let's firstly convert the mixed fraction to improper fraction and then take it from there, keeping in mind that the whole is "x".
![\stackrel{mixed}{5\frac{5}{6}}\implies \cfrac{5\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{35}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{3}x~~ = ~~5\frac{5}{6}\implies \cfrac{7}{3}x~~ = ~~\cfrac{35}{6}\implies 42x=105\implies x=\cfrac{105}{42} \\\\\\ x=\cfrac{21\cdot 5}{21\cdot 2}\implies x=\cfrac{21}{21}\cdot \cfrac{5}{2}\implies x=1\cdot \cfrac{5}{2}\implies x=2\frac{1}{2}](https://tex.z-dn.net/?f=%5Cstackrel%7Bmixed%7D%7B5%5Cfrac%7B5%7D%7B6%7D%7D%5Cimplies%20%5Ccfrac%7B5%5Ccdot%206%2B5%7D%7B6%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B35%7D%7B6%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B7%7D%7B3%7Dx~~%20%3D%20~~5%5Cfrac%7B5%7D%7B6%7D%5Cimplies%20%5Ccfrac%7B7%7D%7B3%7Dx~~%20%3D%20~~%5Ccfrac%7B35%7D%7B6%7D%5Cimplies%2042x%3D105%5Cimplies%20x%3D%5Ccfrac%7B105%7D%7B42%7D%20%5C%5C%5C%5C%5C%5C%20x%3D%5Ccfrac%7B21%5Ccdot%205%7D%7B21%5Ccdot%202%7D%5Cimplies%20x%3D%5Ccfrac%7B21%7D%7B21%7D%5Ccdot%20%5Ccfrac%7B5%7D%7B2%7D%5Cimplies%20x%3D1%5Ccdot%20%5Ccfrac%7B5%7D%7B2%7D%5Cimplies%20x%3D2%5Cfrac%7B1%7D%7B2%7D)
Answer:
∑ (-1)ⁿ⁺³ 1 / (n^½)
∑ (-1)³ⁿ 1 / (8 + n)
Step-by-step explanation:
If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.
Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).
Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).
Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.
Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Answer:
750
Step-by-step explanation:
62.5% choose chocolate
1200 x 62.5% of is 750
Answer:
7/6
Step-by-step explanation:
The width to length ratio is ...
... width / length = (4 2/3 yards)/(4 yards) = (14/3)/4 = 14/12
... width/length = 7/6
