Answer:
x=65
Step-by-step explanation:
the sum of the angles of any triangle is equal to 180°. So, we do 180-50= 130. Then we divide 30 by two because there are two remaining angles so 130/2=65. x=65
Answer: We can expect about 40.13% of bottles to have a volume less than 32 oz.
Step-by-step explanation:
Given : The volumes of soda in quart soda bottles can be described by a Normal model with
![\mu=\text{32.3 oz}\\\\\sigma=\text{1.2 oz}](https://tex.z-dn.net/?f=%5Cmu%3D%5Ctext%7B32.3%20oz%7D%5C%5C%5C%5C%5Csigma%3D%5Ctext%7B1.2%20oz%7D)
Let X be the random variable that represents the volume of a randomly selected bottle.
z-score :![\dfrac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
For x = 32 oz
![z=\dfrac{32-32.3}{1.2}=-0.25](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B32-32.3%7D%7B1.2%7D%3D-0.25)
The probability of bottles have a volume less than 32 oz is given by :-
[Using standard normal table]
In percent, ![0.4012937\times100=40.12937\%\approx40.13\%](https://tex.z-dn.net/?f=0.4012937%5Ctimes100%3D40.12937%5C%25%5Capprox40.13%5C%25)
Hence, we can expect about 40.13% of bottles to have a volume less than 32 oz.
Answer:
the vertex is 14yx
Step-by-step explanation:
The <em>correct answers</em> are:
C) a(n) = 0.3+(n-1)0.6
; and
C) a(n) = 47+ (n-1)(-15)
Explanation:
#1) This is an arithmetic sequence, since we are adding the same value to each term to find the next term. We add 0.6 each time, so this is the common difference. The first term is 0.3. This goes in the formula
![a(n)=a_1+d(n-1) \\a(n)=0.3+0.6(n-1) \\a(n)=0.3+(n-1)(0.6)](https://tex.z-dn.net/?f=%20a%28n%29%3Da_1%2Bd%28n-1%29%20%5C%5Ca%28n%29%3D0.3%2B0.6%28n-1%29%20%5C%5Ca%28n%29%3D0.3%2B%28n-1%29%280.6%29%20)
#2) This is also an arithmetic sequence. This time, we add -15. The first term of this one is 47. This gives us:
![a(n)=a_1+d(n-1) \\a(n)=47+(-15)(n-1) \\a(n)=47+(n-1)(-15)](https://tex.z-dn.net/?f=%20a%28n%29%3Da_1%2Bd%28n-1%29%20%5C%5Ca%28n%29%3D47%2B%28-15%29%28n-1%29%20%5C%5Ca%28n%29%3D47%2B%28n-1%29%28-15%29%20)
The greatest common factor is 4.
28/32 / 4 = 7/8