Answer:
72
Step-by-step explanation:
Answer:
or ![0.325\ liters](https://tex.z-dn.net/?f=0.325%5C%20liters)
Step-by-step explanation:
we know that
To find the total amount of juice Carlos mixed, sum the liters of orange juice plus the liters of pineapple juice
Let
x------> liters of orange juice
y-----> liters of pineapple juice
z----> total amount of juice mixed
so
![z=x+y](https://tex.z-dn.net/?f=z%3Dx%2By)
we have
![x=\frac{2}{10}\ liters](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2%7D%7B10%7D%5C%20liters)
![y=\frac{1}{8}\ liters](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B8%7D%5C%20liters)
substitute
![z=\frac{2}{10}+\frac{1}{8}=\frac{4*2+5*1}{40}=\frac{13}{40}\ liters](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B2%7D%7B10%7D%2B%5Cfrac%7B1%7D%7B8%7D%3D%5Cfrac%7B4%2A2%2B5%2A1%7D%7B40%7D%3D%5Cfrac%7B13%7D%7B40%7D%5C%20liters)
Convert to decimal form
![\frac{13}{40}\ liters=0.325\ liters](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B40%7D%5C%20liters%3D0.325%5C%20liters)
Answer:
No Because the curve indicates that the rate of change is not constant!
Step-by-step explanation:
Linear functions are straight lines diagonally!
This function shows a rate of growth through time which isn't describing constant growth.
Constant = Linear
Answer:
a) 0.00698
b) 0.00127
c) 0.00249
d) (0.00449,0.00947)
Step-by-step explanation:
We are given the following in the question:
Number of people vaccinated, n = 4300
Number of subjects that developed illness after vaccination, x = 30
a) point estimate of the population proportion that were vaccinated with the vaccine but still developed the illness.
![p = \displaystyle\frac{x}{n} = \frac{30}{4300} = 0.00698](https://tex.z-dn.net/?f=p%20%3D%20%5Cdisplaystyle%5Cfrac%7Bx%7D%7Bn%7D%20%3D%20%5Cfrac%7B30%7D%7B4300%7D%20%3D%200.00698)
b) standard error of this estimate
![\text{Standard error} = \sqrt{\displaystyle\frac{pq}{n}} = \sqrt{\displaystyle\frac{p(1-p)}{n}} = \sqrt{\displaystyle\frac{0.00698\times 0.99302}{4300}} = 0.00127](https://tex.z-dn.net/?f=%5Ctext%7BStandard%20error%7D%20%3D%20%5Csqrt%7B%5Cdisplaystyle%5Cfrac%7Bpq%7D%7Bn%7D%7D%20%3D%20%5Csqrt%7B%5Cdisplaystyle%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D%20%3D%20%5Csqrt%7B%5Cdisplaystyle%5Cfrac%7B0.00698%5Ctimes%200.99302%7D%7B4300%7D%7D%20%3D%200.00127)
c) margin of error for a 95% confidence interval
![z_{critical}\text{ at}~\alpha_{0.05} = 1.96](https://tex.z-dn.net/?f=z_%7Bcritical%7D%5Ctext%7B%20at%7D~%5Calpha_%7B0.05%7D%20%3D%201.96)
![\text{Margin of error} = z_\text{critical}\times \text{Standard error}\\= \pm 1.96\times 0.00127 = \pm 0.00249](https://tex.z-dn.net/?f=%5Ctext%7BMargin%20of%20error%7D%20%3D%20z_%5Ctext%7Bcritical%7D%5Ctimes%20%5Ctext%7BStandard%20error%7D%5C%5C%3D%20%5Cpm%201.96%5Ctimes%200.00127%20%3D%20%5Cpm%200.00249)
d) 95% confidence interval
![p\pm \text{Margin of error}\\= 0.00698\pm 0.00249\\=(0.00449,0.00947)](https://tex.z-dn.net/?f=p%5Cpm%20%5Ctext%7BMargin%20of%20error%7D%5C%5C%3D%200.00698%5Cpm%200.00249%5C%5C%3D%280.00449%2C0.00947%29)