Answer:
0.6826
Step-by-step explanation:
Mean(μ) = 37
Standard deviation (σ) = 9
P(28 < x < 46) = ???
Using normal distribution
Z = (x - μ)/σ
For x = 28
Z = (28 - 37)/9
Z = -9/9
Z = -1
For x = 46
Z = (46 - 37)/9
Z = 9/9
Z = 1
We now have
P(-1 < Z < 1)
= P(Z < 1) - P(Z < -1)
From the table, Z = 1 = 0.3413
φ(Z) = 0.3413
Recall that
When Z is positive, P(x<a) = 0.5 +φ(Z)
P(Z<1)= 0.5 + 0.3413
= 0.8413
When Z is negative, P(x<a) = 0.5 - φ(Z)
P(Z< -1)= 0.5 - 0.3413
= 0.1587
We now have
0.8413 - 0.1587
= 0.6826
Proving a relation for all natural numbers involves proving it for n = 1 and showing that it holds for n + 1 if it is assumed that it is true for any n.
The relation 2+4+6+...+2n = n^2+n has to be proved.
If n = 1, the right hand side is equal to 2*1 = 2 and the left hand side is equal to 1^1 + 1 = 1 + 1 = 2
Assume that the relation holds for any value of n.
2 + 4 + 6 + ... + 2n + 2(n+1) = n^2 + n + 2(n + 1)
= n^2 + n + 2n + 2
= n^2 + 2n + 1 + n + 1
= (n + 1)^2 + (n + 1)
This shows that the given relation is true for n = 1 and if it is assumed to be true for n it is also true for n + 1.
<span>By mathematical induction the relation is true for any value of n.</span>
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hope this helps :)
Answer:
-5 is the value
Step-by-step explanation:
47-42=-L
5=-L
L=-5
