This is a 30-60-90 triangle and we can apply rules to easily identify the hypotenuse of this triangle, which is denoted by <em>x</em>.
The length of the longer side of the triangle is given in the problem. To solve the hypotenuse of this triangle, let's solve first for the length of the shorter side of the triangle.
The shorter side can be solved by just dividing the length of the longer side by the square root of 3. Hence, we have
![short=\frac{4}{\sqrt[]{3}}](https://tex.z-dn.net/?f=short%3D%5Cfrac%7B4%7D%7B%5Csqrt%5B%5D%7B3%7D%7D)
Since we already have the values for the length of the shorter side and longer side, we can solve for the hypotenuse using the Pythagorean theorem.
![\begin{gathered} c=\sqrt[]{a^2+b^2} \\ c=\sqrt[]{4^2+(\frac{4}{\sqrt[]{3}})^2} \\ c=\sqrt[]{16+\frac{16}{3}} \\ c=\sqrt[]{\frac{64}{3}} \\ c=\frac{8}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}} \\ c=\frac{8\sqrt[]{3}}{3} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20c%3D%5Csqrt%5B%5D%7Ba%5E2%2Bb%5E2%7D%20%5C%5C%20c%3D%5Csqrt%5B%5D%7B4%5E2%2B%28%5Cfrac%7B4%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%29%5E2%7D%20%5C%5C%20c%3D%5Csqrt%5B%5D%7B16%2B%5Cfrac%7B16%7D%7B3%7D%7D%20%5C%5C%20c%3D%5Csqrt%5B%5D%7B%5Cfrac%7B64%7D%7B3%7D%7D%20%5C%5C%20c%3D%5Cfrac%7B8%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%5Ccdot%5Cfrac%7B%5Csqrt%5B%5D%7B3%7D%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%20%5C%5C%20c%3D%5Cfrac%7B8%5Csqrt%5B%5D%7B3%7D%7D%7B3%7D%20%5Cend%7Bgathered%7D)
Hence, the value of hypotenuse for this right triangle is
![x=\frac{8\sqrt[]{3}}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B8%5Csqrt%5B%5D%7B3%7D%7D%7B3%7D)
Answer:
It is not a Type I error neither a Type II error.
Step-by-step explanation:
Let 
be the true mean match score. The null hypothesis is 
and the alternative hypothesis is 
(upper-tail alternative). When the test shows that the mean match score is more than 80 when actually is equal to 80 a Type I error is made. On the other hand, when the test shows that the mean match score is equal to 80 when actually is more than 80 a type II error is made. Therefore, when the test shows that the mean match score is more than 80 when the person does not actually have a fingerprint match, does not correspond to a Type I error neither to a Type II error.
My calculator said -98 :)
I hope I helped:)
Answer:
<em>A)0.09x</em>
Step-by-step explanation:
The original price of the bicycle is x.
The discounted price of the bicycle is x - 30. It is a $30 discount.
The tax goes on the original price. 0.09x is the 9% tax applied to the original price x.
Answer: 0.09x
Area = Area of rectangle + area of semicircle
Area of rectangle = 5 x 1 = 5 m^2
area of semicircle = πD²/8 = 3.14 x 5² / 8 = 9. 8125
Area = 5 + 9.8125 = 14.8125 m^2
