Question

Which complex number has an absolute value of 5?

A. –3 + 4i
B. 2 + 3i
C. 7 – 2i
D. 9 + 4i

Answer 1

d

Answer 2

"Absolute Value" is sort of unusual language for the modulus of a Complex Number. In any case, the Pythagorean Theorem solves this for you.

D. 9 + 4i ==> 9^2 + 4^2 = 81 + 16 = 97 ==> |9 + 4i| = \(\sqrt{97} > 5\)
C. It should be obvious that one leg of your right triangle greater than 5 is going to have a modulus greater than 5.
B. 2 + 3i ==> 2^2 + 3^2 = 4 + 9 = 13 ==> |2 + 3i| = \(\sqrt{13} < 5\)
A. Let's see what you get on this one.

Answer 3

Class A Class B Class C
80 72 100
85 90 90
87 85 94
92 84 100
86 91 75
90 78 30
94 94 94
100 86 72
75 82 85
45 78 87
85 86 42
38 78 100
72 95 90
94 90 94
62 88 60
Question 1

Analyze the data for Class A and Class B.

Part 1: What are the means and standard deviations for Classes A and B?
Part 2: Make a box plot of the data for Classes A and B. Identify the median, first and third quartiles, and minimum and maximum data points.
Part 3: Explain how the values for Classes A and B vary about the mean and median. What information does this give Mrs. Smith?
Question 2

Analyze and compare the data for Class B and Class C.

Part 1: Make a dot plot for each of Classes B and C.
Part 2: What information is easily seen from the dot plots for Classes B and C?
Part 3: Look at the box plot and dot plot created for Class B. What are the strengths and weaknesses of each type of plot?
Part 4: Which of the two classes (B or C) performed better on the test? Justify your conclusion.
Question 3

Mrs. Smith gives three quizzes before each test. She allows each student to drop their lowest test grade during the grading period and replace it with the average of their quiz grades. The grades in red below were replaced with the average quiz grades.

Class A Class B Class C
80 90 100
85 90 90
87 85 94
92 84 100
86 91 75
90 78 84
94 94 94
100 86 72
75 82 85
70 78 87
85 86 72
38 78 100
72 95 90
94 90 94
82 88 60
Part 1: How does this change the data for Classes A and C?
Part 2: Based upon these changes, which of the three classes did the best on the exam? Justify your answer. SOME ONE HELP