Answer: Sin N =
Step-by-step explanation:
Since we have given that
In triangle MPN, ∠P=90°
As we know the formula for "Trigonometric Ratios":
By Pythagorus theorem , we get
So, we get,
Hence, Sin N =
In a study of 799 randomly selected medical malpractice lawsuits, it was found that 499 of them were dropped or dismissed. Use
1 answer:
Answer:
Claim is true that most medical malpractice lawsuits are dropped or dismissed.
Step-by-step explanation:
Given :In a study of 799 randomly selected medical malpractice lawsuits, it was found that 499 of them were dropped or dismissed.
To Find : Use a 0.05 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed.
Solution:
n = 799
x = 499
We will use one sample proportion test
We are given that the claim is most medical malpractice lawsuits are dropped or dismissed.
Probability of dropped or dismissed is 1/2
Formula of test statistic =
=
= 7.038
p value (z>7.038) is 0
α =0.05
So, p value < α
So, we reject the null hypothesis
So,claim is true
Hence most medical malpractice lawsuits are dropped or dismissed.
You might be interested in
4. To solve this problem, we divide the two expressions step by step:
Here we have inverted the second term since division is just multiplying the inverse of the term.
In this step we factor out the quadratic equation.
Then, we cancel out the like term which is x-1.
We then solve for the final combined expression:
For the restrictions, we just need to prevent the denominators of the two original terms to reach zero since this would make the expression undefined:
Therefore, x should not be equal to 1, -5, or -4.
Comparing these to the choices, we can tell the correct answer.
ANSWER:; 
5. To get the ratio of the volume of the candle to its surface area, we simply divide the two terms with the volume on the numerator and the surface area on the denominator:
We can simplify this expression by factoring out the denominator and cancelling like terms.
We then rationalize the denominator:
![\frac{rh(3r-3 \sqrt{ r^{2} + h^{2} })}{(3r)^{2}-(3 \sqrt{ r^{2} + h^{2} })^{2}}}=\frac{3 r^{2}h -3rh \sqrt{ r^{2} + h^{2} }}{9r^{2} -9 (r^{2} + h^{2} )}=\frac{3rh(r -\sqrt{ r^{2} + h^{2} })}{9[r^{2} -(r^{2} + h^{2} )]}=\frac{rh(r -\sqrt{ r^{2} + h^{2} })}{3[r^{2} -(r^{2} + h^{2} )]}](https://tex.z-dn.net/?f=%5Cfrac%7Brh%283r-3%20%5Csqrt%7B%20r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%7D%29%7D%7B%283r%29%5E%7B2%7D-%283%20%5Csqrt%7B%20r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%7D%29%5E%7B2%7D%7D%7D%3D%5Cfrac%7B3%20r%5E%7B2%7Dh%20-3rh%20%5Csqrt%7B%20r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%7D%7D%7B9r%5E%7B2%7D%20-9%20%28r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%29%7D%3D%5Cfrac%7B3rh%28r%20-%5Csqrt%7B%20r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%7D%29%7D%7B9%5Br%5E%7B2%7D%20-%28r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%29%5D%7D%3D%5Cfrac%7Brh%28r%20-%5Csqrt%7B%20r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%7D%29%7D%7B3%5Br%5E%7B2%7D%20-%28r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%29%5D%7D)
Since the height is equal to the length of the radius, we can replace h with r and further simplify the expression:
![\frac{r*r(r -\sqrt{ r^{2} + r^{2} })}{3[r^{2} -(r^{2} + r^{2} )]}=\frac{ r^{2} (r -\sqrt{2 r^{2} })}{3[r^{2} -(2r^{2} )]}=\frac{ r^{2} (r -r\sqrt{2 })}{-3r^{2} }=\frac{r -r\sqrt{2 }}{-3 }=\frac{r(1 -\sqrt{2 })}{-3 }](https://tex.z-dn.net/?f=%5Cfrac%7Br%2Ar%28r%20-%5Csqrt%7B%20r%5E%7B2%7D%20%2B%20r%5E%7B2%7D%20%7D%29%7D%7B3%5Br%5E%7B2%7D%20-%28r%5E%7B2%7D%20%2B%20r%5E%7B2%7D%20%29%5D%7D%3D%5Cfrac%7B%20r%5E%7B2%7D%20%28r%20-%5Csqrt%7B2%20r%5E%7B2%7D%20%7D%29%7D%7B3%5Br%5E%7B2%7D%20-%282r%5E%7B2%7D%20%29%5D%7D%3D%5Cfrac%7B%20r%5E%7B2%7D%20%28r%20-r%5Csqrt%7B2%20%7D%29%7D%7B-3r%5E%7B2%7D%20%7D%3D%5Cfrac%7Br%20-r%5Csqrt%7B2%20%7D%7D%7B-3%20%7D%3D%5Cfrac%7Br%281%20-%5Csqrt%7B2%20%7D%29%7D%7B-3%20%7D)
By examining the choices, we can see one option similar to the answer.
ANSWER:
Here we have inverted the second term since division is just multiplying the inverse of the term.
In this step we factor out the quadratic equation.
Then, we cancel out the like term which is x-1.
We then solve for the final combined expression:
For the restrictions, we just need to prevent the denominators of the two original terms to reach zero since this would make the expression undefined:
Therefore, x should not be equal to 1, -5, or -4.
Comparing these to the choices, we can tell the correct answer.
ANSWER:
5. To get the ratio of the volume of the candle to its surface area, we simply divide the two terms with the volume on the numerator and the surface area on the denominator:
We can simplify this expression by factoring out the denominator and cancelling like terms.
We then rationalize the denominator:
Since the height is equal to the length of the radius, we can replace h with r and further simplify the expression:
By examining the choices, we can see one option similar to the answer.
ANSWER: