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3 years ago

Which is the median of the following data? 12,8,13,12,15,11,10,7

Mathematics

1 answer:

tensa zangetsu [6.8K]3 years ago

7 0

11.5 beause you take the average of 12 and 11

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Analyze the following pattern 1,2,5,10,7

vodka [1.7K]

Answer:

an + 1 = an + 2n -1 ,a 1=1

a8= 50

Step-by-step explanation:

an+1=an+2n-1,a1=1

a6=a5+2x5-1

a6=26

a7=26+11

a7=37

a8=37+13

a8=50

6 0

3 years ago

Find the 2th term of the expansion of (a-b)^4.

vladimir1956 [14]

The second term of the expansion is $-4a^3b$ .

Solution:

Given expression:

$(a-b)^4$

To find the second term of the expansion.

$(a-b)^4$

Using Binomial theorem,

$(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}$

Here, a = a and b = –b

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

Substitute i = 0, we get

$$\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}=1 \cdot \frac{4 !}{0 !(4-0) !} a^{4}=a^4$

Substitute i = 1, we get

$$\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}=\frac{4 !}{3!} a^{3}(-b)=-4 a^{3} b$

Substitute i = 2, we get

$$\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}=\frac{12}{2 !} a^{2}(-b)^{2}=6 a^{2} b^{2}$

Substitute i = 3, we get

$$\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}=\frac{4}{1 !} a(-b)^{3}=-4 a b^{3}$

Substitute i = 4, we get

$$\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=1 \cdot \frac{(-b)^{4}}{(4-4) !}=b^{4}$

Therefore,

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

$=\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}+\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}+\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}+\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}+\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}$ $=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}$

Hence the second term of the expansion is $-4a^3b$ .

3 0

3 years ago

What shape do you get when you plot and join (in order) the following points? (3, 6), (7, 6), (9, 1) and (1, 1) | plz

Lelechka [254]

isosceles trapezoid

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3 0

3 years ago

Read 2 more answers

1kg-1/4-3/8=<br><br>what is it please help

olga_2 [115]

Answer: it's either kg-5/8 or kg + -5/8

Step-by-step explanation:

4 0

2 years ago

I don’t understand please help!

JulijaS [17]

-5/3 can be turned to a mixed number =-1 2/3
So can 18/11 = 1 7/11
10/4 = 2 2/4 or 2 1/2 simplified
And -3/3 as 1
This may make it easier to graph own the number line

5 0

3 years ago