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Question
Given the following information:
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Compute:
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Solution
The information provided can be interpreted as the price for three fruit baskets with different combinations of the three fruits. This corresponds to a system of linear equations where the price of the three fruits is the vector of unknowns :
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The system of linear equations is then: This can be solved using any solution algorithm, e.g., elimination: Based on the three prices for the different fruits it is straightforward to compute the total price of the fourth fruit basket via:
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False
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True
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False
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False
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False
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Question
What is the distance between the two points and in a Cartesian coordinate system?
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Solution
The distance of and is given by (Pythagorean formula).
Hence .

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False
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True
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False
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False
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False
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Question
What is the derivative of , evaluated at ?
Solution
Using the product rule for , where and , we obtain Evaluated at , the answer is Thus, rounded to two digits we have .
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Question
The daily expenses of summer tourists in Vienna are analyzed. A survey with tourists is conducted. This shows that the tourists spend on average EUR. The sample variance is equal to .
Determine a confidence interval for the average daily expenses (in EUR) of a tourist.
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What is the lower confidence bound?
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What is the upper confidence bound?
Solution
The confidence interval for the average expenses is given by:
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The lower confidence bound is .
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The upper confidence bound is .
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Question
For 63 firms the number of employees and the amount of expenses for continuing education (in EUR) were recorded. The statistical summary of the data set is given by:
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202 |
Variance |
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1889 |
The correlation between and is equal to 0.73.
Estimate the expected amount of money spent for continuing education by a firm with 52 employees using least squares regression.
Solution
First, the regression line is determined. The regression coefficients are given by:
The estimated amount of money spent by a firm with 52 employees is then given by: