Answer:
0.200
Step-by-step explanation:
∑ₓ₌₁⁴⁰ (1 + i)⁻ˣ = 5
∑ₓ₌₁⁴⁰ ((1 + i)⁻¹)ˣ = 5
This is a geometric series. The sum of the first n terms of a geometric series is:
S = a₁ (1 − rⁿ) / (1 − r)
where a₁ is the first term and r is the common ratio.
Here, a₁ = (1 + i)⁻¹, r = (1 + i)⁻¹, and n = 40. For simplicity, let's write both a₁ and r in terms of r. So a₁ = r and r = r.
5 = r (1 − r⁴⁰) / (1 − r)
5 (1 − r) = r (1 − r⁴⁰)
5 − 5r = r − r⁴¹
r⁴¹ − 6r + 5 = 0
Solving with a calculator, r ≈ 0.8334.
Therefore:
(1 + i)⁻¹ = 0.8334
1 + i = 1.200
i = 0.200
Answer:
The z-score is -1.6 and it is not significant .
Step-by-step explanation:
Given : Test score = 48.4
Mean = 66
Standard deviation = 11
To Find :Find the z-score corresponding to the given value and use the z-score to determine whether the value is significant.
Solution:
Formula : 
Substitute the values
So, the z-score is -1.6
Now we are given that Consider a score to be significant if its z-score is less than -2.00 or greater than 2.00.
Since -1.6>-2 and -1.6<2
So, It is not significant
Hence the z-score is -1.6 and it is not significant .
6^(-.5) or 6^(-1/2) are both 1/36
Answer:
$2.17
Step-by-step explanation:
12 goes into 26 2 times.
with 2 left over
2/12 = 1/6
1/6 of a dollar is
divide 100/6 = 16.67
Answer:
k = 13
Step-by-step explanation:
Matrix is;
A =
[2 -5 9]
[-1 3 -5]
[ 7 1 k ]
Number of unknowns is less than the rank of 2. Thus, the determinant has to be zero for us to find k.
Thus, we have;
2((3 × k) - (-5 × 1)) -(-5)((-1 × k) - (-5 × 7)) + 9((-1 × 1) - (7 × 3)) = 0
Simplifying further gives;
2(3k +5) + 5(-k + 35) + 9(-22) = 0
6k + 10 - 5k + 175 - 198 = 0
k - 198 + 185 = 0
k - 13 = 0
k = 13
