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gladu [14]
3 years ago
6

Select the correct answer.

Mathematics
1 answer:
Murljashka [212]3 years ago
3 0

Answer:

Option B.

Step-by-step explanation:

Consider the below figure attached with this question.

The given data set is 47, 48, 49, 50, 50, 53, 54, 54, 55, 56, 59, 61.

Class interval frequency table:

Intervals            Numbers               Frequency

45-49                47,48                         2

49-52              49,50,50                     3

52-56             53,54,54,55                 4

56-60                56,59                        2

60-64                   61                            1

Each histogram represent the frequencies on different intervals.

Frequencies on intervals 45-49, 49-52, 52-56, 56-60, 60-64 of given histogram are

Histogram A: 1, 2, 3, 1, 2

Histogram B: 2, 3, 4, 2, 1

Histogram C: 1, 3, 2, 1, 2

Histogram D: 5, 3, 2, 1, 2

Histogram B represents the given data set.

Therefore, the correct option is B.

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The first term in a geometric sequence is 54, and the 5th term is 2 / 3. Find an explicit form for the geometric sequence.
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Answer:  ar^{n-1}=54(\dfrac{1}{3})^{n-1}

Step-by-step explanation:

The nth term for a geometric sequence is given by :-

a_n=ar^{n-1}    (1)

We are given that The first term in a geometric sequence is 54. i.e. a=54

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Put n=5 and a= 54 in (1), we get

a_5=(54)r^{4}=     (3)

From (2) and (3), we have

\Rightarrow(54)r^{4}=\dfrac{2}{3}\\\\\Rightarrow r^4=\dfrac{2}{3}\times\dfrac{1}{54}=\dfrac{1}{3\times27}=\dfrac{1}{81}\\\\\Rightarrow\ r=(\dfrac{1}{81})^{\frac{1}{4}}=\dfrac{1}{3}

Explicit form for the geometric sequence: ar^{n-1}=54(\dfrac{1}{3})^{n-1}

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