Answer:
The addition rule for probabilities describes two formulas, one for the probability for either of two mutually exclusive events happening and the other for the probability of two non-mutually exclusive events happening.
The first formula is just the sum of the probabilities of the two events. The second formula is the sum of the probabilities of the two events minus the probability that both will occur.
Answer: The blue whale's weight is 150 times heavier than the narwhal's weight.
Step-by-step explanation:
Given: Weight of Blue whale = ![3\times10^5\text{ pounds}](https://tex.z-dn.net/?f=3%5Ctimes10%5E5%5Ctext%7B%20pounds%7D)
Weight of Narwhal = ![2\times10^3\text{ pounds}](https://tex.z-dn.net/?f=2%5Ctimes10%5E3%5Ctext%7B%20pounds%7D)
Number of times blue whale's weight is heavier than the narwhal's weight = ![=\dfrac{\text{Weight of Blue whale}}{\text{Weight of Narwhal }}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B%5Ctext%7BWeight%20of%20Blue%20whale%7D%7D%7B%5Ctext%7BWeight%20of%20Narwhal%20%7D%7D)
![=\dfrac{3\times10^5}{2\times10^3}\\\\=1.5\times10^{5-3}\ \ \ [\dfrac{a^m}{a^n}=a^{m-n}]\\\\=1.5\times10^2\\\\=1.5\times100=150](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B3%5Ctimes10%5E5%7D%7B2%5Ctimes10%5E3%7D%5C%5C%5C%5C%3D1.5%5Ctimes10%5E%7B5-3%7D%5C%20%5C%20%5C%20%5B%5Cdfrac%7Ba%5Em%7D%7Ba%5En%7D%3Da%5E%7Bm-n%7D%5D%5C%5C%5C%5C%3D1.5%5Ctimes10%5E2%5C%5C%5C%5C%3D1.5%5Ctimes100%3D150)
Hence, the blue whale's weight is 150 times heavier than the narwhal's weight.
9514 1404 393
Answer:
x = (ab +a +b +c)/(a +b)
Step-by-step explanation:
Eliminate parentheses, subtract left terms not containing x, divide by the coefficient of x.
![a(x-b)+bx-c=a+b\\\\ax+bx-ab-c=a+b\\\\x(a+b)=ab+a+b+c\\\\\boxed{x=\dfrac{ab+a+b+c}{a+b}}](https://tex.z-dn.net/?f=a%28x-b%29%2Bbx-c%3Da%2Bb%5C%5C%5C%5Cax%2Bbx-ab-c%3Da%2Bb%5C%5C%5C%5Cx%28a%2Bb%29%3Dab%2Ba%2Bb%2Bc%5C%5C%5C%5C%5Cboxed%7Bx%3D%5Cdfrac%7Bab%2Ba%2Bb%2Bc%7D%7Ba%2Bb%7D%7D)
Answer:
![14878.04878miles/hours^2](https://tex.z-dn.net/?f=14878.04878miles%2Fhours%5E2)
Step-by-step explanation:
Let's find a solution by understanding the following:
The acceleration rate is defined as the change of velocity within a time interval, which can be written as:
where:
A=acceleration rate
Vf=final velocity
Vi=initial velocity
T=time required for passing from Vi to Vf.
Using the problem's data we have:
Vf=65miles/hour
Vi=6miles/hour
T=14.8seconds
Using the acceleration rate equation we have:
, but look that velocities use 'hours' unit while 'T' uses 'seconds'.
So we need to transform 14.8seconds into Xhours, as follows:
![X=(14.8seconds)*(1hours/60minutes)*(1minute/60seconds)](https://tex.z-dn.net/?f=X%3D%2814.8seconds%29%2A%281hours%2F60minutes%29%2A%281minute%2F60seconds%29)
![X=0.0041hours](https://tex.z-dn.net/?f=X%3D0.0041hours)
Using X=0.0041hours in the previous equation instead of 14.8seconds we have:
![A=(65miles/hour - 6miles/hour)/0.0041hours](https://tex.z-dn.net/?f=A%3D%2865miles%2Fhour%20-%206miles%2Fhour%29%2F0.0041hours)
![A=(61miles/hour)/0.0041hours](https://tex.z-dn.net/?f=A%3D%2861miles%2Fhour%29%2F0.0041hours)
![A=(61miles)/(hour*0.0041hours)](https://tex.z-dn.net/?f=A%3D%2861miles%29%2F%28hour%2A0.0041hours%29)
![A=61miles/0.0041hours^2](https://tex.z-dn.net/?f=A%3D61miles%2F0.0041hours%5E2)
![A=14878.04878miles/hours^2](https://tex.z-dn.net/?f=A%3D14878.04878miles%2Fhours%5E2)
In conclusion, the acceleration rate is ![14878.04878miles/hours^2](https://tex.z-dn.net/?f=14878.04878miles%2Fhours%5E2)
As a fraction,
35/42, simplified, 5/6
answer=5/6
hope this helps....