A builder is installing a Norman window made up of a rectangle topped by a semicircle. If the radius of the semicircle is r, and
the rectangle is 3r high, find the area of the window as a function of r.
1 answer:
Notice the picture
the semicircle, has a radius of "r", you can use that to get the area of a circle, then half it, that's the area of that semicircle in "r" terms,
now, look at the rectangle the semicircle is sitting on top of, to make up
the normal window, it has a height of 3r, and notice its width
so, get the area of the semicircle, and the area of the rectangle,
both in r-terms
add them up, and that's the area of the window
the semicircle, has a radius of "r", you can use that to get the area of a circle, then half it, that's the area of that semicircle in "r" terms,
now, look at the rectangle the semicircle is sitting on top of, to make up
the normal window, it has a height of 3r, and notice its width
so, get the area of the semicircle, and the area of the rectangle,
both in r-terms
add them up, and that's the area of the window
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The correct answer would be 
In order to solve for this you must first get the equation equal to 0.
<span>x^2=-5x-3 ----> add 5x to both sides.
x^2 + 5x = -3 ----> add 3 to both sides.
x^2 + 5x + 3 = 0
Now knowing this we can use the coefficients of each one in descending order of power as a, b and c.
a = 1 (because it is the coefficient to x^2)
b = 5</span> (because it is the coefficient to x)
c = 3 (because it is the end number)
Now we can plug these values into the quadratic equation.
And those would be your two answers.
In order to solve for this you must first get the equation equal to 0.
<span>x^2=-5x-3 ----> add 5x to both sides.
x^2 + 5x = -3 ----> add 3 to both sides.
x^2 + 5x + 3 = 0
Now knowing this we can use the coefficients of each one in descending order of power as a, b and c.
a = 1 (because it is the coefficient to x^2)
b = 5</span> (because it is the coefficient to x)
c = 3 (because it is the end number)
Now we can plug these values into the quadratic equation.
And those would be your two answers.
Answer:
The decision is to not reject the null hypothesis.
At a significance level of 0.01, there is not enough evidence to support the claim that the proportion of all those using the drug that experience relief is significantly higher than 50% (P-value = 0.1443).
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the proportion of all those using the drug that experience relief is significantly higher than 50%.
Then, the null and alternative hypothesis are:
The significance level is 0.01.
The sample has a size n=200.
The sample proportion is p=0.54.
The standard error of the proportion is:
Then, we can calculate the z-statistic as:
This test is a right-tailed test, so the P-value for this test is calculated as:
As the P-value (0.1443) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.01, there is not enough evidence to support the claim that the proportion of all those using the drug that experience relief is significantly higher than 50%.