Answer:
![P(X \geq0.55) \leq 0.22](https://tex.z-dn.net/?f=P%28X%20%5Cgeq0.55%29%20%5Cleq%200.22)
Step-by-step explanation:
Using central Limit Theorem (CLT), The sum of 100 random variables;
is approximately normally distributed with
Y ~ N (100 ×
) = N ( 50,
)
The approximate probability that it will take this child over 55 seconds to complete spinning can be determined as follows;
N ( 50,
)
![P(Y>55) =P(Z>\frac{55-50}{10/3})](https://tex.z-dn.net/?f=P%28Y%3E55%29%20%3DP%28Z%3E%5Cfrac%7B55-50%7D%7B10%2F3%7D%29)
![P(Y>55) =P(Z>1.5)](https://tex.z-dn.net/?f=P%28Y%3E55%29%20%3DP%28Z%3E1.5%29)
![P(Y>55) =\phi (-1.5)](https://tex.z-dn.net/?f=P%28Y%3E55%29%20%3D%5Cphi%20%28-1.5%29)
![P(Y>55) =0.0668](https://tex.z-dn.net/?f=P%28Y%3E55%29%20%3D0.0668)
Using Chebyshev's inequality:
![P(|X-\mu\geq K)\leq \frac{\sigma^2}{K^2}](https://tex.z-dn.net/?f=P%28%7CX-%5Cmu%5Cgeq%20K%29%5Cleq%20%5Cfrac%7B%5Csigma%5E2%7D%7BK%5E2%7D)
Let assume that X has a symmetric distribution:
Then:
![2P(X-\mu\geq K)\leq) \frac{\sigma^2}{K^2}](https://tex.z-dn.net/?f=2P%28X-%5Cmu%5Cgeq%20K%29%5Cleq%29%20%5Cfrac%7B%5Csigma%5E2%7D%7BK%5E2%7D)
![2P(X \geq \mu+K)\leq) \frac{\sigma^2}{K^2}](https://tex.z-dn.net/?f=2P%28X%20%5Cgeq%20%5Cmu%2BK%29%5Cleq%29%20%5Cfrac%7B%5Csigma%5E2%7D%7BK%5E2%7D)
where: (
)
![P(X \geq0.55) \leq 0.22](https://tex.z-dn.net/?f=P%28X%20%5Cgeq0.55%29%20%5Cleq%200.22)
1 )
![volume = 20 \times 5 \times 8](https://tex.z-dn.net/?f=volume%20%3D%2020%20%5Ctimes%205%20%5Ctimes%208)
![volume = 800 \: \: {m}^{3}](https://tex.z-dn.net/?f=volume%20%3D%20800%20%5C%3A%20%20%5C%3A%20%20%7Bm%7D%5E%7B3%7D%20)
![surface \: \: area \: = 4 \times 20 \times 8](https://tex.z-dn.net/?f=surface%20%5C%3A%20%20%5C%3A%20area%20%5C%3A%20%20%3D%204%20%5Ctimes%2020%20%5Ctimes%208)
![surface \: area \: \: = 640 \: \: {m}^{2}](https://tex.z-dn.net/?f=surface%20%5C%3A%20area%20%5C%3A%20%20%5C%3A%20%20%3D%20640%20%5C%3A%20%20%5C%3A%20%20%7Bm%7D%5E%7B2%7D%20)
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2 )
![v = 15 \times 3 \times 4](https://tex.z-dn.net/?f=v%20%3D%2015%20%5Ctimes%203%20%5Ctimes%204)
![v = 180 \: \: {m}^{3}](https://tex.z-dn.net/?f=v%20%3D%20180%20%5C%3A%20%20%5C%3A%20%20%7Bm%7D%5E%7B3%7D%20)
![s \: a \: = 4 \times 15 \times 4](https://tex.z-dn.net/?f=s%20%5C%3A%20a%20%5C%3A%20%20%3D%204%20%5Ctimes%2015%20%5Ctimes%204)
![s \: a \: = 240 \: \: {m}^{2}](https://tex.z-dn.net/?f=s%20%5C%3A%20a%20%5C%3A%20%20%3D%20240%20%5C%3A%20%20%5C%3A%20%20%7Bm%7D%5E%7B2%7D%20)
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3 )
![v = ( \frac{1}{2} \times 4 \times 5) \times 10 \\](https://tex.z-dn.net/?f=v%20%3D%20%28%20%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes%204%20%5Ctimes%205%29%20%5Ctimes%2010%20%5C%5C%20)
![v = 100 \: \: {m}^{3}](https://tex.z-dn.net/?f=v%20%3D%20100%20%5C%3A%20%20%5C%3A%20%20%7Bm%7D%5E%7B3%7D%20)
![s \: \: a = (10 \times 5) + (10 \times 4) + (10 \times \sqrt{41} ) \\](https://tex.z-dn.net/?f=s%20%5C%3A%20%20%5C%3A%20a%20%3D%20%2810%20%5Ctimes%205%29%20%2B%20%2810%20%5Ctimes%204%29%20%2B%20%2810%20%5Ctimes%20%20%5Csqrt%7B41%7D%20%29%20%5C%5C%20)
![s \: a \: \: = 50 + 40 + 10 \sqrt{41}](https://tex.z-dn.net/?f=s%20%5C%3A%20a%20%5C%3A%20%20%5C%3A%20%20%3D%2050%20%2B%2040%20%2B%2010%20%5Csqrt%7B41%7D%20)
![s \: a \: \: = 90 + 10 \sqrt{41}](https://tex.z-dn.net/?f=s%20%5C%3A%20a%20%5C%3A%20%20%5C%3A%20%20%3D%2090%20%2B%2010%20%5Csqrt%7B41%7D%20)
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4 )
![v = ( \frac{1}{2} \times 3 \times 4) \times 7 \\](https://tex.z-dn.net/?f=v%20%3D%20%28%20%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes%203%20%5Ctimes%204%29%20%5Ctimes%207%20%5C%5C%20)
![v = 42 \: \: \: {m}^{3}](https://tex.z-dn.net/?f=v%20%3D%2042%20%5C%3A%20%20%5C%3A%20%20%20%5C%3A%20%7Bm%7D%5E%7B3%7D%20)
![s \: a \: \: = (3 \times 7) + (4 \times 7) + (5 \times 7)](https://tex.z-dn.net/?f=s%20%5C%3A%20%20a%20%5C%3A%20%20%5C%3A%20%20%3D%20%283%20%5Ctimes%207%29%20%2B%20%284%20%5Ctimes%207%29%20%2B%20%285%20%5Ctimes%207%29)
![s \: a \: \: = 21 + 28 + 35](https://tex.z-dn.net/?f=s%20%5C%3A%20a%20%5C%3A%20%20%5C%3A%20%20%3D%2021%20%2B%2028%20%2B%2035)
![s \: a \: \: = 84 \: \: \: {m}^{2}](https://tex.z-dn.net/?f=s%20%5C%3A%20a%20%5C%3A%20%20%5C%3A%20%20%3D%2084%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%7Bm%7D%5E%7B2%7D%20)
Answer:
All three sides of a scalene triangle have different lengths, they have different measurements also. So your answer would be true.
Step-by-step explanation:
Answer:
6 3/4
Step-by-step explanation:
4 1/4 + 2 1/2
Since they have different Common Denominators, we’ll have to find the LCM for 4 and 2
4: 4, 8, 12, 16…
2, 2, 4, 6, 8…
The LCM would be 4
Now convert 2 1/2 into a denominator of 4
2 1/2 = 2 2/4
Whatever number you multiplied to get 4 is the same number that will get multiplied to find the numerator
Then we’re ready to add! (4 1/4 + 2 2/4)
4 1/4 + 2 2/4 = 6 3/4
Final Answer: 6 3/4
Answer:
Sorry, you didn't post an image. You can repost a new question.
Step-by-step explanation: