Answer:
The standard deviation of the following data set is 32.2
Step-by-step explanation:
step 1
Find the mean
we have
![[56,78,123,34,67,9,20]](https://tex.z-dn.net/?f=%5B56%2C78%2C123%2C34%2C67%2C9%2C20%5D)
Sum the data and divided by the number of elements
![[56+78+123+34+67+91+20]/7=469/7=67](https://tex.z-dn.net/?f=%5B56%2B78%2B123%2B34%2B67%2B91%2B20%5D%2F7%3D469%2F7%3D67)
step 2
For each number: subtract the Mean and square the result
![[(56-67)^{2},(78-67)^{2},(123-67)^{2},(34-67)^{2},(67-67)^{2},(91-67)^{2},(20-67)^{2}]](https://tex.z-dn.net/?f=%5B%2856-67%29%5E%7B2%7D%2C%2878-67%29%5E%7B2%7D%2C%28123-67%29%5E%7B2%7D%2C%2834-67%29%5E%7B2%7D%2C%2867-67%29%5E%7B2%7D%2C%2891-67%29%5E%7B2%7D%2C%2820-67%29%5E%7B2%7D%5D)
![[121,121,3,136,1,089,0,576,2,209]](https://tex.z-dn.net/?f=%5B121%2C121%2C3%2C136%2C1%2C089%2C0%2C576%2C2%2C209%5D)
step 3
Work out the mean of those squared differences
This value is called the "Variance"
step 4
Take the square root of the variance
Answer:
1. slope is 1/2
2. slope is 1/3
3. slope is 2/3
4. slope is 3
5. y=3x-2
Step-by-step explanation:
<h2>
Answer and Explanation to questions 13,14,15</h2>
13)
as given in the question.
14)
Since Y is the midpoint of XZ. So, Y will divide XZ in equal halves into XY and YZ.
15) 
and
. So, 
<h2>
Answer and Explanation to questions 16,17,18</h2>
∠3 is supplementary to ∠1 means: ∠3 + ∠1 = 180°
And, according to figure ∠1 + ∠2 = 180° as ∠1 and ∠2 form a straight line.
∠3 + ∠1 = 180° .............(i)
∠1 + ∠2 = 180° .............(ii)
subtracting equation (i) and (ii) will give ∠3 = ∠2 ..........(iii)
15) ∠3 is supplementary to ∠1 as given in the question
16) ∠2 is supplementary to ∠1 as shown be equation (ii)
18) ∠3 ≅ ∠2 as shown by equation (iii)
<h2>
Answer and Explanation to questions 19</h2>
∠3 and ∠4 form a straight line. Therefore, ∠3 + ∠4 = 180° .......(i)
∠4 and ∠5 form a straight line. Therefore, ∠4 + ∠5 = 180° .......(ii)
subtracting equation (i) and (ii)
∠3 + ∠4 - (∠4 + ∠5) = 180°-(180°)
∠3 + ∠4 - ∠4 - ∠5 = 180°-180°
∠3 - ∠5 = 0
∴ ∠3 = ∠5 (Hence Proved)
54 = 2 × 3 × 3 × 3 ( as a product of its prime factor ).
The value of 2 in 2481 is 1000 less times the value of 2 in 5072