Answer:

Step-by-step explanation:
![\ln \dfrac{4y^5}{x^2}\\\\=\ln(4y^5) - \ln(x^2)~~~~~~~~~~~;\left[ \log_b\left( \dfrac mn \right) = \log_b m - \llog_b n \right]\\\\=\ln 4 + \ln y^5 - 2\ln x~~~~~~~~~~~~;[\log_b m^n = n \log_b m ~\text{and}~\log_b(mn) = \log_b m + \log_b n ]\\\\=\ln 4 + 5 \ln y -2 \ln x\\\\=\ln 4 -2 \ln x +5 \ln y](https://tex.z-dn.net/?f=%5Cln%20%5Cdfrac%7B4y%5E5%7D%7Bx%5E2%7D%5C%5C%5C%5C%3D%5Cln%284y%5E5%29%20-%20%5Cln%28x%5E2%29~~~~~~~~~~~%3B%5Cleft%5B%20%5Clog_b%5Cleft%28%20%5Cdfrac%20mn%20%5Cright%29%20%20%3D%20%5Clog_b%20m%20-%20%5Cllog_b%20n%20%5Cright%5D%5C%5C%5C%5C%3D%5Cln%204%20%2B%20%5Cln%20y%5E5%20-%202%5Cln%20x~~~~~~~~~~~~%3B%5B%5Clog_b%20m%5En%20%3D%20n%20%5Clog_b%20m%20~%5Ctext%7Band%7D~%5Clog_b%28mn%29%20%3D%20%5Clog_b%20m%20%2B%20%5Clog_b%20n%20%5D%5C%5C%5C%5C%3D%5Cln%204%20%2B%205%20%5Cln%20y%20-2%20%5Cln%20x%5C%5C%5C%5C%3D%5Cln%204%20-2%20%5Cln%20x%20%2B5%20%5Cln%20y)
X=5+y
x+y=-15
subsitute 5+y for x
5+y+y=-15
5+2y=-15
minus 5 from both sides
2y=-20
divide both sides by 2
y=-10
sub back
x=5+y
x=5-10
x=-5
the numbers are -10 and -5
Answer:
ok? what is the question?
X + y = 23000
x.08 + y.09 = 2040
x = 23000 - y
(23000 - y) .08 + y.09 = 2040
1840 - .08y + .09y = 2040
Simplify
.01y = 200
Simplify
Y = 20000
X + 20000 = 23000
X = 3000
CHECK: .08x + .09(20000) = 2040
.08x + 1800 = 2040
Simply .08x = 240
X = 3000
Answer: P(odd) = 0.499
Step-by-step explanation:
Given:
Total number of people = 20
Number of men = 12
Number of women = 8
Number of jury to be selected = 6
For the jury to have an odd number of women. it must have either of the three.
1. 1 woman , 5 men
2. 3 women, 3 men
3. 5 women, 1 man
The total possible ways of selecting the 6 people jury is;
N = 20C6 = 20!/6!(20-6)!
N = 38760
The possible ways of selecting;
Case 1 : 1 woman, 5 men
N1 = 8C1 × 12C5
N1 = 8 × 792 = 6336
Case 2 : 3 women , 3 men
N2 = 8C3 × 12C3
N2 = 12320
Case 3 : 5 women, 1 man
N3 = 8C5 × 12C1
N3 = 672
P(Odd) = (N1+N2+N3)/N
P(odd) = (6336+12320+672)/38760
P(odd) = 19328/38760
P(odd) = 0.499