10, 30, 90 continue the pattern
2 answers:
Answer:
- geometric sequence: 10, 30, 90, 270, 810, 2430, ...
- quadratic sequence: 10, 30, 90, 190, 330, 510, ...
Step-by-step explanation:
Three terms of a sequence can be the first three terms of many different kinds of sequences. Here the ratios of terms are constant:
30/10 = 90/30 = 3
so the pattern could be that of a geometric sequence. In that sequence, each term is 3 times the previous one.
This pattern continues ...
10, 30, 90, 270, 810, 2430, ...
___
Another way to look at sequences of numbers is to consider their differences. Here the differences are not constant, and there aren't enough terms to tell how the differences change.
30 -10 = 20
90 -30 = 60
The second of these differences can be viewed several ways. One is to say that it is 40 more than the first of the differences. If each successive difference is 40 more than the last, then the pattern is described by a quadratic function:
This pattern continues ...
10, 30, 90, 190, 330, 510, ...
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Answer:
(1) A Normal approximation to binomial can be applied for population 1, if <em>n</em> = 100.
(2) A Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50 and 40.
(3) A Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50, 40 and 20.
Step-by-step explanation:
Consider a random variable <em>X</em> following a Binomial distribution with parameters <em>n </em>and <em>p</em>.
If the sample selected is too large and the probability of success is close to 0.50 a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
- np ≥ 10
- n(1 - p) ≥ 10
The three populations has the following proportions:
p₁ = 0.10
p₂ = 0.30
p₃ = 0.50
(1)
Check the Normal approximation conditions for population 1, for all the provided <em>n</em> as follows:
Thus, a Normal approximation to binomial can be applied for population 1, if <em>n</em> = 100.
(2)
Check the Normal approximation conditions for population 2, for all the provided <em>n</em> as follows:
Thus, a Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50 and 40.
(3)
Check the Normal approximation conditions for population 3, for all the provided <em>n</em> as follows:
Thus, a Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50, 40 and 20.
The answer must be 
since the triangular pyramid has 4 faces and each has an area of 30 
we should multiply that by 4 , so :
