Answer:
We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 mg .
Step-by-step explanation:
Given -
The sample size is large then we can use central limit theorem
n = 50 ,
Standard deviation
= 7.1
Mean 
= 110
1 - confidence interval = 1 - .98 = .02
= 2.33
98% confidence interval for the mean caffeine content for cups dispensed by the machine = 
= 
= 
First we take + sign
= 112.34
now we take - sign
= 107.66
We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 .
Answer:
No
Step-by-step explanation:
An extraneous solution is a root of a transformed equation which is not a root of the original equation because it was not included in the domain of the original equation.
Ahmed is solving ![2\sqrt[3]{x-7}+11=3](https://tex.z-dn.net/?f=2%5Csqrt%5B3%5D%7Bx-7%7D%2B11%3D3)
for x.
His steps were:
![\begin{aligned}2\sqrt[3]{x-7}&=-8\\ \sqrt[3]{x-7}&=-4\\ \left(\sqrt[3]{x-7}\right)^3&=(-4)^3\\ x-7&=-64 \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D2%5Csqrt%5B3%5D%7Bx-7%7D%26%3D-8%5C%5C%20%20%5Csqrt%5B3%5D%7Bx-7%7D%26%3D-4%5C%5C%20%20%5Cleft%28%5Csqrt%5B3%5D%7Bx-7%7D%5Cright%29%5E3%26%3D%28-4%29%5E3%5C%5C%20%20x-7%26%3D-64%20%5Cend%7Baligned%7D)
Since cube roots <u>do not give two solutions when solved</u>, it is <u>not necessary </u>to check his answers for extraneous solutions.
To figure out the average of Michael and Melissa we must add up all their test scores and divide the by 7; which is the number of tests they took.
Michael:
(80+76+73+70+40+25+10)/7
Melissa:
(88+83+75+70+60+65+62)/7
Michael's average is 53.4
Melissa's average is 71.9
So Melissa is earning a C in Latin.
I think that
the triangle is 6
the square is -5
and the star is -20
but i would get a second answer bc i cant certainly say that<span />
