Which statements are true about reflections? Check all that apply
2 answers:
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We have been given a graph of function g(x) which is a transformation of the function
Now we have to find the equation of g(x)
Usually transformation involves shifting or stretching so we can use the graph to identify the transformation.
First you should check the graph of
You will notice that it is always above x-axis (equation is x=0). Because x-axis acts as horizontal asymptote.
Now the given graph has asymptote at x=-2
which is just 2 unit down from the original asymptote x=0
so that means we need shift f(x), 2 unit down hence we get:
but that will disturb the y-intercept (0,1)
if we multiply by 3 again then the y-intercept will remain (0,1)
Hence final equation for g(x) will be:
Answer:
There is sufficient statistical evidence to prove that the standard deviation of the technology-related workers and the standard deviation of the non-technology workers are equal.
Step-by-step explanation:
Here we have our null hypothesis as H₀: σ² = s²
Our alternative hypothesis is then Hₐ: σ² ≠ s²
We therefore have a two tailed test
To test the hypothesis of difference in standard deviation which is the Chi squared test given as follows
Where:
n = Size of sample
s² = Variance of sample = 950²
σ² = Variance of population = 650²
Degrees of freedom = n - 1 = 71 - 1 = 70
α = Significance level = 0.1
Therefore, we use 1 - 0.1 = 0.9
From the Chi-square table, we have the critical value as
1 - α/2 = 51.739,
α/2 = 90.531
Plugging the values in the above Chi squared test equation, we have;
Therefore, since the test value within the critical region, we do not reject the null hypothesis, hence there is sufficient statistical evidence to prove that the standard deviation of the technology-related workers and the standard deviation of the non-technology workers are equal.