Answer:
c)A cylinder with a volume of π(w³ +2w² )in³
where w represents the width of the cylinder.
Step-by-step explanation:
A cylinder with a volume of π(w³ +2w² )in³
where w represents the width of the cylinder.
The volume of a cylinder is given by V=Bh or V=πr²h
where B is the area of the base and h is the height of the cylinder.
V=πr²h-------equation1
V= π(w³ +2w² )--------- equation2
Comparing equation 1 and equation 2
πr²h=π(w³ +2w² )
r²h=(w³ +2w² )
r²h= w²(w +2 )
Taking w² common leaves w+2 which gives the height or length of the cylinder.
Therefore radius = width and height = length which gives the volume of the cylinder.
false 2z + 10= 12z
2(z + 5) = 10z
Answer:
The probability is ![P(X \le 0.305 ) = 0.01795](https://tex.z-dn.net/?f=P%28X%20%5Cle%200.305%20%29%20%3D%20%20%200.01795)
Step-by-step explanation:
From the question we are told that
The population mean is ![\mu = 0.966 \ grams](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%200.966%20%5C%20grams)
The standard deviation is ![\sigma = 0.315 \ grams](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%20%200.315%20%5C%20%20grams)
Given that the amounts of nicotine in a certain brand of cigarette are normally distributed
Then the probability of randomly selecting a cigarette with 0.305 grams of nicotine or less is mathematically represented as
![P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(\frac{X - \mu }{\sigma } > \frac{0.305 - \mu }{\sigma } )](https://tex.z-dn.net/?f=P%28X%20%5Cle%200.305%20%29%20%3D%20%201%20-%20P%28X%20%3E%20%200.305%29%20%3D%20%201%20-%20%20P%28%5Cfrac%7BX%20-%20%5Cmu%20%7D%7B%5Csigma%20%7D%20%20%3E%20%5Cfrac%7B0.305%20-%20%5Cmu%20%7D%7B%5Csigma%20%7D%20%20%20%29)
Generally
![\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of X )](https://tex.z-dn.net/?f=%5Cfrac%7BX%20-%20%5Cmu%20%7D%7B%5Csigma%20%7D%20%20%3D%20%20Z%20%20%28The%20%20%5C%20standardized%20%5C%20%20value%20%20%5C%20%20of%20%20X%20%29)
So
![P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(Z > \frac{0.305 - 0.966 }{0.315} )](https://tex.z-dn.net/?f=P%28X%20%5Cle%200.305%20%29%20%3D%20%201%20-%20P%28X%20%3E%20%200.305%29%20%3D%20%201%20-%20%20P%28Z%20%3E%20%5Cfrac%7B0.305%20-%200.966%20%7D%7B0.315%7D%20%20%20%29)
![P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(Z >-2.0984 )](https://tex.z-dn.net/?f=P%28X%20%5Cle%200.305%20%29%20%3D%20%201%20-%20P%28X%20%3E%20%200.305%29%20%3D%20%201%20-%20%20P%28Z%20%3E-2.0984%20%29)
From the z-table(reference calculator dot net ) value of ![P(Z >-2.0984 ) =0.98205](https://tex.z-dn.net/?f=P%28Z%20%3E-2.0984%20%29%20%3D0.98205)
So
![P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - 0.98205](https://tex.z-dn.net/?f=P%28X%20%5Cle%200.305%20%29%20%3D%20%201%20-%20P%28X%20%3E%20%200.305%29%20%3D%20%201%20-%20%200.98205)
=> ![P(X \le 0.305 ) = 1 - P(X > 0.305) = 0.01795](https://tex.z-dn.net/?f=P%28X%20%5Cle%200.305%20%29%20%3D%20%201%20-%20P%28X%20%3E%20%200.305%29%20%3D%200.01795)
=> ![P(X \le 0.305 ) = 0.01795](https://tex.z-dn.net/?f=P%28X%20%5Cle%200.305%20%29%20%3D%20%20%200.01795)
Negative minus negative greater negative get rid of the ()
Answer:
-2 3/8
Step-by-step explanation:
-19/20 * 5/2 =
Multiply the numerators
-19*5 = -95
Multiply the denominators
20*2 = 40
-95/40
Both numerator and denominator can be divided by 5
95/5 =19
40/5 =8
=-19/8
If we want to change the improper fraction to a mixed number
8 goes into 19 2 times with 3 left over (2*8 = 16 19-16 = 3)
-2 3/8