Kyle saves 8% of his income for a new car this year his salary was $2000 less than in the previous year and he saved $3000 what
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Using the z-distribution, it is found that the 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).
If we had increased the confidence level, the margin of error also would have increased.
<h3>What is a confidence interval of proportions?</h3>A confidence interval of proportions is given by:
In which:
is the sample proportion.
- z is the critical value.
- n is the sample size.
In this problem, we have a 95% confidence level, hence, z is the value of Z that has a p-value of
, so the critical value is z = 1.96. Increasing the confidence level, z also increases, hence the margin of error also would have increased.
The sample size and the estimate are given as follows:
.
The lower and the upper bound of the interval are given, respectively, by:
The 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).
More can be learned about the z-distribution at brainly.com/question/25890103
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When a shape is rotated, it must be rotated around a point.
<em>To determine the location of the new triangle, Sonja must subtract (5,-1) from the coordinates of the original triangle, before rotating by </em><em>.</em>
<em />
From the question, we have:
--- the center of rotation
Let the vertices of the triangle be (x,y).
First, she must subtract the coordinates of the center of rotation from the vertices of the triangle.
This gives:
Then the vertices are rotated by
<u />
<u>The rule of </u><u> rotation is:</u>
So, we have:
From the attachment, the coordinates of the triangle are: (0,2), (0,5) and (4,2)
After rotation, the coordinates are calculated as follows:
Hence, the coordinates are: (-3,-5), (-6,-5) and (-3,-1)
Read more about rotations at: