Answer:
The minimum number of drivers you would need to survey is 601.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of
.
The margin of error is:
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
95% confidence level
So
, z is the value of Z that has a p-value of
, so
.
What is the minimum number of drivers you would need to survey to be 95% confident that the population proportion is estimated to within 0.04?
The number is n for which M = 0.04.
We don't have an estimate for the proportion, so we use
. Then
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
![0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}](https://tex.z-dn.net/?f=0.04%20%3D%201.96%5Csqrt%7B%5Cfrac%7B0.5%2A0.5%7D%7Bn%7D%7D)
![0.04\sqrt{n} = 1.96*0.5](https://tex.z-dn.net/?f=0.04%5Csqrt%7Bn%7D%20%3D%201.96%2A0.5)
![\sqrt{n} = \frac{1.96*0.5}{0.04}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B1.96%2A0.5%7D%7B0.04%7D)
![(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E2%20%3D%20%28%5Cfrac%7B1.96%2A0.5%7D%7B0.04%7D%29%5E2)
![n = 600.25](https://tex.z-dn.net/?f=n%20%3D%20600.25)
Rounding up:
The minimum number of drivers you would need to survey is 601.
Answer:
<h3>x is any real number except 0.</h3>
Step-by-step explanation:
![\text{Domain}:\ x\neq0](https://tex.z-dn.net/?f=%5Ctext%7BDomain%7D%3A%5C%20x%5Cneq0)
![\dfrac{1}{x}-\dfrac{1}{3x}=\dfrac{1}{2x}+\dfrac{1}{6x}\qquad\text{multiply both sides by 6}\\\\6\cdot\dfrac{1}{x}-6\!\!\!\!\diagup^2\cdot\dfrac{1}{\not3_1x}=6\!\!\!\!\diagup^3\cdot\dfrac{1}{\not2_1x}+6\!\!\!\!\diagup^1\cdot\dfrac{1}{\not6_1x}\\\\\dfrac{6}{x}-\dfrac{2}{x}=\dfrac{3}{x}+\dfrac{1}{x}\qquad\text{subtract}\ \dfrac{3}{x}\ \text{and}\ \dfrac{1}{x}\ \text{from both sides}\\\\\dfrac{6}{x}-\dfrac{2}{x}-\dfrac{3}{x}-\dfrac{1}{x}=0\\\\\dfrac{6-2-3-1}{x}=0\\\\\dfrac{0}{x}=0\\\\0=0\ TRUE](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7Bx%7D-%5Cdfrac%7B1%7D%7B3x%7D%3D%5Cdfrac%7B1%7D%7B2x%7D%2B%5Cdfrac%7B1%7D%7B6x%7D%5Cqquad%5Ctext%7Bmultiply%20both%20sides%20by%206%7D%5C%5C%5C%5C6%5Ccdot%5Cdfrac%7B1%7D%7Bx%7D-6%5C%21%5C%21%5C%21%5C%21%5Cdiagup%5E2%5Ccdot%5Cdfrac%7B1%7D%7B%5Cnot3_1x%7D%3D6%5C%21%5C%21%5C%21%5C%21%5Cdiagup%5E3%5Ccdot%5Cdfrac%7B1%7D%7B%5Cnot2_1x%7D%2B6%5C%21%5C%21%5C%21%5C%21%5Cdiagup%5E1%5Ccdot%5Cdfrac%7B1%7D%7B%5Cnot6_1x%7D%5C%5C%5C%5C%5Cdfrac%7B6%7D%7Bx%7D-%5Cdfrac%7B2%7D%7Bx%7D%3D%5Cdfrac%7B3%7D%7Bx%7D%2B%5Cdfrac%7B1%7D%7Bx%7D%5Cqquad%5Ctext%7Bsubtract%7D%5C%20%5Cdfrac%7B3%7D%7Bx%7D%5C%20%5Ctext%7Band%7D%5C%20%5Cdfrac%7B1%7D%7Bx%7D%5C%20%5Ctext%7Bfrom%20both%20sides%7D%5C%5C%5C%5C%5Cdfrac%7B6%7D%7Bx%7D-%5Cdfrac%7B2%7D%7Bx%7D-%5Cdfrac%7B3%7D%7Bx%7D-%5Cdfrac%7B1%7D%7Bx%7D%3D0%5C%5C%5C%5C%5Cdfrac%7B6-2-3-1%7D%7Bx%7D%3D0%5C%5C%5C%5C%5Cdfrac%7B0%7D%7Bx%7D%3D0%5C%5C%5C%5C0%3D0%5C%20TRUE)
There are several process for finding the HCF or Highest Common factor for any numbers given. In this case the two numbers given are 240 and 1500.
Firstly we need to divide 1500 by 240 and check if there are any remainders. On dividing we get quotient is 6 and remainder is 60. Now again we have to divide 240 by 60 which we found as remainder previously. Then on dividing 240 by 60 we get no remainder. So the 60 is the HCF or the Highest Common Factor of 240 and 1500. This is the easiest process by which the HCF of any set of numbers can be found.
Answer:
y=3.5x
Step-by-step explanation:
Since when x is 0 when y is 0, there is no y-intercept. The ratio with the other values gives the equation y=3.5x, because y is 3.5 times larger than x.
The probability is 3/5 or three out of five