Answer: x + 7/2
Explanation:
1/2(2x + 7) = x + 7/2
Answer:
63 men said no.
Step-by-step explanation
3/5 * 2/2 = 6/10, 6/10 - 3/10 (women) = 3/10 meaning 7/10 men said no. 90*1.7 = 153, 153-90=63
Answer:
Your parents will retire in 18 years. ... You expect to earn 12% annually on the account. ... An investment will pay $100 at the end of each of the next 3 years, $200 at the end of Year 4, ...
![f(n)\in\mathcal O(g(n))](https://tex.z-dn.net/?f=f%28n%29%5Cin%5Cmathcal%20O%28g%28n%29%29)
is to say
![|f(n)|\le M_1|g(n)|](https://tex.z-dn.net/?f=%7Cf%28n%29%7C%5Cle%20M_1%7Cg%28n%29%7C)
for all
![n](https://tex.z-dn.net/?f=n)
beyond some fixed
![n_1](https://tex.z-dn.net/?f=n_1)
.
Similarly,
![d(n)\in\mathcal O(h(n))](https://tex.z-dn.net/?f=d%28n%29%5Cin%5Cmathcal%20O%28h%28n%29%29)
is to say
![|d(n)|\le M_2|h(n)|](https://tex.z-dn.net/?f=%7Cd%28n%29%7C%5Cle%20M_2%7Ch%28n%29%7C)
for all
![n\ge n_2](https://tex.z-dn.net/?f=n%5Cge%20n_2)
.
From this we can gather that
![|f(n)+d(n)|\le|f(n)|+|d(n)|\le M_1|g(n)|+M_2|h(n)|\le M(|g(n)|+|h(n)|)](https://tex.z-dn.net/?f=%7Cf%28n%29%2Bd%28n%29%7C%5Cle%7Cf%28n%29%7C%2B%7Cd%28n%29%7C%5Cle%20M_1%7Cg%28n%29%7C%2BM_2%7Ch%28n%29%7C%5Cle%20M%28%7Cg%28n%29%7C%2B%7Ch%28n%29%7C%29)
where
![M](https://tex.z-dn.net/?f=M)
is the larger of the two values
![M_1](https://tex.z-dn.net/?f=M_1)
and
![M_2](https://tex.z-dn.net/?f=M_2)
, or
![M=\max\{M_1,M_2\}](https://tex.z-dn.net/?f=M%3D%5Cmax%5C%7BM_1%2CM_2%5C%7D)
. Then the last term is bounded above by
![M(|g(n)|+|h(n)|)\le2M\max\{|g(n)|,|h(n)|\}](https://tex.z-dn.net/?f=M%28%7Cg%28n%29%7C%2B%7Ch%28n%29%7C%29%5Cle2M%5Cmax%5C%7B%7Cg%28n%29%7C%2C%7Ch%28n%29%7C%5C%7D)
from which it follows that
Answer:
Step-by-step explanation:
a). Mean of the given data set = ![\frac{32+28+18+40+22}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B32%2B28%2B18%2B40%2B22%7D%7B5%7D)
= 28
b). x
![(x-\overline{x})^2](https://tex.z-dn.net/?f=%28x-%5Coverline%7Bx%7D%29%5E2)
32 32-28 = 4 16
28 28 - 28 = 0 0
18 18 - 28 = -10 100
40 40 - 28 = 12 144
22 22 - 28 = -6 36
= 296
c). Standard deviation = ![\sqrt{\frac{\sum (x-\overline{x})^2}{n}}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B%5Csum%20%28x-%5Coverline%7Bx%7D%29%5E2%7D%7Bn%7D%7D)
= ![\sqrt{\frac{296}{5} }](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B296%7D%7B5%7D%20%7D)
= 7.69
d). Mean of the new set of weights = ![\frac{32+33+34+35+36}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B32%2B33%2B34%2B35%2B36%7D%7B5%7D)
= 34
Since mean of the data set is more close to each data, standard deviation will be less than the deviation given in part (c).