Answer:
51 trees
Step-by-step explanation:
Start at one end of the 50-foot line segment.
At position 0 ft, put one tree.
Then 1 ft from 0 ft, put tree number 2.
One more foot over, at position 2 ft from the start, put tree number 3.
Notice that each tree number is one more than the number of feet.
That means at 50 ft from the stat, you put tree number 51.
Answer: 51 trees
Answer:
![H0: mu = 8.9 fl oz.\\\\](https://tex.z-dn.net/?f=H0%3A%20mu%20%3D%208.9%20fl%20oz.%5C%5C%5C%5C)
![Ha: mu ≠8.9 fluid oz](https://tex.z-dn.net/?f=Ha%3A%20mu%20%E2%89%A08.9%20fluid%20oz)
Step-by-step explanation:
Given that A perfume company claims that the mean weight of ther new perfume is at least 8.9 fluid oz
For testing this claim, in Statistics we perform a certain measures called hypothesis testing.
For this first step is to create null and alternate hypothesis.
Normally null hypothesis would have some statistic = something
Here we want to test the mean weight of perfume
Hence null hypothesis would be
H0: mu = 8.9 fl oz.
Alternate hypothesis would be opposite of this claim
i.e.
Ha: mu ≠8.9 fluid oz
Hence answer is
![H0: mu = 8.9 fl oz.\\\\](https://tex.z-dn.net/?f=H0%3A%20mu%20%3D%208.9%20fl%20oz.%5C%5C%5C%5C)
![Ha: mu ≠8.9 fluid oz](https://tex.z-dn.net/?f=Ha%3A%20mu%20%E2%89%A08.9%20fluid%20oz)
Answer: The required value of y is 19.
Step-by-step explanation: We are given to find the value of y in the solution to the following system of equations :
![y=12x+7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=-6x+25~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)](https://tex.z-dn.net/?f=y%3D12x%2B7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%28i%29%5C%5C%5C%5Cy%3D-6x%2B25~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%28ii%29)
Comparing equations (i) and (ii), we get
![12x+7=-6x+25\\\\\Rightarrow 12x+6x=25-7\\\\\Rightarrow 18x=18\\\\\Rightarrow x=\dfrac{18}{18}\\\\\Rightarrow x=1.](https://tex.z-dn.net/?f=12x%2B7%3D-6x%2B25%5C%5C%5C%5C%5CRightarrow%2012x%2B6x%3D25-7%5C%5C%5C%5C%5CRightarrow%2018x%3D18%5C%5C%5C%5C%5CRightarrow%20x%3D%5Cdfrac%7B18%7D%7B18%7D%5C%5C%5C%5C%5CRightarrow%20x%3D1.)
From equation (i), we get
![y=12\times1+7=12+7=19.](https://tex.z-dn.net/?f=y%3D12%5Ctimes1%2B7%3D12%2B7%3D19.)
Thus, the required value of y is 19.
The formula<span> will be a</span>n<span> = a</span>12n - 1<span> or a</span>n<span> = (1)2</span>n - <span>1</span>
Answer:
![n\geq 23](https://tex.z-dn.net/?f=n%5Cgeq%2023)
Step-by-step explanation:
-For a known standard deviation, the sample size for a desired margin of error is calculated using the formula:
![n\geq (\frac{z\sigma}{ME})^2](https://tex.z-dn.net/?f=n%5Cgeq%20%28%5Cfrac%7Bz%5Csigma%7D%7BME%7D%29%5E2)
Where:
is the standard deviation
is the desired margin of error.
We substitute our given values to calculate the sample size:
![n\geq (\frac{z\sigma}{ME})^2\\\\\geq (\frac{1.96\times 12}{5})^2\\\\\geq 22.13\approx23](https://tex.z-dn.net/?f=n%5Cgeq%20%28%5Cfrac%7Bz%5Csigma%7D%7BME%7D%29%5E2%5C%5C%5C%5C%5Cgeq%20%28%5Cfrac%7B1.96%5Ctimes%2012%7D%7B5%7D%29%5E2%5C%5C%5C%5C%5Cgeq%2022.13%5Capprox23)
Hence, the smallest desired sample size is 23