Answer:
The probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days is P(M>54)=0.00004.
Step-by-step explanation:
In this case, we have a population lifetime normally distributed with mean 49 and standard deviation 10.2.
We take a sample of size n=64.
Then, we can calculate the z-score for a sample mean M=54, in order to calculate P(M>54):
The probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days is P(M>54)=0.00004.
It would be, 5+(-7) = 5-7 = -2
B)Option B is your answer........
Answer:
x = 12
Step-by-step explanation:
x - 5 = 84/x
x² - 5x = 84
x² - 5x - 84 = 0
x = (5 ±√(5² - 4(1)(-84))) / 2
x = (5 ± 19) / 2
x = -7 ignore
x = 12
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)
