First simplify the square root of 1/25
-√1/25
Rewrite using the quote by rule for radicals.
-√1/√25
Any root of 1 is 1
-1/√25
Simplify the denominator. (find the square root of 25)
-1/5
The result can be shown in both exact and decimal forms.
Exact form: -1/5
Decimal form: -0.2
If your wondering how much each pair costs individually then its 7.89 per pair
Answer:
The smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income is 48.
Step-by-step explanation:
The complete question is:
The mean salary of people living in a certain city is $37,500 with a standard deviation of $2,103. A sample of n people will be selected at random from those living in the city. Find the smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income. Round your answer up to the next largest whole number.
Solution:
The (1 - <em>α</em>)% confidence interval for population mean is:
The margin of error for this interval is:
The critical value of <em>z</em> for 90% confidence level is:
<em>z</em> = 1.645
Compute the required sample size as follows:
![n=[\frac{z_{\alpha/2}\cdot\sigma}{MOE}]^{2}\\\\=[\frac{1.645\times 2103}{500}]^{2}\\\\=47.8707620769\\\\\approx 48](https://tex.z-dn.net/?f=n%3D%5B%5Cfrac%7Bz_%7B%5Calpha%2F2%7D%5Ccdot%5Csigma%7D%7BMOE%7D%5D%5E%7B2%7D%5C%5C%5C%5C%3D%5B%5Cfrac%7B1.645%5Ctimes%202103%7D%7B500%7D%5D%5E%7B2%7D%5C%5C%5C%5C%3D47.8707620769%5C%5C%5C%5C%5Capprox%2048)
Thus, the smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income is 48.
Answer:
y = x - 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = 
with (x₁, y₁ ) = (0, - 5) and (x₂, y₂ ) = (5, 0) ← 2 points on the line
m = 
= 
= 1
The line crosses the y- axis at (0, - 5) ⇒ c = - 5
y = x - 5 ← equation of line
The perimeter of a rectangle is twice the length plus twice the width. Thus,
2w + 2l = 36.
2l = 36 - 2w
l = 18 - w
The area is length times width.
36 = lw
36 = (18 - w)w
36 = 18w - w^2
w^2 - 18w + 36 = 0
w = (18 +- sqrt(18^2 - 4 * 36))/2
w = (18 +- sqrt(180))/2
w = 9 +- sqrt(45)
Thus, one of the side lengths is 9 + sqrt(45), and the other is 9 - sqrt(45).
