Answer:
<h3>
- 128 Superscript StartFraction 3 Over x EndFraction
</h3><h3>
- (4RootIndex 3 StartRoot 2 EndRoot)x
</h3><h3>
- (4 (2 Superscript one-third Baseline) ) Superscript x</h3><h3>
Step-by-step explanation:</h3>
Given the indicinal equation ![(\sqrt[3]{128} )^{x}\\](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7B128%7D%20%29%5E%7Bx%7D%5C%5C)
According to one of the law of indices,
![(\sqrt[a]{m} )^{b}\\= (\sqrt{m})^\frac{b}{a}](https://tex.z-dn.net/?f=%28%5Csqrt%5Ba%5D%7Bm%7D%20%29%5E%7Bb%7D%5C%5C%3D%20%28%5Csqrt%7Bm%7D%29%5E%5Cfrac%7Bb%7D%7Ba%7D)
Applying this law to the question;
![(\sqrt[3]{128} )^{x}\\ = {128} ^\frac{x}{3}\\ \\= (\sqrt[3]{64*2})^{x} \\ = (4\sqrt[3]{2})^{x} \\= (4(2^{1/3} )^{x} )](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7B128%7D%20%29%5E%7Bx%7D%5C%5C%20%3D%20%7B128%7D%20%5E%5Cfrac%7Bx%7D%7B3%7D%5C%5C%20%5C%5C%3D%20%28%5Csqrt%5B3%5D%7B64%2A2%7D%29%5E%7Bx%7D%20%5C%5C%20%3D%20%284%5Csqrt%5B3%5D%7B2%7D%29%5E%7Bx%7D%20%5C%5C%3D%20%284%282%5E%7B1%2F3%7D%20%29%5E%7Bx%7D%20%29)
The following are therefore true based on the following calculation
128 Superscript StartFraction 3 Over x EndFraction
(4RootIndex 3 StartRoot 2 EndRoot)x
(4 (2 Superscript one-third Baseline) ) Superscript x
Surface area of a sphere = <span>4π<span>r2</span></span>
the volume of a sphere= <span><span>43</span>π<span>r3</span></span>
so <span>5000π=<span>4/3</span><span>πr3
</span></span><span>> r^3 = 5000 x 3 / 4
=>
r^3 = 3750
</span>taking cube root on both sides
r=15.53616
hope it helps
Answer:
0.335
Step-by-step explanation:
1. There is a 30 percent chance of a flight being delayed because of icy weather ,then the probability of being delayed is 0.3 and of being not delayed is 0.7.
2. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem, then the probability of being delayed is 0.1 and the probabilty of not being delayed is 0.9.
3. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem (MP), then the probability of being delayed is 0.05 and the probabilty of not being delayed is 0.95. (See attached probability tree)
Delayed of icy weather - 0.3
Delayed of MP when weather is not icy - 0.7·0.05=0.035
Now, if one flight is selected at random from the airport in January, the probability that the flight selected will have at least one of the two types of delays is
0.3+0.035=0.335
Step-by-step explanation:
to be honest I'm not sure how to do
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