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alexira [117]
3 years ago
10

The simple formula for the nth term of an arithmetic sequence is an = 5n + 15. What is the explicit formula corresponding to the

simple formula?
A. an = 15 + 5n
B. an = 15 + (n - 1)(5)
C. an = 20 + (n)/(5)
D. an = 20 + (n - 1)(5)
E. an = 5 + (n - 1)(15)
Mathematics
1 answer:
Nikitich [7]3 years ago
7 0
Sequence will look like this:
Term 1: 20 --------- 20 + 5(0)
Term 2: 25 --------- 20 + 5(1)
Term 3: 30 --------- 20 + 5(2)
Term 4: 35 --------- 25 + 5(3)
ETC.

It cab noted that the numbers in the bracket (that is, 0, 1, 2, 3, 3, etc) = n-1

Then, the explicit formula will be;
an = 20 + 5(n-1).

The correct answer is D.
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3 years ago
Assume that body masses of Goldfinch birds follow a normal distribution with standard deviation equal to 0.04 oz. An ornithologi
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Answer:

The formula to generate 70% confidence interval is: [\overline{x} - 0.013, \overline{x} + 0.013], in which \overline{x}  is the sample mean.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.7}{2} = 0.15

Now, we have to find z in the Z-table as such z has a p-value of 1 - \alpha.

That is z with a pvalue of 1 - 0.15 = 0.85, so Z = 1.037.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

Assume that body masses of Goldfinch birds follow a normal distribution with standard deviation equal to 0.04 oz.

This means that \sigma = 0.04.

Sample of 10 birds:

This means that n = 10.

The margin of error is of:

M = z\frac{\sigma}{\sqrt{n}}

M = 1.037\frac{0.04}{\sqrt{10}}

M = 0.013

The lower end of the interval is the sample mean of \overline{x} subtracted by M.

The upper end of the interval is the sample mean of \overline{x} added to M.

Then, the formula to generate 70% confidence interval is: [\overline{x} - 0.013, \overline{x} + 0.013], in which \overline{x}  is the sample mean.

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If line a is perpendicular to line b and the slope of line a is 7 whats the slope of line b
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Answer:

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Moving onto the second part which is to get the reciprocal of the number which means that if we have \frac{1}{2} then we would switch it to 2.  In our case our number is -7 so we would make that into a fraction like this -\frac{1}{7}.

In conclusion, our final slope of the perpendicular line is -\frac{1}{7}.

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