Check the attached file for the answer.
2 to the power of x plus 2 to the power of negative x equals 5/2
1 answer:
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Answer:
A. Null and alternative hypothesis:
B. Yes. At a significance level of 0.05, there is enough evidence to support the claim that there is signficant difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.
P-value = 0.00002
C. As the difference is calculated as (population 1 − population 2), being population 1: groceries and population 2: dinning out, and knowing there is evidence that the true mean difference is positive, we can say that the groceries annual credit card charge is higher than dinning out annual credit card charge.
The point estimate is the sample mean difference d=$840.
The 95% confidence interval for the mean difference between the population means is (490, 1190).
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that there is signficant difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample has a size n=42.
The sample mean is M=840.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=1123.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
This test is a two-tailed test, with 41 degrees of freedom and t=4.848, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.00002) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that there is signficant difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.
We have to calculate a 95% confidence interval for the mean difference.
The t-value for a 95% confidence interval and 41 degrees of freedom is t=2.02.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the mean difference is (490, 1190).
The circumcenter is found by finding the intersection of at least 2 perpendicular bisector segments.
Find the perpendicular bisector to segment AB. This is the line y = -3.5; the idea is that you find the equation of the horizontal line through the midpoint of AB. The midpoint has a y coordinate of -3.5. This line is shown in red horizontal line in the attached image below.
The midpoint of AC is 2.5, so the perpendicular bisector to AC is x = 2.5 which is shown as the vertical green line in the same diagram.
The red and green lines cross at the location (2.5, -3.5) which is the circumcenter's location. If you were to draw a circle through all three points A, B, & C, then this circle would be centered at (2.5, -3.5)
If point D is the circumcenter, then we know this
AD = BD = CD
basically the distance from the center to any point on the triangle is the same. This is due to the fact that all radii of the same circle are the same length.
<h3>Answer: (2.5, -3.5)</h3>note: 2.5 in fraction form is 5/2 while -3.5 in fraction form is -7/2
