Answer:
E) we will use t- distribution because is un-known,n<30
the confidence interval is (0.0338,0.0392)
Step-by-step explanation:
<u>Step:-1</u>
Given sample size is n = 23<30 mortgage institutions
The mean interest rate 'x' = 0.0365
The standard deviation 'S' = 0.0046
the degree of freedom = n-1 = 23-1=22
99% of confidence intervals
(from tabulated value).
![The mean value = 0.0365](https://tex.z-dn.net/?f=The%20mean%20value%20%3D%200.0365)
![x±t_{0.01} \frac{S}{\sqrt{n-1} }](https://tex.z-dn.net/?f=x%C2%B1t_%7B0.01%7D%20%5Cfrac%7BS%7D%7B%5Csqrt%7Bn-1%7D%20%7D)
![0.0365±2.82 \frac{0.0046}{\sqrt{23-1} }](https://tex.z-dn.net/?f=0.0365%C2%B12.82%20%5Cfrac%7B0.0046%7D%7B%5Csqrt%7B23-1%7D%20%7D)
![0.0365±2.82 \frac{0.0046}{\sqrt{22} }](https://tex.z-dn.net/?f=0.0365%C2%B12.82%20%5Cfrac%7B0.0046%7D%7B%5Csqrt%7B22%7D%20%7D)
![0.0365±2.82 \frac{0.0046}{4.690 }](https://tex.z-dn.net/?f=0.0365%C2%B12.82%20%5Cfrac%7B0.0046%7D%7B4.690%20%7D)
using calculator
![0.0365±0.00276](https://tex.z-dn.net/?f=0.0365%C2%B10.00276)
Confidence interval is
![(0.0365-0.00276,0.0365+0.00276)](https://tex.z-dn.net/?f=%280.0365-0.00276%2C0.0365%2B0.00276%29)
![(0.0338,0.0392)](https://tex.z-dn.net/?f=%280.0338%2C0.0392%29)
the mean value is lies between in this confidence interval
(0.0338,0.0392).
<u>Answer:-</u>
<u>using t- distribution because is unknown,n<30,and the interest rates are not normally distributed.</u>
Hello there, my fellow human being!
The answer is 1.37 miles.
Hope this helped!
~Ruru
Answer: 184
Step-by-step explanation:
The nth term of am arithmetic sequence is calculated as:
Nth term= a+(n-1)d
where a = first term
d = common difference
a = -10
d = -8 -(-10) = -8+10 = 2
98th term= a+(n-1)d
= -10 + (98-1)(2)
= -10 + (97×2)
= -10 + 194
= 184
The 98th term of the arithmetic sequence is 184
Let ABC be a triangle in the 3rd quadrant, right-angled at B.
So, AB-> Perpendicular BC -> Base AC -> Hypotenuse.
Given: sinθ=-3/5 cosecθ=-5/3
According to Pythagorean theorem, square of the hypotenuse is equal to the sum of square of the other two sides.
Therefore in triangle ABC, 〖AC〗^2=〖AB〗^2+〖BC〗^2 ------
--(1)
Since sinθ=Perpendicular/Hypotenuse ,
AC=5 and AB=3
Substituting these values in equation (1)
〖BC〗^2=〖AC〗^2-〖AB〗^2
〖BC〗^2=5^2-3^2
〖BC〗^2=25-9
〖BC〗^2=16
BC=4 units
Since the triangle is in the 3rd quadrant, all trigonometric ratios, except tan
and cot are negative.
So,cosθ=Base/Hypotenuse Cosθ=-4/5
secθ=Hypotnuse/Base secθ=-5/4
tanθ=Perpendicular/Base tanθ=3/4
cotθ=Base/Perpendicular cotθ=4/3
Answer:
Subsets of the given set = 32
Proper subset of the given set = 31
Step-by-step explanation:
Given set is {18, 8, 14, 9, 6} having 5 elements.
We know number of subsets of a set having n elements are represented by
![2^{n}](https://tex.z-dn.net/?f=2%5E%7Bn%7D)
where n is the number of elements in the set.
Therefore, subsets of the given set = ![2^{5}](https://tex.z-dn.net/?f=2%5E%7B5%7D)
= 32
Since original set itself is a subset of its own, is not a proper subset.
Therefore, proper subset of a set = ![2^{n}-1](https://tex.z-dn.net/?f=2%5E%7Bn%7D-1)
= ![2^{5}-1](https://tex.z-dn.net/?f=2%5E%7B5%7D-1)
= 32 - 1
= 31