Find the minimum value of the function for the polygonal convex set determined by the given system of inequalities.
1 answer:
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9514 1404 393
Answer:
5 hours
Step-by-step explanation:
A quick way to look at this is to compare the difference in hourly charge to the difference in 0-hour charge.
The first day, the charge is $3 more than $12 per hour.
The second day, the charge is $12 less than $15 per hour.
The difference in 0-hour charges is 3 -(-12) = 15. The difference in per-hour charges is 15 -12 = 3. The ratio of these is ...
$15/($3/h) = 5 h
The charges are the same after 5 hours.
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If you write equations for the charges, they will look like ...
y1 = 15 + 12(x -1)
y2 = 3 + 15(x -1)
Equating these charges, we have ...
15 +12(x -1) = 3 + 15(x -1)
12x +3 = 15x -12 . . . . . . . . eliminate parentheses
15 = 3x . . . . . . . . . . add 12-12x
x = 15/3 = 5 . . . . . . divide by 3
You might notice that the math here is very similar to that described in words, above.
The charges are the same after 5 hours.
Answer:
a) The hypothesis that the mean annual income is the same could not be rejected. There is no enough evidence to claim they are different.
b) The critical values for this two-sided test are t=±1.711.
Step-by-step explanation:
<em>The question is incomplete:</em>
<em>(a) Identify the claim and state H0 and Ha. </em>
<em> Which is the correct claim below?</em>
<em>(b) Find the critical value(s) and identify the rejection region(s). </em>
<em> Enter the critical value(s) below.</em>
We have an hypothesis test on the difference of two means.
The null and alternative hypothesis are:
The claim of the alternative hypothesis is that the mean annual income is different in County A and County B.
The null hypothesis is that the mean annual income is equal in both counties.
The significance level is α=0.10.
The sample from County A has a mean of S40,400, a s.d. of $8,700 and a sample size of 18 residents.
The sample from County B has a mean of S39,200, a s.d. of $6,000 and a sample size of 8 residents.
The standard error of the difference of means is:
The degrees of freedom are:
Then, the test statistic is:
For a statistic t=0.407, and df=24, the P-value is P=0.69. As the P-value is bigger than the significance level, the null hypothesis failed to be rejected.
If we would use the critial value approach, we would have to calculate the critical values for t, for df=24, two sided test and α=0.10.
The critical values, looking in a table, are t=1.711.