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iris
1 month ago
11

Suppose that you have two different algorithms for solving a problem. to solve a problem of size n, the first algorithm uses exa

ctly n(log(n)) operations and the second algorithm uses exactly n3=2 operations. as n grows, which algorithm uses fewer operations? justify your answer using definitional proof.
Mathematics
1 answer:
tester [12.3K]1 month ago
5 0
<span>We have two expressions: n(log(n)) and n3=2. The second expression involves fewer operations. From it, we can derive n = 2/3. For the left-hand side to equal the right-hand side, n cannot go beyond 2/3. No further operations can be applied at that level. Conversely, if we set n = 10, we find 10(log(10)) = 1. As we escalate n to 100, 100(log(100)) equals 200, and for n = 300, 300(log(300)) results in about 743.1. The logarithmic function increases without limit, while for the first operation, once n hits 2/3, it halts. Therefore, the second expression has fewer operations overall.</span>
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Here’s a counterexample: consider

B = \{1, 2, 3, 4, 5\},\quad D = \{A, B, C, D, 5\}

Select the subsets in the following manner:

A = \{1, 5\},\quad C = \{A, B, C\}

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8 0
1 month ago
Ethan bought 4 packages of pencils. After he gave 8 pencils to his friends, he had 40 pencils left over. How many pencils were i
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Answer:

12 pencils per package.

Step-by-step explanation:

Details provided:

Ethan purchased 4 packages of pencils.

Number of Packages = 4

Number of pencils shared with friend = 8 pencils

Pencils remaining = 40 pencils

∴Total Number of Pencils = Pencils given to friend + Pencils remaining = 40+8 =48

Total Pencils in each package = \frac{\textrm{Total Number of Pencils}}{\textrm{No Of Packages}}= \frac{48}{4}= 12 \ pencils

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1 month ago
Emerson drives 135 miles at 60 miles per hour to get to the train station. He waits 20 minutes for a train. Then he travels 350
Inessa [12570]

Response: 4.4

Detailed breakdown:

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1 month ago
The random variable KK has a geometric distribution with mean 16. Which of the following is closest to the standard deviation of
Inessa [12570]

Answer:

E 240

Step-by-step explanation:

Mean of the geometric distribution = (1- p) / p

16 = (1 - p) / p

16p = 1 - p;  17p = 1; thus, p = 1/17 = 0.058  

Standard Deviation = (1 - p) / p^2

= (1 - 0.058) / (0.058)^2

0.942 / 0.003364

= 280, which is closest to 240

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Response:

12 Hours

Step-by-step rationale:

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1 month ago
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