span><span>and that the wave's frequency is 29.4 Hz
</span><span>The wave's speed of propagation, v, is given by:
</span>
The general form of the equation of a transverse wave is given by:
where A is the amplitude,
Given that a certain transverse wave is described by:
Thus, the amplitude is b = 5.90 mm = 5.9\times10^{-3} \ m
Part B:
The general form of the equation of a transverse wave is given by:
where A is the amplitude,
Given that a certain transverse wave is described by:
<span>Thus,
Part C:
</span><span>The general form of the equation of a transverse wave is given by:
where A is the amplitude,
</span><span>Given that a certain transverse wave is described by:
</span>
<span>The wave's frequency, f, is given by:
</span>
Part D:
Given that the <span>the wavelength is
</span><span>The wave's speed of propagation, v, is given by:
</span>