Answer:
Step-by-step explanation:
Pattern 6 will have 35
9514 1404 393
Answer:
c = -3; d = 5
Step-by-step explanation:
The function is differentiable if it is continuous and the derivative is continuous.
This function will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
5(3^2) +c = 45 +c
From the right, the limit is ...
d(3^2) -3 = 9d -3
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The derivative will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
f'(x) = 10x
= 10(3) = 30
From the right, the limit is ...
f'(x) = 2dx
= 2d(3) = 6d
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This gives us a pair of simultaneous equations in 'c' and 'd':
45 +c = 9d -3
6d = 30
The latter tells us d = 5. Then the former tells us ...
45 +c = 9(5) -3 ⇒ c = -3
The function is differentiable if c = -3 and d = 5.
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<em>Additional comment</em>
With these values, the function becomes ...
Answer: All real numbers
Step-by-step explanation: The domain should be all real numbers, there are no restrictions
Answer:
(D)
Step-by-step explanation:
The box plot is a visual representation of the 5-number summary of the data. It shows the extremes, the quartiles and the median.
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Each data set has 11 elements, sorted into increasing order.
<h3>extremes</h3>
The first and last elements of the data set correspond to the ends of the whiskers, so you are looking for a set that ranges from 3 to 18. (This eliminates choice B.)
<h3>median</h3>
The median will be the middle element, the 6th from either end. The vertical line in the box identifies its value as 10. (This eliminates choice A.)
<h3>quartiles</h3>
The first quartile is the middle element of the bottom half of the data set (what remains after the median and above elements are removed). There are 5 elements in the bottom half, so the first quartile is the 3rd one. It is signified by the left end of the box in the box plot. Its value is 7. (This eliminates choice C.)
Similarly, the third quartile is the 3rd element from the right end of the data set. The value 13 in choice D matches the right end of the box in the box plot.
The box plot represents the data set in Choice D.
Aproximately 15%
975-829=146 (difference)
(146/975)×100 = 14.974435897
