Answer:
a) yes
b) ( 0.0280 , 0.1720 )
c) No
Step-by-step explanation:
A) Determine if the sample sizes are large enough
where :
ages between ( 18 to 29 )
p1 = 0.48 ,
n1 = 178 , ∴ n1 P1 = 85.44 also n1 ( 1 - p1 ) = 92.56
ages between ( 50 to 64 )
P2 = 0.03 ,
n2 = 427 ∴ n2p2 = 12.81 also n2( 1 -p2 ) = 414.19
<em>since all the values ae above 10 we can conclude that the sample sizes are large enough </em>
<em>answer = yes </em>
<u>B) Estimate the difference in the proportion of adult Americans aged 18 to 29</u>
= ( 0.0280 , 0.1720 )
attached below is the detailed solution
C) zero is not included in the interval
Answer:
The answer is B.
Step-by-step explanation:
There are three 20 second time periods in 1 minute. Three times eight is equal to 24.
The dimensions of the square base after cutting the corners will be (40-2x). The depth of the box will be x, so its volume is given by
V = x(40-2x)²
You can differentiate this to get
V' = 12x² -320x -1600
Setting this to zero and factoring gives
(3x-20)(x-20) = 0
The appropriate choice of solutions is
x = 20/3 = 6 2/3
The
dimensions of the box of maximum volume are
26 2/3 in square by 6 2/3 in deepThe
maximum volume is
(80/3 in)²(20/3 in) =
4740 20/27 in³
Answer:
3*2*3^m*4^m=3^8*2^n
3^m+1*2^2m+1=3^8*2^n
m+1=8
m=7
2m+1=n
n=15
Step-by-step explanation:
from the diagram, we can see that the height or line perpendicular to the parallel sides is 8.5.
likewise we can see that the parallel sides or "bases" are 24.3 and 9.7, so
![\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{parallel~sides}{bases}\\[-0.5em] \hrulefill\\ h=8.5\\ a=24.3\\ b=9.7 \end{cases}\implies \begin{array}{llll} A=\cfrac{8.5(24.3+9.7)}{2}\\\\ A=\cfrac{8.5(34)}{2}\implies A=144.5~in^2 \end{array}](https://tex.z-dn.net/?f=%5Ctextit%7Barea%20of%20a%20trapezoid%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7Bh%28a%2Bb%29%7D%7B2%7D~~%20%5Cbegin%7Bcases%7D%20h%3Dheight%5C%5C%20a%2Cb%3D%5Cstackrel%7Bparallel~sides%7D%7Bbases%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20h%3D8.5%5C%5C%20a%3D24.3%5C%5C%20b%3D9.7%20%5Cend%7Bcases%7D%5Cimplies%20%5Cbegin%7Barray%7D%7Bllll%7D%20A%3D%5Ccfrac%7B8.5%2824.3%2B9.7%29%7D%7B2%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7B8.5%2834%29%7D%7B2%7D%5Cimplies%20A%3D144.5~in%5E2%20%5Cend%7Barray%7D)
