Step-by-step explanation:
2 consecutive numbers is X+X+2
so X+X+2=-8
ad the X and 2
2x=-8 (divide by 2 as -8 can divide by 2)
X=-4
so the two numbers are both -4
Answer:
b. 98
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
![\alpha = \frac{1-0.9}{2} = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B1-0.9%7D%7B2%7D%20%3D%200.05)
Now, we have to find z in the Ztable as such z has a pvalue of
.
So it is z with a pvalue of
, so ![z = 1.645](https://tex.z-dn.net/?f=z%20%3D%201.645)
Now, find M as such
![M = z*\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%2A%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which
is the standard deviation of the population and n is the size of the sample.
In this problem, we have that:
![M = 0.5, \sigma = 3](https://tex.z-dn.net/?f=M%20%3D%200.5%2C%20%5Csigma%20%3D%203)
![M = z*\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%2A%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
![0.5 = 1.645*\frac{3}{\sqrt{n}}](https://tex.z-dn.net/?f=0.5%20%3D%201.645%2A%5Cfrac%7B3%7D%7B%5Csqrt%7Bn%7D%7D)
![0.5\sqrt{n} = 4.935](https://tex.z-dn.net/?f=0.5%5Csqrt%7Bn%7D%20%3D%204.935)
![\sqrt{n} = 9.87](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%209.87)
![n = 97.42](https://tex.z-dn.net/?f=n%20%3D%2097.42)
So a sample of at least 98 is required.
The correct answer is:
b. 98
The formula for simple annual interest is:
I = Prt
where,
I = Interest accumulated = $910.90
P = Principal Amount = $62000
r = Interest rate = 9.4% = 0.094
t = time in years
Using the values in above equation, we get:
910.90 = 62000 x 0.094 x t
⇒ t = 910.90/(62000 x 0.094) = 0.156
This is the time in years. Since there are 365 days in a year, the time in days will be:
t = 0.156 x 365 = 57 (rounded to nearest day)
This means, Nate kept the borrowed money for 57 days