Answer:
![-0.674 = \frac{X -0.904}{0.295}](https://tex.z-dn.net/?f=%20-0.674%20%3D%20%5Cfrac%7BX%20-0.904%7D%7B0.295%7D)
![X= 0.904 -0.674*0.295 = 0.705](https://tex.z-dn.net/?f=%20X%3D%200.904%20-0.674%2A0.295%20%3D%200.705)
![0.674 = \frac{X -0.904}{0.295}](https://tex.z-dn.net/?f=%200.674%20%3D%20%5Cfrac%7BX%20-0.904%7D%7B0.295%7D)
![X= 0.904 +0.674*0.295 = 1.103](https://tex.z-dn.net/?f=%20X%3D%200.904%20%2B0.674%2A0.295%20%3D%201.103)
So we expect about 50% of the middle values within 0.705 and 1.103 g
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the amounts of nicotine in a certain brand of a population, and for this case we know the distribution for X is given by:
Where
and
And the best way to solve this problem is using the normal standard distribution and the z score given by:
We want to find a two values that accumulates the middel 50% of the data. So we need to find a quantile who accumulates (1-0.5)/2 = 0.25 of the area on each tail and we got:
![z = \pm 0.674](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cpm%200.674)
Since P(Z<-0.674) = 0.25 and P(Z>0.674) =0.25. And using this value we can find the possible values of X
![-0.674 = \frac{X -0.904}{0.295}](https://tex.z-dn.net/?f=%20-0.674%20%3D%20%5Cfrac%7BX%20-0.904%7D%7B0.295%7D)
![X= 0.904 -0.674*0.295 = 0.705](https://tex.z-dn.net/?f=%20X%3D%200.904%20-0.674%2A0.295%20%3D%200.705)
![0.674 = \frac{X -0.904}{0.295}](https://tex.z-dn.net/?f=%200.674%20%3D%20%5Cfrac%7BX%20-0.904%7D%7B0.295%7D)
![X= 0.904 +0.674*0.295 = 1.103](https://tex.z-dn.net/?f=%20X%3D%200.904%20%2B0.674%2A0.295%20%3D%201.103)
So we expect about 50% of the middle values within 0.705 and 1.103 g
sin (x) = -1
arcsin (-1) = x
x = -90
and multiples of 360
x =-90, 270,....
x =-90 + 360n where n is an integer
or in radians
-pi/2 + 2*pi *n where n is an integer
Answer:
89
Step-by-step explanation:
cuz
Answers: A) $44,944
B) $50,499.0784
Math: Using the percentage calculator linked below 6% of $40,000 is $2,400. Since you're getting your second raise after your first and since it is a 6% raise from what you're getting paid at that time we add pay raise 1 to your starting pay before calculating the 6% for pay raise 2. $40,000+$2,400=$42,400. 6% of $42,400 is $2,544. $42,400+$2,544=$44,944, Since that is two pay raises that would be your earnings at the end of year two (answer A).
We continue calculating 6% then adding that onto the total before calculating it for the next year for problem B.
6% of $44,944 is $2,696.64. $44,944+$2,696.64=$47,640.64.
6% of $47,640.64 is $2,858.4384. $47,640.64+$2,858.4384=$50,499.0784. That's answer B.
Hopefully you can figure out C on your own! I feel a little bad for giving a partial answer but I think you can do this!
Percentage calculator used-https://percentagecalculator.net/
Note: can't handle commas, remove all commas before entering data in.
Answer:
8 and 3
Step-by-step explanation:
8+3=11
8-3= 5