5. Kal Tire installs automobile tires on a first-come first-served basis. A random sample of 50 customers experienced an average
1 answer:
5.7099 is the margin of error.
<h3>What is standard deviation ?</h3>
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.
Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
According to the question,
The standard sampling error of the sample mean is σₓ ,
The sampling distribution is: N (u,σₓ/n)
Therefore,
By using the standard deviation formula:
σₓ = √∑(xi -μ)/N
Where,
∑= population standard deviation
N= the size of the population
xi= each value from the population
μ =the population mean
So ,
σₓ = = 2.913
Since, a = 1- 95% = 0.05
therefore = (1-0.005 x 2) = 1.959964
Here, the margin of error for a 95% confidence interval for this sample is given by:
* σₓ = 1.959964 x 2.913
= 5.7099
5.7099 is the margin of error for a 95% confidence interval for this sample.
Learn more about standard deviation here:
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Answer:
x = 2
Step-by-step explanation:
These equations are solved easily using a graphing calculator. The attachment shows the one solution is x=2.
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<h3>Squaring</h3>The usual way to solve these algebraically is to isolate radicals and square the equation until the radicals go away. Then solve the resulting polynomial. Here, that results in a quadratic with two solutions. One of those is extraneous, as is often the case when this solution method is used.
The solutions to this equation are the values of x that make the factors zero: x=2 and x=-1. When we check these in the original equation, we find that x=-1 does not work. It is an extraneous solution.
x = -1: √(-1+2) +1 = √(3(-1)+3) ⇒ 1+1 = 0 . . . . not true
x = 2: √(2+2) +1 = √(3(2) +3) ⇒ 2 +1 = 3 . . . . true . . . x = 2 is the solution
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<h3>Substitution</h3>Another way to solve this is using substitution for one of the radicals. We choose ...
Solutions to this equation are ...
u = 2, u = -1 . . . . . . the above restriction on u mean u=-1 is not a solution
The value of x is ...
x = u² -2 = 2² -2
x = 2 . . . . the solution to the equation
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<em>Additional comment</em>
Using substitution may be a little more work, as you have to solve for x in terms of the substituted variable. It still requires two squarings: one to find the value of x in terms of u, and another to eliminate the remaining radical. The advantage seems to be that the extraneous solution is made more obvious by the restriction on the value of u.
Answer:
sinθ = y/r sinθ =
cosθ = x/r cosθ =
tanθ = y/x tanθ =
cscθ = r/y cscθ =
secθ = r/x secθ =
cotθ = x/y cotθ =
explanation:
r =
r = 10
x = 8
y = -6
r =
r = 5
x = 4
y = 3