Answer:
p value is 0.1343
Step-by-step explanation:
Null: u>= 442
Alternative: u < 442
Using the formula for z score:
(x - u)/sd/√n
Where x is 438, u = 442 sd can be determined from the variance = √variance =√576 = 24 and n = 44
z score = 438-442 / (24/√44)
z score = -4/(24/6.6332)
z = -4/3.6182
z =-1.1055
Now let's find the p value at 0.1 significance level using a z score of -1.1055, using a p value calculator, p value is 0.1343 which greatest than 0.1 meaning the day is not sufficient enough to conclude that the machine is underfilling the bags.
His first payment is $100, thus a₁ = 100.
the next "term", month will be 1.1 times more than the one before, namely r = 1.1, the common ratio.
![\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=100\\ r=1.1\\ n=20 \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7Bsum%20of%20a%20finite%20geometric%20sequence%7D%0A%5C%5C%5C%5C%0AS_n%3D%5Csum%5Climits_%7Bi%3D1%7D%5E%7Bn%7D%5C%20a_1%5Ccdot%20r%5E%7Bi-1%7D%5Cimplies%20S_n%3Da_1%5Cleft%28%20%5Ccfrac%7B1-r%5En%7D%7B1-r%7D%20%5Cright%29%5Cquad%20%0A%5Cbegin%7Bcases%7D%0An%3Dn%5E%7Bth%7D%5C%20term%5C%5C%0Aa_1%3D%5Ctextit%7Bfirst%20term%27s%20value%7D%5C%5C%0Ar%3D%5Ctextit%7Bcommon%20ratio%7D%5C%5C%0A----------%5C%5C%0Aa_1%3D100%5C%5C%0Ar%3D1.1%5C%5C%0An%3D20%0A%5Cend%7Bcases%7D)
![\bf \sum\limits_{i=1}^{20}~100(1.1)^{i-1}\qquad \qquad\qquad \qquad S_{20}=100\left( \cfrac{1-1.1^{20}}{1-1.1} \right) \\\\\\ S_{20}=100\left( \cfrac{1-\stackrel{\approx}{6.727499949}}{-0.1} \right)\implies S_{20}\approx 100(57.27499949) \\\\\\ S_{20}\approx 5727.4999493256](https://tex.z-dn.net/?f=%5Cbf%20%5Csum%5Climits_%7Bi%3D1%7D%5E%7B20%7D~100%281.1%29%5E%7Bi-1%7D%5Cqquad%20%5Cqquad%5Cqquad%20%20%5Cqquad%20S_%7B20%7D%3D100%5Cleft%28%20%5Ccfrac%7B1-1.1%5E%7B20%7D%7D%7B1-1.1%7D%20%5Cright%29%0A%5C%5C%5C%5C%5C%5C%0AS_%7B20%7D%3D100%5Cleft%28%20%5Ccfrac%7B1-%5Cstackrel%7B%5Capprox%7D%7B6.727499949%7D%7D%7B-0.1%7D%20%5Cright%29%5Cimplies%20S_%7B20%7D%5Capprox%20100%2857.27499949%29%0A%5C%5C%5C%5C%5C%5C%0AS_%7B20%7D%5Capprox%205727.4999493256)
is the serie divergent or convergent?
well, to make it short, when the common ratio is 0 < | r | < 1, namely a fraction between 0 and 1, only then the serie is convergent, namely it reaches a fixed value, now in this case, 1.1 is a value larger than anything between 0 and 1, so no dice.
Answer:
0.625
Step-by-step explanation:
Answer:
She spend 6y dollars on scarves.
Step-by-step explanation:
The question states that y represents the number of scarves she bought, so the first and second statements would be incorrect. You don't know how much she spent in total, so the fourth statement would also be wrong. So it's the third statement.
Also, you can just do 2*(3y), which is 6y.
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36