Answer:12,376
Step-by-step explanation:
Given
Connie has 17 Pairs of jeans
She has to choose 6 pairs out of 17
We know, no of ways to pick r items out of n items is ![^nC_r](https://tex.z-dn.net/?f=%5EnC_r)
![\therefore \text{No of ways is =}^{17}C_6\\\\\Rightarrow \dfrac{17!}{(17-6)!6!}=12,376\ \text{ways}](https://tex.z-dn.net/?f=%5Ctherefore%20%5Ctext%7BNo%20of%20ways%20is%20%3D%7D%5E%7B17%7DC_6%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7B17%21%7D%7B%2817-6%29%216%21%7D%3D12%2C376%5C%20%5Ctext%7Bways%7D)
1908
Step-by-step explanation:2% of 1800 is 36 36 x 3 is 108 + 1800 =1908
Answer:
x = 1
Explanation:
![\sf \rightarrow log(3x) + log(x + 4) = log(15)](https://tex.z-dn.net/?f=%5Csf%20%5Crightarrow%20log%283x%29%20%2B%20log%28x%20%2B%204%29%20%3D%20log%2815%29)
Rule: log(a) + log(b) = log(ab)
![\sf \rightarrow log(3x(x + 4)) = log(15)](https://tex.z-dn.net/?f=%5Csf%20%5Crightarrow%20log%283x%28x%20%2B%204%29%29%20%3D%20%20log%2815%29)
cancel out log on both sides
![\sf \rightarrow 3x(x + 4) = 15](https://tex.z-dn.net/?f=%5Csf%20%5Crightarrow%203x%28x%20%2B%204%29%20%3D%2015)
relocate constant variable
![\sf \rightarrow 3x^2 + 12x -15 = 0](https://tex.z-dn.net/?f=%5Csf%20%5Crightarrow%203x%5E2%20%2B%2012x%20-15%20%3D%200)
take 3 as a common factor
![\sf \rightarrow 3(x^2 + 4x -5) = 0](https://tex.z-dn.net/?f=%5Csf%20%5Crightarrow%203%28x%5E2%20%2B%204x%20-5%29%20%3D%200)
divide both sides by 3
![\sf \rightarrow x^2 + 4x -5 = 0](https://tex.z-dn.net/?f=%5Csf%20%5Crightarrow%20x%5E2%20%2B%204x%20-5%20%3D%200)
middle term split
![\sf \rightarrow x^2 + 5x -x-5 = 0](https://tex.z-dn.net/?f=%5Csf%20%5Crightarrow%20x%5E2%20%2B%205x%20-x-5%20%3D%200)
factor common terms
![\sf \rightarrow x(x + 5) -1(x+5)= 0](https://tex.z-dn.net/?f=%5Csf%20%5Crightarrow%20x%28x%20%20%2B%205%29%20-1%28x%2B5%29%3D%200)
collect into groups
![\sf \rightarrow (x-1)(x+5)= 0](https://tex.z-dn.net/?f=%5Csf%20%5Crightarrow%20%28x-1%29%28x%2B5%29%3D%200)
set to zero
![\sf \rightarrow x-1 = 0 , \ x+5= 0](https://tex.z-dn.net/?f=%5Csf%20%5Crightarrow%20x-1%20%3D%200%20%2C%20%5C%20x%2B5%3D%200)
relocate variables
![\sf \rightarrow x = 1, \ x = -5](https://tex.z-dn.net/?f=%5Csf%20%5Crightarrow%20x%20%3D%201%2C%20%20%5C%20x%20%3D%20-5)
There must be a positive solution for log, so the solution is only x = 1
30 because it is in the tenths place