Step-by-step explanation:
These are all examples of p-series:
∑(1 / nᵖ), where p>0.
If p > 1, the series converges. If 0 < p ≤ 1, the series diverges.
First option:
∑(1/n⁵)
Here, p = 5. Since 5 > 1, the series converges.
Second option:
∑((√n+3)/n³)
∑((√n)/n³) + ∑(3/n³)
∑(1/n^2.5) + 3 ∑(1/n³)
In the first sum, p = 2.5. In the second sum, p = 3. Both are greater than 1, so the series converges.
Third option:
∑((n−4)/(n⁴√n))
∑(1/(n³√n)) − ∑(4/(n⁴√n))
∑(1/n^3.5) − 4 ∑(1/n^4.5)
In the first sum, p = 3.5. In the second sum, p = 4.5. Both are greater than 1, so the series converges.
Fourth option:
∑(1/∛n)
∑(1/n^⅓)
Here, p = ⅓. This is less than 1, so the series diverges.
Note: if a series is converging, then the limit is 0.
However, if the limit of a series is 0, it does not necessarily mean that series is converging.
Here, the limit of all 4 options is 0. However, the fourth option is a diverging series.
The minimum sample size required to estimate a population proportion or percentage is 306.
In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.
In order to determine the minimum sample size required to estimate a population proportion or percentage, we will use the following formula:
n = (z×p×q)/m²
where is the minimum sample size, z is the z-score corresponding to the desired confidence level, p is the population proportion, q is 1-p, and m is the desired margin of error.
In this case, the confidence level is 95%, so the corresponding z-score is 1.96. Since we don't know the population proportion, we will use the symbol p and q to represent it. Therefore, the formula becomes:
n = (1.96×p×q)/(0.04)²
To determine the minimum sample size, we need to determine the value of p and q. Since p + q = 1, if we set p to 0.5, then q will also be 0.5. Therefore, the minimum sample size is:
n = (1.96×0.5×0.5)/(0.04)² = 306.25
≈ 306
Therefore, the minimum sample size required to estimate a population proportion or percentage is 306.
Learn more about the random sample here:
brainly.com/question/12719656.
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Answer: 25 students per teacher and 12 students per tutor. They need 2.4 tutors for the school
Answer:
126
Step-by-step explanation:
4 is less than 126 so 126 > 4
The expression 2 * √36 + 9 evaluates to 21.
The expression 2 * √36 + 9 evaluates to 21 when you follow the order of operations known as BODMAS. You first calculate the square root of 36, then multiply the result by 2 and finally add 9.
To evaluate the given mathematical expression, we must first understand the order of operations, also known as BODMAS.
The acronym BODMAS stands for Brackets, Orders, Division/Multiplication (from left to right), Addition/Subtraction (from left to right). It represents the sequence in performing mathematical operations.
Let's apply this to the question: 2 * √36 + 9?
First, consider the 'Order', which is the square root (√). The square root of 36 is 6.
Next, apply the 'Multiplication'. So, 2 multiplied by 6 equals 12.
Finally, apply the 'Addition'. 12 plus 9 equals 21.
So, the expression 2 * √36 + 9 evaluates to 21.
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