A geometric sequence is one in which consecutive terms form a fixed ratio r. In other words, if aₙ is the nth term in the sequence, then
For example, if a₁ = a is the 1st term, then
2nd term = a₂ = a₁r
3rd term = a₃ = a₂r = a₁r²
4th term = a₄ = a₃r = a₁r³
and so on. It's fairly easy to infer that
nth term =
14. We're given the 2nd and 5th terms, a₂ = -243 and a₅ = -9, and we use them to find the ratio r.
a₅ = a₄r = a₃r² = a₂r³
-9 = -243 r³
r³ = 1/27
⇒ r = 1/3
Then the 1st term is
a₁ = a₂/r = -243/(1/3) = -729
and the nth term is recursively given by
and explicitly by
15. Now we have a₄ = 1/72 and a₃ = -1/12. Using what we know about geometric sequences, we have
a₄ / a₃ = (a₃r) / a₃ = r
so that
r = (1/72) / (-1/12) = -1/6
Then the 1st term is
a₁ = a₂/r = a₃/r² = (-1/12) / (-1/6)² = -3
and the nth term is recursively given by
and explicitly by
Which statement best describes the point (0, 0) on the graph?
No fine is paid if the laptop is returned 1 minute past the time it is due.
A fine of $0.35 is paid if the laptop is returned at the time it is due.
A fine of $0.35 is paid if the laptop is returned 1 minute past the time it is due.
No fine is paid if the laptop is returned exactly at the time at which it is due.
The statement which best describes the point (0, 0) on the graph is:
The horizontal axis i.e. the x-axis represent the number of minutes a loaner laptop is overdue.
and the vertical axis i.e, the y-axis represents the fine that a college student pays to the library based on the x-value.
The ordered pairs on the graph are:
(0,0) , (2,0.70) , (4,1.40) and (6,2.10).
The coordinate (0,0) represents that the number of minutes overdue were zero i.e. it is the initial time and at that time there will be no fine on the laptop.
( Since, the first ordinate i.e. time is zero and the second ordinate i.e. the fine is also zero)
This means if the laptop is returned at the right time then there will be no fine.
B. the points scored by a basketball player compared to his minutes played
C. the height of a woman compared to her age
D. the hours of daylight in a city throughout the year
The hours of daylight in a city throughout the year represent the negative linear correlation coefficient. Then the correct option is D.
Independent quantities with an inverse relationship tend to move in different directions.
In essence, any figure between 0 and -1 denotes an opposing movement of the equity stocks.
When the correlation coefficient becomes less than 0, there is a negative (opposite) correlation. This suggests that both parameters are moving in the obverse direction.
The hours of daylight in a city throughout the year represent the negative linear correlation coefficient
Then the correct option is D.
More about the negative linear correlation coefficient link is given below.
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Answer:
D. the hours of daylight in a city throughout the year
Step-by-step explanation:
The statement presented in the question is an example of inductive reasoning, where a general conclusion is drawn based on specific observations or examples.
The statement presented in the question is an example of inductive reasoning. Inductive reasoning is the process of making generalizations based on specific observations or examples. In this case, the student observes several elderly people passing by on the sidewalk and concludes that only elderly people live in their neighborhood. However, this conclusion may or may not be correct, as it is based on a limited number of observations.
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