Answer:
The coefficients are therefore
1,1
1,2,1
1,3,3,1
1,4,6,4,1
1,5,10,10,5,1
1,6,15,20,15,6,1
1,7,21,35,35,21,7,1
Step-by-step explanation:
(a+b)^n
=a^n+na^(n-1)b+(n(n-1)/2)a^(n-2)b²+...+nab^(n-1)+b^n
=C(n,0)a^n+C(n,1)a^(n-1)b+C(n-2)a^(n-2)b^sup2;.....C(n,n)b^n
For n=1
(a+b)1=a+b
(a+b)2=a²+2ab+b^sup2;
(a+b)3=a³+3a^sup2;b+3ab²+b³
...
The coefficients are therefore
1,1
1,2,1
1,3,3,1
1,4,6,4,1
1,5,10,10,5,1
1,6,15,20,15,6,1
1,7,21,35,35,21,7,1
...
This is the Pascal's triangle
The sum of each pair of adjacent numbers gives rise to a number on the next line.
This also means that
(a+b)7
=a^7+7a^6b+21a^5b²+35a^4b³+....+7ab^6+b^7 ............(A)
which is almost the solution to the problem.
To solve the problem using the Pascal's triangle, substitute a=x, and b=2y in equation (A) to give the expression of the final answer.
Answer:
slope= 0.52
Step-by-step explanation:
For American women
Mean (x) = 64 inches
Standard deviation (sx) = 2.7 inches
For American Men
Mean(ÿ) = 69.3 inches
Standard deviation (sy) = 2.8 inches
r = 0.5
Slope = ??
Husband height = Y
Wife height = X
the general equation of regression line
y = a + bx
The slope of the regression line is the linear correlation coefficient multiplied by the standard deviation for Y
b = r (sy/sx)
b = 0.5(2.8/2.7)
b = 0.52
The intercept a = ÿ - bx
a = 69.3 - 0.52(64)
a = 69.3 - 33.28
a = 36.02
The equation of the regression line y = a + bx
y = 36.02 + 0.52x
-2x would be the missing term.
Given ratio: 5 (goats) : (to) 8 (sheep.)
The question asked that if Giles had 32 sheep, then how many goats would he have. We can figure out how many goats he would have by cross multiplying fractions.
5 z
- x -
8 32
To figure out the z variable, we simply cross multiply 5 and 32, which gets us 160. Now we divide it by 8. Whatever we get for z, that is our answer for goats. The answer would be <span>20.
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