Which function represents g(x), a reflection of f(x) = 6(one-third) Superscript x across the y-axis?
2 answers:
The function represents a reflection of
across the y-axis ⇒ 3rd answer
Step-by-step explanation:
Let us revise the reflection across the axes
- If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)
∵
∵ g(x) is the image of f(x) after reflection across the y-axis
- From the rule above reflection across the y-axis changes the sign of x
∴
∵
∵
∴
∴
The function represents a reflection of
across the y-axis
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Answer:
8 shifts.
Step-by-step explanation:
Brianna worked a total of 44 hours stacking shelves.
If she worked hour shifts,
How many shifts did she work?
So 1 shift takes 5.5 hours
The number of shifts she worked in 5.5 hours is;
= 8 shifts.
Answer:
The mean commute time in the U.S. is less than half an hour.
Step-by-step explanation:
In this case we need to test whether the mean commute time in the U.S. is less than half an hour.
The information provided is:
(a)
The hypothesis for the test can be defined as follows:
<em>H</em>₀: The mean commute time in the U.S. is not less than half an hour, i.e. <em>μ</em> ≥ 30.
<em>Hₐ</em>: The mean commute time in the U.S. is less than half an hour, i.e. <em>μ</em> < 30.
(b)
As the population standard deviation is not known we will use a t-test for single mean.
Compute the test statistic value as follows:
Thus, the test statistic value is -1.58.
(c)
Compute the p-value of the test as follows:
*Use a t-table.
The p-value of the test is 0.061.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
p-value = 0.061> α = 0.05
The null hypothesis will not be rejected at 5% level of significance.
Thus, concluding that the mean commute time in the U.S. is less than half an hour.