So if we do 60,000*0.18=10,800 which is the number the price will decrease annually.
1=49,200
2=38,400
3=27,600
4=16,800
:D Hope this helps!
Answer:
Step-by-step explanation:
Set this up under the "mound" curve with 7 in the dead center. One standard deviation to the right is 8, another one is 9, another one is 10. Do the same going to the left, but go down from 7 to 6 to 5 to 4. Between the 6 and the 8 you will find 68% of the weights; between the 5 and the 9 you will find 95 % of the weights; and between 4 and 10 you will find 99.7% of the weights.
The percentage of the oranges from the orchard weighing between 4 oz and 10 oz is 99.7%
I think it's 80 pounds when rounded to the nearest tenth.
Answer:
Remember, the expansion of
is
, where
.
a)
![(1+\sqrt{2})^5=\sum_{k=0}^5 \binom{5}{k}1^{5-k}\sqrt{2}^k=\sum_{k=0}^5 \binom{5}{k}2^{\frac{k}{2}}\\=\binom{5}{0}2^{\frac{0}{2}}+\binom{5}{1}2^{\frac{1}{2}}+\binom{5}{2}2^{\frac{2}{2}}+\binom{5}{3}2^{\frac{3}{2}}+\binom{5}{4}2^{\frac{4}{2}}+\binom{5}{5}2^{\frac{5}{2}}\\=1+5\sqrt{2}+10*2+10*2^{\frac{3}{2}}+5*4+1*2^{\frac{5}{2}}\\=41+5\sqrt{2}+10*2^{\frac{3}{2}}+2^{\frac{5}{2}}](https://tex.z-dn.net/?f=%281%2B%5Csqrt%7B2%7D%29%5E5%3D%5Csum_%7Bk%3D0%7D%5E5%20%5Cbinom%7B5%7D%7Bk%7D1%5E%7B5-k%7D%5Csqrt%7B2%7D%5Ek%3D%5Csum_%7Bk%3D0%7D%5E5%20%5Cbinom%7B5%7D%7Bk%7D2%5E%7B%5Cfrac%7Bk%7D%7B2%7D%7D%5C%5C%3D%5Cbinom%7B5%7D%7B0%7D2%5E%7B%5Cfrac%7B0%7D%7B2%7D%7D%2B%5Cbinom%7B5%7D%7B1%7D2%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%2B%5Cbinom%7B5%7D%7B2%7D2%5E%7B%5Cfrac%7B2%7D%7B2%7D%7D%2B%5Cbinom%7B5%7D%7B3%7D2%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%2B%5Cbinom%7B5%7D%7B4%7D2%5E%7B%5Cfrac%7B4%7D%7B2%7D%7D%2B%5Cbinom%7B5%7D%7B5%7D2%5E%7B%5Cfrac%7B5%7D%7B2%7D%7D%5C%5C%3D1%2B5%5Csqrt%7B2%7D%2B10%2A2%2B10%2A2%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%2B5%2A4%2B1%2A2%5E%7B%5Cfrac%7B5%7D%7B2%7D%7D%5C%5C%3D41%2B5%5Csqrt%7B2%7D%2B10%2A2%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%2B2%5E%7B%5Cfrac%7B5%7D%7B2%7D%7D)
b)
![(1+i)^9=\sum_{k=0}^9 \binom{9}{k}1^{9-k}i^k=\sum_{k=0}^9 \binom{9}{k}i^k\\=\binom{9}{0}i^0+\binom{9}{1}i^1+\binom{9}{2}i^2+\binom{9}{3}i^3+\binom{9}{4}i^4+\binom{9}{5}i^5+\binom{9}{6}i^6+\\+\binom{9}{7}i^7+\binom{9}{8}i^8+\binom{9}{9}i^9\\=1+9i-36-84i+126+126i-+84-36i+9+i\\=16+16i](https://tex.z-dn.net/?f=%281%2Bi%29%5E9%3D%5Csum_%7Bk%3D0%7D%5E9%20%5Cbinom%7B9%7D%7Bk%7D1%5E%7B9-k%7Di%5Ek%3D%5Csum_%7Bk%3D0%7D%5E9%20%5Cbinom%7B9%7D%7Bk%7Di%5Ek%5C%5C%3D%5Cbinom%7B9%7D%7B0%7Di%5E0%2B%5Cbinom%7B9%7D%7B1%7Di%5E1%2B%5Cbinom%7B9%7D%7B2%7Di%5E2%2B%5Cbinom%7B9%7D%7B3%7Di%5E3%2B%5Cbinom%7B9%7D%7B4%7Di%5E4%2B%5Cbinom%7B9%7D%7B5%7Di%5E5%2B%5Cbinom%7B9%7D%7B6%7Di%5E6%2B%5C%5C%2B%5Cbinom%7B9%7D%7B7%7Di%5E7%2B%5Cbinom%7B9%7D%7B8%7Di%5E8%2B%5Cbinom%7B9%7D%7B9%7Di%5E9%5C%5C%3D1%2B9i-36-84i%2B126%2B126i-%2B84-36i%2B9%2Bi%5C%5C%3D16%2B16i)
c)
![(1-\pi)^5=\sum_{k=0}^5 \binom{5}{k}1^{9-k}(-\pi)^k=\sum_{k=0}^5 \binom{5}{k}(-\pi)^k\\=\binom{5}{0}(-\pi)^0+\binom{5}{1}(-\pi)^1+\binom{5}{2}(-\pi)^2+\binom{5}{3}(-\pi)^3+\binom{5}{4}(-\pi)^4+\binom{5}{5}(-\pi)^5\\=1-5+10\pi^2-10\pi^3+5\pi^4-\pi^5](https://tex.z-dn.net/?f=%281-%5Cpi%29%5E5%3D%5Csum_%7Bk%3D0%7D%5E5%20%5Cbinom%7B5%7D%7Bk%7D1%5E%7B9-k%7D%28-%5Cpi%29%5Ek%3D%5Csum_%7Bk%3D0%7D%5E5%20%5Cbinom%7B5%7D%7Bk%7D%28-%5Cpi%29%5Ek%5C%5C%3D%5Cbinom%7B5%7D%7B0%7D%28-%5Cpi%29%5E0%2B%5Cbinom%7B5%7D%7B1%7D%28-%5Cpi%29%5E1%2B%5Cbinom%7B5%7D%7B2%7D%28-%5Cpi%29%5E2%2B%5Cbinom%7B5%7D%7B3%7D%28-%5Cpi%29%5E3%2B%5Cbinom%7B5%7D%7B4%7D%28-%5Cpi%29%5E4%2B%5Cbinom%7B5%7D%7B5%7D%28-%5Cpi%29%5E5%5C%5C%3D1-5%2B10%5Cpi%5E2-10%5Cpi%5E3%2B5%5Cpi%5E4-%5Cpi%5E5)
d)
![(\sqrt{2}+i)^6=\sum_{k=0}^6 \binom{6}{k}\sqrt{2}^{6-k}i^k\\=\binom{6}{0}\sqrt{2}^{6}i^0+\binom{6}{1}\sqrt{2}^{5}i+\binom{6}{2}\sqrt{2}^{4}i^2+\binom{6}{3}\sqrt{2}^{3}i^3+\binom{6}{4}\sqrt{2}^{2}i^4+\binom{6}{5}\sqrt{2}i^5+\binom{6}{6}\sqrt{2}^{0}i^6](https://tex.z-dn.net/?f=%28%5Csqrt%7B2%7D%2Bi%29%5E6%3D%5Csum_%7Bk%3D0%7D%5E6%20%5Cbinom%7B6%7D%7Bk%7D%5Csqrt%7B2%7D%5E%7B6-k%7Di%5Ek%5C%5C%3D%5Cbinom%7B6%7D%7B0%7D%5Csqrt%7B2%7D%5E%7B6%7Di%5E0%2B%5Cbinom%7B6%7D%7B1%7D%5Csqrt%7B2%7D%5E%7B5%7Di%2B%5Cbinom%7B6%7D%7B2%7D%5Csqrt%7B2%7D%5E%7B4%7Di%5E2%2B%5Cbinom%7B6%7D%7B3%7D%5Csqrt%7B2%7D%5E%7B3%7Di%5E3%2B%5Cbinom%7B6%7D%7B4%7D%5Csqrt%7B2%7D%5E%7B2%7Di%5E4%2B%5Cbinom%7B6%7D%7B5%7D%5Csqrt%7B2%7Di%5E5%2B%5Cbinom%7B6%7D%7B6%7D%5Csqrt%7B2%7D%5E%7B0%7Di%5E6)
e)
![(2-i)^6=\sum_{k=0}^6 \binom{6}{k}2^{6-k}(-i)^k\\=\binom{6}{0}2^{6}(-i)^0+\binom{6}{1}2^{5}(-i)^1+\binom{6}{2}2^{4}(-i)^2+\binom{6}{3}2^{3}(-i)^3+\binom{6}{4}2^{2}(-i)^4+\binom{6}{5}2^{1}(-i)^5+\binom{6}{k}2^{0}(-i)^6\\=1-32i+\binom{6}{2}16i^2-\binom{6}{3}8i^3+\binom{6}{4}4i^4-\binom{6}{5}2i^5+\binom{6}{k}i^6](https://tex.z-dn.net/?f=%282-i%29%5E6%3D%5Csum_%7Bk%3D0%7D%5E6%20%5Cbinom%7B6%7D%7Bk%7D2%5E%7B6-k%7D%28-i%29%5Ek%5C%5C%3D%5Cbinom%7B6%7D%7B0%7D2%5E%7B6%7D%28-i%29%5E0%2B%5Cbinom%7B6%7D%7B1%7D2%5E%7B5%7D%28-i%29%5E1%2B%5Cbinom%7B6%7D%7B2%7D2%5E%7B4%7D%28-i%29%5E2%2B%5Cbinom%7B6%7D%7B3%7D2%5E%7B3%7D%28-i%29%5E3%2B%5Cbinom%7B6%7D%7B4%7D2%5E%7B2%7D%28-i%29%5E4%2B%5Cbinom%7B6%7D%7B5%7D2%5E%7B1%7D%28-i%29%5E5%2B%5Cbinom%7B6%7D%7Bk%7D2%5E%7B0%7D%28-i%29%5E6%5C%5C%3D1-32i%2B%5Cbinom%7B6%7D%7B2%7D16i%5E2-%5Cbinom%7B6%7D%7B3%7D8i%5E3%2B%5Cbinom%7B6%7D%7B4%7D4i%5E4-%5Cbinom%7B6%7D%7B5%7D2i%5E5%2B%5Cbinom%7B6%7D%7Bk%7Di%5E6)