Think about all of the ways in which a circle and a parabola can intersect. Select all of the number of ways in which a circle a
nd a parabola can intersect.
2 answers:
Answer:
A circle can intersect a parabola in
1. One point [ when circle just touches the parabola]
2. Two points [ When circle cuts the parabola in two distinct points. ]
3. Three points [Circle just touches at one point and cuts the parabola in two distinct points]
4. Four points [ Either parabola or circle meeting each other or crossing at four distinct points]
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Answer:
Compatible width of rectangular banquet hall could be 90 feet approximately.
Step-by-step explanation:
Given
Area of a rectangular banquet hall = 7400 square feet
Length of rectangular banquet hall = 82 feet
We need to calculate width of the rectangular banquet hall.
Now Area of rectangle is equal to length times width.
Framing in equation form we get;
Substituting the given values we get;
Now by definition of Compatible numbers which state that:
"Compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally. Compatible numbers are close in value to the actual numbers that make estimating the answer and computing problems easier."
Now By Using width as 90 feet and length as 82 feet we get area as 7380 sq ft. which is closet to actual area which is 7400 sq ft.
Hence we can say compatible width could be 90 feet approximately.
Answer:
a)
So then we can conclude that the true proportion of women with cosmetic dermatitis from using eye shadow at 95% of confidence is between (0.0422 and 0.1410)
b)
So then we can conclude that the true proportion of women with cosmetic dermatitis from using mascara at 95% of confidence is between (0.0628 and 0.1372)
c) For this case we see that both confidence intervals contains the value of 0.12 so then we can't conclude that only one group is referenced at the significance level of 0.05 used.
Step-by-step explanation:
Part a
The estimated proportion of women with cosmetic dermatitis from using eye shadow is given by:
The confidence interval is at 95% of confidence, our significance level would be given by and
. And the critical value would be given by:
The confidence interval for the proportion is given by the following formula:
Replacing we got:
So then we can conclude that the true proportion of women with cosmetic dermatitis from using eye shadow at 95% of confidence is between (0.0422 and 0.1410)
Part b: A 95% confidence interval for the women with cosmetic dermatitis from using mascara
So then we can conclude that the true proportion of women with cosmetic dermatitis from using mascara at 95% of confidence is between (0.0628 and 0.1372)
Part c: Suppose you are informed that the true proportion with a nickel allergy for one of the two groups (eye shadow or mascara) is .12. Can you determine which group is referenced? Explain.
For this case we see that both confidence intervals contains the value of 0.12 so then we can't conclude that only one group is referenced at the significance level of 0.05 used.