Suppose that we examine the relationship between high school GPA and college GPA. We collect data from students at a local colle
1 answer:
Answer:
The typical error between a predicted college GPA using this regression model and an actual college GPA for a given student will be about 0.374 grade points in size (absolute value).
Step-by-step explanation:
The linear regression line for College GPA based on High school GPA is:
<em>College GPA</em> = 1.07 + 0.62 <em>High-school GPA</em>
It is provided that the standard error of the regression line is,
The standard error of a regression line is the average distance between the predicted value and the regression equation.
It is the square root of the average squared deviations.
It is also known as the standard error of estimate.
The standard error of 0.374 implies that:
The typical error between a predicted college GPA using this regression model and an actual college GPA for a given student will be about 0.374 grade points in size (absolute value).
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Answer:
27.
<em>Equation of 2 tangent lines at the given curve going through point P is:</em>
<em>y = -7x + 1</em>
<em>y = x + 1</em>
28.
<u>Part 1:</u> 400 feet
<u>Part 2:</u> Velocity is +96 feet/second (or 96 feet/second UPWARD) & Speed is 96 feet per second
<u>Part 3:</u> acceleration at any time t is -32 feet/second squared
<u>Part 4:</u> t = 10 seconds
29.
<u>Part 1:</u> Average Rate of Change = -15
<u>Part 2:</u> The instantaneous rate of change at x = 2 is -8 & at x = 3 is -23
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Step-by-step explanation:
27.
First of all, the equation of tangent line is given by:
Where m is the slope, or the derivative of the function
Now,
If we take a point x, the corresponding y point would be , so the point would be
Also, the derivative is:
Hence, we can equate the DERIVATIVE (slope) and the slope expression through the point given (0,1) and the point we found
The slope is
So we have:
Now, we equate:
We need to solve this for x. Shown below:
So, this is the x values of the point of tangency. We evaluate the derivative at these 2 points, respectively.
Now, we find 2 equations of tangent lines through the point (0,1) and with respective slopes of -7 and 1. Shown below:
and
<em>So equation of 2 tangent lines at the given curve going through point P is:</em>
<em>y = -7x + 1</em>
<em>y = x + 1</em>
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28.
<u>Part 1:</u>
The highest point is basically the maximum value of the position function. To get maximum, we differentiate and set it equal to 0. Let's do this:
So, at t = 5, it reaches max height. We plug in t = 5 into position equation to find max height:
max height = 400 feet
<u>Part 2:</u>
Velocity is speed, but with direction.
We also know the position function differentiated, is the velocity function.
Let's first find time(s) when position is at 256 feet. So we set position function to 256 and find t:
At t = 2, the velocity is:
It is going UPWARD at this point, so the velocity is +96 feet/second or 96 feet/second going UPWARD
The corresponding speed (without +, -, direction) is simply 96 feet/second
<u>Part 3:</u>
We know the acceleration is the differentiation of the velocity function. let's find it:
hence, the acceleration at any time t is -32 feet/second squared
<u>Part 4:</u>
The rock hits the ground when the position is 0 (at ground). So we equate the position function, s(t), to 0 and find time when it hits the ground. Shown below:
We disregard t = 0 because that's basically starting. So we take t = 10 seconds as our answer and we know rock hits the ground at t = 10 seconds.
29.
<u>Part 1:</u>
The average rate of change is basically the slope, which is
Slope = Change in y/ Change in x
The x values are given, from 2 to 3, and we need to find corresponding y values by plugging in the x values in the function. So,
When x = 2,
When x = 3,
Hence,
Average Rate of Change =
<u>Part 2:</u>
The instantaneous rate of change is got by differentiating the function and plugging the 2 points and finding the difference.
First, let's differentiate:
Now, find the derivative at 3,
finding derivative at 2,
The instantaneous rate of change at x = 2 is -8 & at x = 3 is -23