Which sequences are geometric? Check all that apply.
2 answers:
Answer:
–2.7, –9, –30, –100, ...
–1, 2.5, –6.25, 15.625, ...
8, 0.8, 0.08, 0.008, ...
Explanation:
A geometric sequence is a sequence with the ratio between two consecutive terms constant. This ratio is called the common ratio.
now check all the sequence one by one.
For sequence –2.7, –9, –30, –100, ...
r =
=
=
We see that, all the ratios are same.
So this is geometric sequence.
For sequence –1, 2.5, –6.25, 15.625, ...
r =
This is also geometric sequence.
For sequence 9.1, 9.2, 9.3, 9.4, ...
In this sequence, common ratio is not same.
So, it is not a geometric sequence.
For sequence 8, 0.8, 0.08, 0.008, ...
Common ratio is same so, it is geometric sequence.
For sequence 4, –4, –12, –20, ...
Common ratio is not same. So, it is not geometric sequence .
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Answer:
The bulbs should be replaced each 1060.5 days.
Step-by-step explanation:
Problems of normally distributed samples are solved using 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 problem, we have that:
How often should the bulbs be replaced so that no more than 1% burn out between replacement periods?
This is the first percentile, that is, the value of X when Z has a pvalue of 0.01. So X when Z = -2.325.
The bulbs should be replaced each 1060.5 days.