What is the solution of the system
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The shortest distance separating Julio from Sarah is 111.8ft
To know the distance of the shortest bridge between Julio and Sarah, the following procedure must be carried out.
We know that Julio walked 100ft to one side and Sarah walked 20ft to the opposite side, that is, on the <em>y-axis</em> they are 120ft apart.
On the other hand, Julio stayed by the river and Sarah walked 9ft away from the river, that is, on the <em>x-axis</em> they are separated by a distance of 59ft (assuming that the width of the river is 50ft).
To know the linear distance that separates them, it is necessary to use the following formula of the Pythagorean theorem.
c² = a² + b²
c=
From this operation we know the value of a and b:
a = 120ft
b = 59ft
Now we just have to replace the values in the formula.
c =
c =
c =
c = 133,7
However, 133.5ft is not the value of the bridge distance because Sarah went 9ft away form the river. Then a portion must be subtracted from her to calculate the exact portion of the distance above the river.
For this we must calculate the distance that separates them that is above the Earth, for this we use the same mathematical formula.
c =
c =
c =
c = 21,9ft
So the distance a part of the Earth covers is 21.9ft. To find out how far the bridge should be over the river, we subtract 21.9ft from the total distance 133.7ft
133,7ft - 21,9ft = 111,8ft
Note: This question is incomplete because it has missing information (the length and width of the river).
Learn more in: brainly.com/question/25292638
Answer:
Nominee d receive 202 votes.
Step-by-step explanation:
Given : In a poll 303 students voted. Nominee d received of the votes.
To find : How many votes did nominee d receive ?
Solution :
The number of votes = 303
Nominee d received of the votes.
i.e.
Therefore, nominee d receive 202 votes.
Answer:
So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.
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".
The population proportion have the following distribution
Solution to the problem
The margin of error for the proportion interval is given by this formula:
(a)
If solve n from equation (a) we got:
(b)
The margin of error desired for this case is equivalent to 2% points
For this case we need to assume a confidence level, let's assume 95%. And since we don't have prior estimation for the population proportion of interest the best value to do an approximation is
In order to find the critical value we need to take in count that we are finding the margin of error for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. And the critical value would be given by:
Now we have all the values needed and if we replace into equation (b) we got:
So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.