Solve the problem.A quality-control inspector examined 290 calculators and found 15 of them to be defective. At this rate, how many defective calculators will there be in a batch of 15,370 calculators?
A. 4 calculators
B. 53 calculators
C. 795 calculators
D. 4350 calculators
Answer: C
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Factor the trinomial completely. If the polynomial cannot be factored, write "prime."x2 + 12xy + 32y2
A. prime B. (x - 4y)(x + y) C. (x + 4y)(x + 8y) D. (x - 4y)(x + 8y)
Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ? The least-squares line must pass through at least one data point. ?
A. It is false.
?
Example. Find the least-squares line for the data
?
?
Solution. Here, we have 
and
?
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 |  |  |  |  |
?
?
The least-squares line for the data is given by linear equation
?
?
where the constants m and b satisfy the normal equations
?
?
?
?
Then, we obtain the normal equations
?
?
Solving them, we found 
?
Therefore, the required least-squares line is 
?
The scatter diagram and the least-squares line are shown in the figure. We can see that the line does not pass through any data point.
?
B. It is true
?
Suppose that we are given two data points
?
?
If we try to fit a straight line to these data points, the line will miss the first and the second data points by the amountsd1,d2, respectively.
?
?
The principle of least squares states that the straight line L that fits the data points best is the one chosen by requiring that the sum of the squares
?
?
be made as small as possible. But it is possible only in case when least-squares line passes through at least one data point.
Solve the problem.Find 24% of 725 workers.
A. 174 workers B. 3 workers C. 551 workers D. 3021 workers
Based on the graph, find the range of y = f(x).
A. [0, 
]
B. [0, ?)
C. [0, 5]
D. [0, 5)