Ques tion 1 (3 points)
Ques
tion 1 (3 points)
Q1. Using the general term an = 7n – 1, what is a75 ?
Your Answer:
Question 1 options:
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Question 2 (3 points)
Q2. Using the general term an = n2 – 13n, what is the 19th term?
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Question 2 options:
Answer
Question 3 (3 points)
Q3. Evaluate {“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>6</mn></munderover></math>”} 4n2 – 7n.
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Question 3 options:
Answer
Question 4 (3 points)
Q4. What is a30 for the arithmetic sequence with a1 = 6 and d = 4?
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Question 4 options:
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Question 5 (3 points)
Q5. Evaluate the arithmetic series{“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>100</mn></munderover><mstyle displaystyle=”false”></mstyle></math>”}8n + 7.
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Question 5 options:
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Question 6 (3 points)
Q6. What is a10 for the geometric sequence with a1 = 3 and r = 2?
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Question 6 options:
Answer
Question 7 (3 points)
Q7
Your Answer:
7. Evaluate the geometric series 14*3n-1.
Answer
Question 8 (3 points)
Q8. Suppose g1 = 1 and g2 = 3. The rest of the terms in a recursive sequence are given by the formula gn = n·gn-1 + gn-2.
Find the 7th term of the sequence, g7.
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Question 8 options:
Answer
Question 9 (3 points)
Q9. Consider the following algorithm:
sum = 0
For j starting at 1 and ending with 13:
sum = sum + (4*j + 6)
print(sum)
What is printed as a result of executing this algorithm?
Your Answer:
Question 9 options:
Answer
Question 10 (3 points)
Q10. Consider the following algorithm:
g1 = 7
g2 = 5
For k starting at 0 and ending with 8:
gk = (k-1)·gk-1 + gk-2
What is the last term, g8, of the recursive sequence generated as a result of executing this algorithm?
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Question 10 options:
Answer
Question 11 (3 points)
Q11. Let A = {1, 2, 3, 4, …, 12}. What is the cardinality of the power set of A, P(A)?
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Answer
Question 12 (3 points)
Q12. Fill in the missing element of B such that A = B.
A = {7, 19, g, #, 2, 4, &, f, 17, 1, k}
B = {#, 1, 7, __, k, 2, f, 19, g, 4, &}
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Question 12 options:
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Question 13 (3 points)
Q13. Let A = {y ∈ Z : 10 {“version”:”1.1″,”math”:”<math style=”font-family:’Times New Roman'” xmlns=”http://www.w3.org/1998/Math/MathML”><mstyle mathsize=”18px”><mo><</mo></mstyle></math>”} y {“version”:”1.1″,”math”:”<math style=”font-family:’Times New Roman'” xmlns=”http://www.w3.org/1998/Math/MathML”><mstyle mathsize=”18px”><mo>≤</mo></mstyle></math>”} 14 and y is even}. What is |A|?
Your Answer:
Question 13 options:
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Question 14 (3 points)
Q14D. Define the sets A, B, C, and D as follows:
A = {-3, 1, 6, 7, 10}
B = {-10, -5, 1, 4, 6}
C = {x ∈ Z: x is odd}
D = {x ∈ Z: x is positive}
Find A ∩ D.
*Express the set using roster notation and with values ordered smallest to largest, such as {-10, -3, 1, 6} (braces and commas are required; a space after each comma is also required).
Question 14 options:
Question 15 (3 points)
Q15B. Define the sets A, B, C, and D as follows:
A = {y ∈ Z : 2 {“version”:”1.1″,”math”:”<math style=”font-family:’Times New Roman'” xmlns=”http://www.w3.org/1998/Math/MathML”><mstyle mathsize=”18px”><mo><</mo></mstyle></math>”} y {“version”:”1.1″,”math”:”<math style=”font-family:’Times New Roman'” xmlns=”http://www.w3.org/1998/Math/MathML”><mstyle mathsize=”18px”><mo>≤</mo></mstyle></math>”} 9 and y is odd}.
B = {1, 4, 6}
C = {y ∈ Z : y {“version”:”1.1″,”math”:”<math style=”font-family:’Times New Roman'” xmlns=”http://www.w3.org/1998/Math/MathML”><mstyle mathsize=”18px”><mo>≤</mo></mstyle></math>”} 10 and y is even}.
D = {y ∈ Z : y {“version”:”1.1″,”math”:”<math style=”font-family:’Times New Roman'” xmlns=”http://www.w3.org/1998/Math/MathML”><mstyle mathsize=”18px”><mo>≤</mo></mstyle></math>”} 7 and y is positive}
E = {-3, -1, 0, 5}
Find A ∪ E.
*Express the set using roster notation and with values ordered smallest to largest, such as {-10, -3, 1, 6} (braces and commas are required; a space after each comma is also required).
Question 15 options:
Question 16 (3 points)
Q16D. Define the sets A and B as shown. Find {“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><menclose notation=”top”><mi>A</mi></menclose></math>”}.
*Express the set using roster notation and with letters ordered alphabetically, such as {d, n, x, z}.
(Braces and commas are required; a space after each comma is also required.)
Question 16 options:
Question 17 (3 points)
Q17B. Define the sets A, B, C, and D as shown. Find A ∪ (B ∩ D).
*Express the set using roster notation and with letters ordered alphabetically, such as {d, n, x, z}.
(Braces and commas are required; a space after each comma is also required.)
Question 17 options:
Question 18 (3 points)
Q18A. Define the sets A and B as shown. Select all statements which are true.
Question 18 options:
{a, f, g, h, m, s} ⊆ B
{a, c, m, p, s, w} ⊂ A
{m, s} ⊆ A
{a, g, s, m} ⊆ A
{a, f} ⊂ B
Question 19 (3 points)
Q19C. Define the sets A, B, C, and D as shown. Select all statements which are true.
Question 19 options:
D ⊆ B
{m, s} ⊂ C
{a, c, p, w} ⊂ A
{a, c, m, p, s, w} ⊂ A
C ⊆ B
Question 20 (3 points)
Q20. Suppose a computer program has been initialized such that the following sets have been stored for use in any algorithm:
A = {1, 2, 3, …, 47}
B = {-7, -6, -5, …, 30}
Consider the following algorithm, which represents one part of the whole computer program (comments may occur after the # symbol on any line and are not used in computations):
#Part 1: computes A – B and its cardinality
AminusB = set()
for element in A: # this line runs through every element in A
if not(element in B): #A – B is the set of elements that are in A and are not in B
AminusB.add(element) # Add to AminusB every element in A if the element is also not in B
n = len(AminusB) #len() returns the number of elements in the array
print(n)
What value is printed as a result of executing this algorithm?
Your Answer:
Complete Answer:
