The solution is n = 5 and r = 4
Step-by-step explanation:
Given,
nCr : (n+1)Cr : (n+2)Cr = 1:3:7
To find the value of n and r.
Formula
nCr = 
[ n! means = n.(n-1).(n-2)....3.2.1]
Now,
nCr : (n+1)Cr = 1:3 and (n+1)Cr : (n+2)Cr = 3:7
or, : 
= 1:3 or, : 
= 
or, × 
= 
or, ×
=
or, 
= or, 
=
or, 3(n+1-r) = n+1 or, 7(n+2-r) = 3(n+2)
or, 3n+3-3r = n+1 or, 7n+14-7r = 3n+6
or, 2n-3r = -2 or, 4n-7r = -8
Now, by solving
2n-3r = -2 -----(1)
4n-7r = -8 -----(2) we will get n and r
Multiplying (1) by and then subtract with (2) we get,
2(2n-3r) - (4n-7r) = -4-(-8)
or, 4n-6r-4n+7r = 4
or, r = 4
From (1) we get,
2n = -2+3(4)
or, 2n = 10
or, n = 5
Hence,
n = 5 and r = 4
Complete question is in comment section :
Answer:
68%
Step-by-step explanation:
Mean = 25
Standard deviation = 5
The percentage of trees between 20 and 30
20 trees = 1 standard deviation below the mean ; mean - 1(standard deviation)
25 - 5 = 20
30 trees = 1 standard deviation above the mean ;
Mean + 1(standard deviation) ;
25 + 5 = 30
This means, 20 and 30 lies ±1 standard deviation from the mean which according to the empirical rule is 68%
According to the empirical rule :
Answer:
Step-by-step explanation:
1
Given x³, we can write the equivalent expression -----------
x^(-3)
1
Given y^(-4) we can rewrite this as ----------
y^4
Here we're applying the "rule of negative exponents."
is there more to this? if so i would love to help.
