Answer:
2 students in each group
Step-by-step explanation:
If there were 5 groups and after a while 7 students leave early and 3 students remain to do the activity, if you add 7 + 3 = 10 divide it by 5, the number of groups in the activity, you would get 2 students in each group.
Given:
Population proportion,
![\mu _{p}](https://tex.z-dn.net/?f=%5Cmu%20_%7Bp%7D)
= 57% = 0.57
Population standard deviation, σ = 3.5% = 0.035
Sample size, n = 40
Confidence level = 95%
The standard error is
![SE_{p} = \sqrt{ \frac{p(1-p)}{n} } = \sqrt{ \frac{0.57*0.43}{40} } =0.0783](https://tex.z-dn.net/?f=SE_%7Bp%7D%20%3D%20%20%5Csqrt%7B%20%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%20%7D%20%3D%20%5Csqrt%7B%20%5Cfrac%7B0.57%2A0.43%7D%7B40%7D%20%7D%20%3D0.0783)
The confidence interval is
![\hat{p} \pm z^{*}SE_{p}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%20%5Cpm%20z%5E%7B%2A%7DSE_%7Bp%7D)
where
![\hat{p}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D)
= sample proportion
z* = 1.96 at the 95% confidence lvvel
The sample proportion lies in the interval
(0.57-1.96*0.0783, 0.57+1.96*0.0783) = (0.4165, 0.7235)
Answer: Between 0.417 and 72.4), or between (41% and 72%)
Answer:
Step-by-step explanation:
11.04 = 10(1.02)^n
1.104 = 1.02^n
ln 1.104 = ln 1.02^n
ln 1.104 = n ln 1.02
n = ln 1.104/ ln 1.02
n = 4.99630409516
4.99 can be rounded to 5.
So a reasonable domain would be 0 ≤ x < 5
PART B)
f(0) = 10(1.02)^0
f(0) = 10(1)
f(0) = 10
The y-intercept represents the height of the plant when they began the experiment.
f(1) = 10(1.02)^1
f(1) = 10(1.02)
f(1) = 10.2
(1, 10.2)
f(5) = 10(1.02)^5
f(5) = 10(1.1040808)
f(5) = 11.040808
f(1)=10(1.02)^1
f(1)=10.2
Average rate= (fn2-fn1)/(n2-n1)
=11.04-10.2/(5-1)
=0.22
the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.
The Pythagorean theorem is the idea that the sum of the two legs which are both squared is equal to the hypotenuse's length squared.
*<em>look at the image I attached for a better explanation</em>
By looking at the picture, we are missing the leg's length, and by using the Pythagorean theorem, we get the equation
![?^2+5^2 = 13^2\\?^2 + 25 = 169\\?^2 = 144\\? = 12](https://tex.z-dn.net/?f=%3F%5E2%2B5%5E2%20%3D%2013%5E2%5C%5C%3F%5E2%20%2B%2025%20%3D%20169%5C%5C%3F%5E2%20%3D%20144%5C%5C%3F%20%3D%2012)
Thus the <u>missing side length is 12 cm</u>
Hope that helps!