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PtichkaEL [24]
3 years ago
6

What is the rule for the following sequence: 2, 9, 21, 65

Mathematics
1 answer:
Helga [31]3 years ago
5 0

There is no common ratio or common difference. The first three terms increases more slowly than a cubic, but the last three increase more quickly than the cube of n. The pattern is not obvious to me. When the sequence is cast in recursive terms, you get

... a[n] = (48/13)a[n-2] + (59/39)a[n-1] . . . . a[1] = 2, a[2] = 9

The next term using this rule is 174 34/39, not an integer.

The coefficients p and q for a[n-2] and a[n-1] can be found from

2p+9q=21\\9p+21q=65

_____

Any sequence of 4 numbers can be matched by a polynomial of degree 3 or less. Here, a calculator's polynomial regression function tells us the rule could be

... a[n] = 4.5n³ -24.5n² +49n -27

Using this rule, the next two terms are 168 and 357.

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1. A random sample of 25 of the 400 members of the Bigtime Theater
natulia [17]

Answer:

Minimum value = 1

Maximum value = 10

First Quartile or 25th percentile = 2.5

Third Quartile or 75th percentile = 5

Median = 4

Inter Quartile Range (IQR) = 2.5

Range = 9

Number of variables = 25

Outliers = 10

Step-by-step explanation:

Note that a box and whiskers plot shows 5 major information about the distribution of data. It shows:

- The maximum variable

Simply the maximum value of the distribution.

This is usually read from the whiskers, the tail end on the whiskers at the top of the plot. But this distribution has an outlier (represented by the singular dot, which can now serve as the maximum value. Maximum value = 10

- The minimum variable

Simply the minimum value of the distribution.

This is also easily read from the whiskers, the very beginning of the whiskers at the bottom. For this distribution, the minimum value is 1.

- The first Quartile or the 25th percentile

This is the beginning of the boxplot. For this distribution, it is 2.5.

- The third quartile or the 75th percentile

This is the end of the boxplot. For this distribution, it is 5.

- The Median

This is the number at the middle of the distribution when all the variables are arranged in ascending or descending order.

This is represented by the point that coincides with the line drawn on the boxplot. For this distribution, the Median is 4.

The other variables describing the dataset that can be obtained from the boxplot include;

1) The Interquartile Range (IQR)

The IQR is a measure of the spread of the distribution and it is given mathematically as the difference between the third and first quartile.

IQR = (Third quartile or 75th percentile) - (First quartile or 25th percentile)

IQR = 5 - 2.5 = 2.5

2) The range.

The range is given as the difference between the maximum and minimum values of a distribution.

Range = (Maximum value) - (Minimum Value) = 10 - 1 = 9.

Hope this Helps!!!

4 0
3 years ago
Write y=-2/3x-4 in standard form using integers
Scilla [17]

Answer:

<h2>2x + 3y = -12</h2>

Step-by-step explanation:

The standard form of an equation of a line:

Ax+By=C

We have:

y=-\dfrac{2}{3}x-4

Convert to the standard form:

y=-\dfrac{2}{3}x-4            <em>multiply both sides by 3</em>

3y=-2x-12              <em>add 2x to both sides</em>

2x+3y=-12

5 0
3 years ago
George bought a bag of dog food that was 1/3 pounds. He fed his dog 5 times with this bag of food. How many pounds of food did h
miv72 [106K]

Answer:

\dfrac{5}{3}\ \text{pounds}

Step-by-step explanation:

George bought a bag of dog food that was 1/3 pounds.

George fed his dog 5 times with this bag of food.

We need to find how many pounds of food did the dog eat at each feeding. Let it be x.

x=\dfrac{1}{3}\times 5\\\\x=\dfrac{5}{3}\ \text{pounds}

So, the dog eat \dfrac{5}{3}\ \text{pounds} of food at each feeding.

3 0
3 years ago
Tuto
Damm [24]

Answer:

8r+8pg-pq

Step-by-step explanation:

The subtractable pg cancels out one of the 9 pg's. So 9 pg-1 pg= 8 pg

Hope this helps!

8 0
3 years ago
The area of a circle is 100π cm². What is the circumference, in centimeters? Express your answer in terms of \piπ.
Montano1993 [528]
35.45 cm squared. Hope this helps
3 0
3 years ago
Read 2 more answers
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