What are the coordinates of the image of vertex F after a reflection across the line y = –x?
1 answer:
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Answer:
Step-by-step explanation:
Given that:
To evaluate the expression, we must simply substitute the given value of , which is
, for
:
Multiply:
Subtract:
-
To check your work, simply set the given expression equal to our solution, :
Add to both sides of the equation:
Divide both sides of the equation by the coefficient of , which is
:
Since it matches the given value of , our solution is correct!
Answer:
a) The point estimate of the proportion of items returned for the population of
sales transactions at the Houston store = 12/80 = 0.15
b) The 95% confidence interval for the proportion of returns at the Houston store = [0.0718 < p < 0.2282].
c) Yes.
We set an hypothesis and construct a test statistics. The test statistics result gives us:
Z calculated = 2.2545, and this gives us the p-value = 0.0121. We assumed 95% confident interval. Hence, the level of significance (α) = 5%. Conclusively, since the p-value ==> 0.0121 is less than (α) = 5%, the test is significant. Hence, the proportion of returns at the Houston store is significantly different from the returns for the nation as a whole.
Step-by-step explanation:
a) Point estimate of the proportion = number of returned items/ total items sold = 12/80 = 0.15.
b) By formula of confident interval:
CI(95%) = p ± Z*,
CI(95%) = [0.0718 < p < 0.2282]
c) The hypothesis:
: The proportion of returns at the Houston store is not significantly different from the returns for the nation as a whole.
: The proportion of returns at the Houston store is significantly different from the returns for the nation as a whole.
The test statistics:
Z = , where
is the proportion of nation returns.
Z calculated = 2.2545, and this gives us the p-value = 0.0121. We assumed 95% confident interval. Hence, the level of significance (α) = 5%. Conclusively, since the p-value ==> 0.0121 is less than (α) = 5%, the test is significant. Hence, the proportion of returns at the Houston store is significantly different from the returns for the nation as a whole.