Larry wants to buy some carpet for his living room. The length of the room is 3 times the width and the total area of the room i
2 answers:
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9514 1404 393
Answer:
- vertical shift: 7 (up)
- horizontal shift: 2 (right)
- vertical asymptote: x=2
- domain: x > 2
- range: all real numbers
Step-by-step explanation:
For any function f(x), the transformation f(x -h) +k represents a horizontal shift of h units to the right and k units upward.
Here, the parent function is log₂(x) and the transformation to log₂(x -2) +7 represents translation 2 units right and 7 units upward.
The parent function has a vertical asymptote at x=0, so the shifted function will have a vertical asymptote at x-2=0, or x = 2.
The parent function has a domain of x > 0, so the shifted function will have a domain of x-2 > 0, or x > 2.
The parent function has a range of "all real numbers." Shifting the function vertically does not change that range. The range of the shifted function is still "all real numbers."
The graph is shown below. The vertical asymptote is the dashed orange line.
_____
The "work" is in matching the pattern f(x -h) +k to the function log₂(x -2) +7.
Answer:
The degrees of freedom are given by:
The p value for this case is given by:
Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense
Step-by-step explanation:
Information given
represent the sample mean
represent the sample standard deviation
sample size
represent the value to verify
represent the significance level
t would represent the statistic (variable of interest)
represent the p value
Hypothesis to est
We want to test if the true mean is at least 26 mpg, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic for this case is given by;
(1)
Replacing the info given we got:
The degrees of freedom are given by:
The p value for this case is given by:
Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense