Answer:
Among the given samples the sample which constitute a biased sample is given by, the sample obtained by,
'Surveying randomly among seventh grade girls of a school to determine what theme the whole school would prefer for the dance.'
Step-by-step explanation:
Among the given samples the sample which constitute a biased sample is given by, the sample obtained by,
'Surveying randomly among seventh grade girls of a school to determine what theme the whole school would prefer for the dance.' since the choices of those seventh grade girls in the sample may not reflect those of the whole school.
Answer:
In Exercises 1-15 use mathematical induction to establish the formula for n ≥ 1.
1. 1
2 + 22 + 32 + · · · + n
2 =
n(n + 1)(2n + 1)
6
Proof:
For n = 1, the statement reduces to 12 =
1 · 2 · 3
6
and is obviously true.
Assuming the statement is true for n = k:
1
2 + 22 + 32 + · · · + k
2 =
k(k + 1)(2k + 1)
6
, (1)
we will prove that the statement must be true for n = k + 1:
1
2 + 22 + 32 + · · · + (k + 1)2 =
(k + 1)(k + 2)(2k + 3)
6
. (2)
The left-hand side of (2) can be written as
1
2 + 22 + 32 + · · · + k
2 + (k + 1)2
.
In view of (1), this simplifies to:
7844=7400(1+(8/12)r)
Solve for r
R=0.09*100=9%