What is the equation of y = x^3 with the given transformations? Vertical stretch by a factor of 3, horizontal shift 4 units to t
2 answers:
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A. Our diagram have six location: my house (2,1), a movie theater (5,3), the school (6,6), the police station (3,-2), the airport (-3,3), and the mall (-2,-3)
B. Distance between my house and the movie theater:
To calculate the distance we are going to use the points (2,1) and (5,3) to create a right triangle with tow legs of measures 3 and 2; the hypotenuse of the right triangle will be the distance between my house and the movie theater.
Using the Pythagorean theorem:
We can conclude that the distance between my house and the movie theater is
Our second distance is the distance between the police station and the airport:
This time we are using the points (3,-2) and (-3,3) to create a right triangle with legs of measures 6 and 5; the hypotenuse of our triangle will be the the distance between our points:
We can conclude that the distance between the police station and the airport is
C. Distance form the park to the Fire Station:
We can conclude that the distance from the park to the Fire Station is
Distance from the stadium to the mall:
We can conclude that the distance from the stadium to the mall is
D. What is the distance between your house and the mall?
Answer:
We can conclude that the distance between my house and the mall is
What is the distance between the movie theater and the school?
answer:
We can conclude that the distance between the movie theater and the school is
B. Distance between my house and the movie theater:
To calculate the distance we are going to use the points (2,1) and (5,3) to create a right triangle with tow legs of measures 3 and 2; the hypotenuse of the right triangle will be the distance between my house and the movie theater.
Using the Pythagorean theorem:
We can conclude that the distance between my house and the movie theater is
Our second distance is the distance between the police station and the airport:
This time we are using the points (3,-2) and (-3,3) to create a right triangle with legs of measures 6 and 5; the hypotenuse of our triangle will be the the distance between our points:
We can conclude that the distance between the police station and the airport is
C. Distance form the park to the Fire Station:
We can conclude that the distance from the park to the Fire Station is
Distance from the stadium to the mall:
We can conclude that the distance from the stadium to the mall is
D. What is the distance between your house and the mall?
Answer:
We can conclude that the distance between my house and the mall is
What is the distance between the movie theater and the school?
answer:
We can conclude that the distance between the movie theater and the school is
Answer:
And rounded up we have that n=385
Step-by-step explanation:
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".
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We can use as an estimator for p . And replacing into equation (b) the values from part a we got:
And rounded up we have that n=385