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4 years ago

246, 299, 360, 404, 379, 199, 279, 749, 794, 849, 914

Mathematics

1 answer:

Sholpan [36]4 years ago

5 0

Answer:

Mean = 497.5

Median = 379.0

First Quartile = 289

Third Quartile = 771.5

Step-by-step explanation:

Mean is used to measure the central tendency of data which represents the whole data in the best way. It can be found as the ratio of the sum of all the observations to the total number of observations.

⇒ $Mean=\frac{246+ 299+ 360+ 404+ 379+ 199+ 279+ 749+ 794+ 849+ 914}{11}$

⇒ Mean = 497.5

Median is the middle observation of given data. It can be found by following steps:

Arranging data in ascending or descending order.

Taking the average of middle two value if the total number of observation is even, and this average is our median.

or, if we odd number of observation then the most middle value is our median.

Here, number of observation is 11.

So the middle value is (11+1)÷2 = 6th term

⇒ Median = 379

The mode is the observation which has a high number of repetitions (frequency).

Here frequency of all observation is same. So, it is multi- modal data.

First Quartile is the middle value between Minimum value and Median of data after arranging data in ascending order.

First Quartile (Q₁) = 289

The third Quartile is the middle value between Median and Maximum Value of data after arranging data in ascending order.

Third Quartile (Q₃) = 771.5

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Match each series with the equivalent series written in sigma notation

PIT_PIT [208]

Answer:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

Step-by-step explanation:

Given

See attachment for complete question

Required

Match equivalent expressions

Solving (a):

$3 + 12 + 48 + 192 + 768$

The expression can be written as:

$3 \to 3*4^{0$ --- 0

$12 \to 3 * 4^{1$ ---- 1

$48 \to 3 * 4^{2$ --- 2

$192 \to 3 * 4^{3$ ---- 3

$768 \to 3 * 4^{4$ ---- 4

For the nth term, the expression is:

$Term = 3 * 4^{n$ ---- n

So, the summation is:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

Solving (b):

$4 + 32 + 256 + 2048 + 16384$

The expression can be written as:

$4 \to 4 * 8^0$ --- 0

$32 \to 4 * 8^1$ ---- 1

$256 \to 4 * 8^2$ --- 2

$2048 \to 4 * 8^3$ ---- 3

$16384 \to 4 * 8^4$ ---- 4

For the nth term, the expression is:

$Term \to 4 * 8^n$ ---- n

So, the summation is:

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

Solving (c):

$2 + 6 + 18 + 54 + 162$

The expression can be written as:

$2 \to 2 * 3^0$ --- 0

$6 \to 2 * 3^1$ ---- 1

$18 \to 2 * 3^2$ --- 2

$54 \to 2 * 3^3$ ---- 3

$162 \to 2 * 3^4$ ---- 4

For the nth term, the expression is:

$Term \to 2 * 3^n$ ---- n

So, the summation is:

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

Solving (d):

$3 + 15 + 75 + 375 + 1875$

The expression can be written as:

$3 \to 3 * 5^0$ --- 0

$15 \to 3 * 5^1$ ---- 1

$75 \to 3 * 5^2$ --- 2

$375 \to 3 * 5^3$ ---- 3

$1875 \to 3 * 5^4$ ---- 4

For the nth term, the expression is:

$Term \to 3 * 5^n$ ---- n

So, the summation is:

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

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3 years ago

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abruzzese [7]

Answer:

4. SR= 17 (opposite angle of parallogram are equal)

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3 years ago

Which statement is true about every rectangular pyramid?

Ratling [72]

Answer:

At least two of the lateral faces are congruent.

Step-by-step explanation:

Because the words "at least" are used this means that at a minimum 2 of the faces are congruent. Because the base is in the shape of a triangle, this will definitely be true.

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3 years ago

Read 2 more answers

For every 3 laps that Jackie swims, Ronnie swims 4 laps. During practice, they swam a combined total of 63 laps. How many laps d

Flura [38]

Answer:

36 laps Ronnie swim during practice .

Step-by-step explanation:

Let us assume that the laps that Ronnie swims be x .

Let us assume that the laps that Jackie swims be y .

As given

For every 3 laps that Jackie swims, Ronnie swims 4 laps.

i.e

3 × laps that Ronnie swims = 4 × laps that Jackie swims

3 × x = 4 × y

3x = 4y

Equation becomes

x + y = 63

Thus by using 3x = 4y .

$y = \frac{3x}{4}$

Thus

$x +\frac{3x}{4} = 63$

4x + 3x = 63 × 4

7x = 252

x = 36

Put the value of x in the equation x + y = 63

36 + y = 63

y = 63 - 36

y = 27

Therefore the 36 laps Ronnie swim during practice .

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Quadrilateral BCDE is inscribed in circle A. The measure of ⏜ is 73°. The measure of ⏜ is 53° and the measure of ⏜ is 102°. Dete

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Answer: c

Step-by-step explanation:

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3 years ago