Consider the equation One-fourth(x – 5) = (y – 2)2. What is the equation of the directrix?
1 answer:
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When we find a geometric sequence using the first and second terms, what we do is divide the second by the first to find a "common ratio," the number you multiply by to get to the next term.
In this case, we only have the second and fifth terms. From the second to the fifth term, we've multiplied by that common ratio three times.
What we can do is divide the fifth by the second and then take the <em>cube root</em> to find our common ratio.
![2304\div-36=-64\\\sqrt[3]-64=\boxed{-4}](https://tex.z-dn.net/?f=2304%5Cdiv-36%3D-64%5C%5C%5Csqrt%5B3%5D-64%3D%5Cboxed%7B-4%7D)
Now we know we're multiplying by -4 each time, let's find the first term.
The opposite of multiplying by -4 would be dividing by -4. We work back from our second term -36 to find that the first term would be 9.
For each sucessive term, we then multiply by -4.
Our equation is
In this case, we only have the second and fifth terms. From the second to the fifth term, we've multiplied by that common ratio three times.
What we can do is divide the fifth by the second and then take the <em>cube root</em> to find our common ratio.
Now we know we're multiplying by -4 each time, let's find the first term.
The opposite of multiplying by -4 would be dividing by -4. We work back from our second term -36 to find that the first term would be 9.
For each sucessive term, we then multiply by -4.
Our equation is
Answer:
90% confidence interval: (2186.53;2881.47)
95% confidence interval: (2118.73;2949.27)
99% confidence interval: (1987.37;3080.63)
For the last part is not the best way say : "This interval describes the price of 95% of the rents of all the unfurnished one-bedroom apartments in the Boston area."
The best interpretation is this one: "We are 95% confident that the actual mean for the rents of unfurnished one-bedroom apartments in the Boston area is between (2118.73;2949.27)"
Step-by-step explanation:
1) Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean
population mean (variable of interest)
represent the population standard deviation
n=10 represent the sample size
90% confidence interval
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.90 or 90%, the value of and
, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 90% confidence interval would be given by (2186.53;2881.47)
95% confidence interval
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (2118.73;2949.27)
99% confidence interval
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.99 or 99%, the value of and
, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 99% confidence interval would be given by (1987.37;3080.63)
For the last part is not the best way say : "This interval describes the price of 95% of the rents of all the unfurnished one-bedroom apartments in the Boston area."
The best interpretation is this one: "We are 95% confident that the actual mean for the rents of unfurnished one-bedroom apartments in the Boston area is between (2118.73;2949.27)"