Answer:
(a)
-- Population Mean
(b)
--- Population standard deviation
(c) See Explanation
Step-by-step explanation:
Given:
Cigarette tax for 20 regions
Solving (a): The population mean
This is calculated as:
![\bar x = \frac{\sum x}{n}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B%5Csum%20x%7D%7Bn%7D)
![\sum x = 1.36 + 1.70 + 2.50 + 0.45 + 1.18 + 0.64 + 3.46 + 0.57 + 2.00 + 0.80 + 1.60 +0.98 + 0.36 + 2.24 + 4.35 + 0.62 + 2.70 + 1.78 + 1.53 + 0.84](https://tex.z-dn.net/?f=%5Csum%20x%20%3D%201.36%20%2B%201.70%20%2B%202.50%20%2B%200.45%20%2B%201.18%20%2B%200.64%20%2B%203.46%20%2B%200.57%20%2B%202.00%20%2B%200.80%20%2B%201.60%20%2B0.98%20%2B%200.36%20%2B%202.24%20%2B%204.35%20%2B%200.62%20%2B%202.70%20%2B%201.78%20%2B%201.53%20%2B%200.84)
![\sum x = 31.66](https://tex.z-dn.net/?f=%5Csum%20x%20%3D%2031.66)
![n = 20](https://tex.z-dn.net/?f=n%20%3D%2020)
So, we have:
![\bar x= \frac{31.66}{20}](https://tex.z-dn.net/?f=%5Cbar%20x%3D%20%5Cfrac%7B31.66%7D%7B20%7D)
![\bar x= 1.583](https://tex.z-dn.net/?f=%5Cbar%20x%3D%201.583)
Solving (b): The population standard deviation
This is calculated as:
![s = \sqrt{\frac{\sum( x - \bar x)^2}{n}](https://tex.z-dn.net/?f=s%20%3D%20%5Csqrt%7B%5Cfrac%7B%5Csum%28%20x%20-%20%5Cbar%20x%29%5E2%7D%7Bn%7D)
![\sum (x -\bar x)^2 = (1.36 - 1.583)^2 + (1.70 - 1.583)^2+ (2.50 - 1.583)^2+ (0.45 - 1.583)^2+ (1.18 - 1.583)^2+ (0.64 - 1.583)^2+ (3.46 - 1.583)^2+ (0.57 - 1.583)^2+ (2.00 - 1.583)^2+ (0.80 - 1.583)^2+ (1.60 - 1.583)^2+(0.98 - 1.583)^2+ (0.36 - 1.583)^2+ (2.24 - 1.583)^2+ (4.35 - 1.583)^2+ (0.62 - 1.583)^2+ (2.70 - 1.583)^2+ (1.78 - 1.583)^2+ (1.53 - 1.583)^2+ (0.84- 1.583)^2](https://tex.z-dn.net/?f=%5Csum%20%28x%20-%5Cbar%20x%29%5E2%20%3D%20%281.36%20-%201.583%29%5E2%20%2B%20%281.70%20-%201.583%29%5E2%2B%20%282.50%20-%201.583%29%5E2%2B%20%280.45%20-%201.583%29%5E2%2B%20%281.18%20-%201.583%29%5E2%2B%20%280.64%20-%201.583%29%5E2%2B%20%283.46%20-%201.583%29%5E2%2B%20%280.57%20-%201.583%29%5E2%2B%20%282.00%20-%201.583%29%5E2%2B%20%280.80%20-%201.583%29%5E2%2B%20%281.60%20-%201.583%29%5E2%2B%280.98%20-%201.583%29%5E2%2B%20%280.36%20-%201.583%29%5E2%2B%20%282.24%20-%201.583%29%5E2%2B%20%284.35%20-%201.583%29%5E2%2B%20%280.62%20-%201.583%29%5E2%2B%20%282.70%20-%201.583%29%5E2%2B%20%281.78%20-%201.583%29%5E2%2B%20%281.53%20-%201.583%29%5E2%2B%20%280.84-%201.583%29%5E2)
![\sum (x -\bar x)^2 = 21.29222](https://tex.z-dn.net/?f=%5Csum%20%28x%20-%5Cbar%20x%29%5E2%20%3D%2021.29222)
So:
![s = \sqrt{\frac{21.2922}{20}](https://tex.z-dn.net/?f=s%20%3D%20%5Csqrt%7B%5Cfrac%7B21.2922%7D%7B20%7D)
![s = \sqrt{1.06461}](https://tex.z-dn.net/?f=s%20%3D%20%5Csqrt%7B1.06461%7D)
![s = 1.032](https://tex.z-dn.net/?f=s%20%3D%201.032)
Solving (c):
Population mean tells the average amount while the standard deviation represents the spread from the calculated mean
Option (4) is correct
Answer:
Never
Step-by-step explanation:
Adding together an obtuse angle (greater than 90°) and acute angle (less than 90°) should result in an obtuse angle every time
Answer:
y is the same as 1y. so 9y + 1y = 10y
51.36 is the answer.
The equation is total=original(1+% in decimal form)
Well, first of all, the first statement (ABC = ADC) looks like it just says
that the two halves of the little square ... each side of the diagonal ...
are congruent. That's no big deal, and it's no help in answering the
question.
The effect of the dilation is that all the DIMENSIONS of the square
are doubled ... each side of the square becomes twice as long.
Then, when you multiply (length x width) to get the area, you'd have
Area = (2 x original length) x (2 x original width)
and that's
the same as (2 x 2) x (original length x original width)
= (4) x (original area) .
Here's an easy, useful factoid to memorize:
-- Dilate a line (1 dimension) by 'x' times . . . multiply the length by x¹
-- Dilate a shape (2 dimensions) by 'x' . . . multiply area by x²
-- Dilate a solid (3 dimensions) by 'x' . . . multiply volume by x³
And that's all the dimensions we have in our world.
_______________________________
Oh, BTW . . .
-- Dilate a point (0 dimensions) by 'x' . . . multiply it by x⁰ (1)