How to round number to the given place value position
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Let <em>a </em>(<em>n</em>) denote the <em>n</em>-th term of the given sequence.
Check the forward differences, and denote the <em>n</em>-th difference by <em>b </em>(<em>n</em>). That is,
<em>b </em>(<em>n</em>) = <em>a </em>(<em>n</em> + 1) - <em>a </em>(<em>n</em>)
These so-called first differences are
<em>b</em> (1) = <em>a</em> (2) - <em>a</em> (1) = 25 - 7 = 18
<em>b</em> (2) = <em>a</em> (3) - <em>a</em> (2) = 51 - 25 = 26
<em>b </em>(3) = <em>a</em> (4) - <em>a</em> (3) = 85 - 51 = 34
<em>b</em> (4) = <em>a </em>(5) - <em>a</em> (4) = 127 - 85 = 42
Now consider this sequence of differences,
18, 26, 34, 42, …
and notice that the difference between consecutive terms in this sequence <em>b</em> is 8:
26 - 18 = 8
34 - 26 = 8
42 - 34 = 8
and so on. This means <em>b</em> is an arithmetic sequence, and in particular follows the rule
<em>b</em> (<em>n</em>) = 18 + 8 (<em>n</em> - 1) = 8<em>n</em> + 10
for <em>n</em> ≥ 1.
So we have
<em>a </em>(<em>n</em> + 1) - <em>a </em>(<em>n</em>) = 8<em>n</em> + 10
or, replacing <em>n</em> + 1 with <em>n</em>,
<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + 8 (<em>n</em> - 1) + 10
<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + 8<em>n</em> + 2
We can solve for <em>a</em> (<em>n</em>) by iteratively substituting:
<em>a</em> (<em>n</em>) = [<em>a</em> (<em>n</em> - 2) + 8 (<em>n</em> - 1) + 2] + 8<em>n</em> + 2
<em>a</em> (<em>n</em>) = <em>a </em>(<em>n</em> - 2) + 8 (<em>n</em> + (<em>n</em> - 1)) + 2×2
<em>a</em> (<em>n</em>) = [<em>a</em> (<em>n</em> - 3) + 8 (<em>n</em> - 2) + 2] + 8 (<em>n</em> + (<em>n</em> - 1)) + 2×2
<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 3) + 8 (<em>n</em> + (<em>n</em> - 1) + (<em>n</em> - 2)) + 3×2
and so on. The pattern should be clear; we end up with
<em>a</em> (<em>n</em>) = <em>a</em> (1) + 8 (<em>n</em> + (<em>n</em> - 1) + … + 3 + 2) + (<em>n</em> - 1)×2
The middle group is the sum,
so that
<em>a</em> (<em>n</em>) = <em>a</em> (1) + (4<em>n</em> ² + 4<em>n</em> - 8) + 2 (<em>n</em> - 1)
<em>a</em> (<em>n</em>) = 4<em>n</em> ² + 6<em>n</em> - 3
Answer:
The minimum value of the bill that is greater than 95% of the bills is $37.87.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
What are the minimum value of the bill that is greater than 95% of the bills?
This is the 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.
The minimum value of the bill that is greater than 95% of the bills is $37.87.
Answer: One tail test.
Step-by-step explanation:
Given : A sample of 36 observations is selected from a normal population. The sample mean is 12, and the population standard deviation is 3.
Also, The set of hypothesis to conduct a test :-
The kind of test need to perform is dependent upon the alternative hypothesis.
Since, the alternative hypothesis is one tailed (right-tailed), so the test is one tail test.
Answer:
Step-by-step explanation:
Given : Number of choices for novels = 4
Number of choices for plays = 6
Number of choices for poetry books = 5
Number of choices for nonfiction books = 5
Total books =4+6+5+5=20
If he wants to include all 4 novels, then the number of books left to select = 9-4=5
Remaining choices for books = 20-4=16
Number of combinations of n things taking r at a time :
Then, the number of different reading schedules are possible :_
Hence, the required answer is .