Answer: 4004ways
Step-by-step explanation:
Total number of Students =15
Total number of students to be on the committee =5
Since two members are of the same major and must not be on the committee, then we are left with choosing 5 people from just 14 People after we eventually remove one from those two students with same majors.
Hence to select 5 people from 14 people, we use the combination formula 14C5.
From the two students with same major we also use the combination Formula in knowing the number of ways any of the two students can be chosen. To choose one from these two students, we use the combination Formula 2C1.
Hence, the total number of ways to choose the committee of 5 and ensuring the two students with same major aren't on the committee becomes:
= 14C5 * 2C1
= 2002 * 2
= 4004ways.
Y=1x because if you draw it on the line you’ll see the linear variation
<h3>
4 Answers: A, C, E, and F</h3>
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Explanation:
Choice A is true assuming we have ![a_n = (-1)^n*b_n](https://tex.z-dn.net/?f=a_n%20%3D%20%28-1%29%5En%2Ab_n)
In this case,
and ![b_n = \frac{1}{\sqrt{n}}](https://tex.z-dn.net/?f=b_n%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7Bn%7D%7D)
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Choice B is false. See choice A above.
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Choice C is true. The sequence
is decreasing. As n gets larger,
gets smaller. This is because the denominator is growing larger with the numerator held constant.
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Choice D is false. This contradicts choice C.
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Choice E is true since the denominator is growing forever
This is similar to ![\displaystyle \lim_{n \to \infty} \frac{1}{n} = 0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B1%7D%7Bn%7D%20%3D%200)
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Choice F is true due to choices C and E being true.
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Choice G is false because it contradicts choice F.
Answer:
This sampling distribution will only reflect the nature of its population distribution (strongly skewed right because the sample size of each sample, 9, is way less than the sample size of 30 required for the sampling distribution to be approximately normal) with mean 404 inches and standarddeviation of sampling distribution equal to 43 inches.
Step-by-step explanation:
The Central limit theorem explains that for an independent, any random set of sample taken from such a population distribution will have a distribution that is approximately normal (provided that the sample size is large enough) with the mean of sampling distribution also approximately equal to the population mean and the standard deviation of the sampling distribution is given as
σₓ = (σ/√n)
where
σ = population standard deviation
n = sample size
To work these out,
Mean of sampling distribution = population mean
μₓ = μ = 404 inches
Standard deviation of the sampling distribution = σₓ = (σ/√n)
σ = population standard deviation = 129 inches
n = sample size = 9
σₓ = (129/√9) = 43 inches.
For most databases, the 'large enough' criteria for the sampling distribution to be approximately normal is a sample size of about 30 and it gets closer as the sample size becomes larger.
The sample size in the question is 9 which is way less than 30, hence, this sampling distribution will only reflect the nature of its population distribution (strongly skewed right) with mean 404 inches and standarddeviation of sampling distribution equal to 43 inches.
Hope this Helps!!!