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Murrr4er [49]
2 years ago
12

What is the smallest positive integer $n$ such that $3n$ is a perfect square and $2n$ is a perfect cube?

Mathematics
1 answer:
Agata [3.3K]2 years ago
6 0

Answer:

108

Step-by-step explanation:

Since 3n is a perfect square, that means that n has to be a multiple of 3. Since 2n is a perfect cube, then n has to be divisible by 2^2=4. Since n is a multiple of 3, then n also has to be divisible by 3^3=27. Therefore, the smallest value for n is 4*27=108.

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Find the mean median mode and range for the following data 77 60 59 70 89 95
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Answer:

Mean = 75

Median = 73.5

Mode = 95

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Step-by-step explanation:

Given:

  • 77,60,59,70,89,95

Sort:

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To find:

  • Mean
  • Median
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Mean:

\displaystyle \large{\dfrac{1}{n}\sum_{i =1}^n x_i = \dfrac{x_1+x_2+x_3+...+x_n}{n}}

Sum of all data divides by amount.

\displaystyle \large{\dfrac{59+60+70+77+89+95}{6}=\dfrac{450}{6}}\\\\\displaystyle \large{\therefore mean=75}

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Median:

If it’s exact middle then that’s the median. However, if two data or values happen to be in <em>middle</em>:

\displaystyle \large{\dfrac{x_1+x_2}{2}}

From 59,60,70,77,89,95, since 70 and 77 are in middle:

\displaystyle \large{\dfrac{70+77}{2} = \dfrac{147}{2}}\\\displaystyle \large{\therefore median = 73.5}

Therefore, median = 73.5

Mode:

The highest value or/and the highest amount of data. Mode can have more than one.

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Therefore, mode = 95

Range:

\displaystyle \large{x_{max}-x_{min}} or highest value - lowest value

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\displaystyle \large{95-59 = 36}

Therefore, range = 36

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