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AST10111 Basic Calculus and Linear Algebra Tutorial 7 (Your submission must reach the designated submission box at Moodle no later than the end of 1 December 2024.) Question 1 Express $(\frac{\sqrt{3}}{2} + \frac{1}{2}i)(-2 + 2\sqrt{3}i)$, where $i = \sqrt{-1}$, in standard form. Question 2 Express $\frac{-14i}{1+i}$, where $i = \sqrt{-1}$, in standard form. Question 3 Find the eighth roots of 256. Express the results in polar form. Question 4 Find the square roots of $(1 + \sqrt{3}i)$. Express the results in standard form.

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For the following statements i) Adam Smith was a highly vocal supporter of division of labour ii) The classical era is described by "one best way of doing things" iii) period in between 1970-90 is known as the era of values and beliefs All of the above are true All of the above are false Only one of the above is true Only two of the above are true

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For each matrix, consider the corresponding system of linear equations. How many free variables are there in the solution? a. $ \square $ $ \left[\begin{array}{rrrr|r}1 & 0 & 0 & -9 & -8 \\ 0 & 1 & 0 & 0 & 6 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0\end{array}\right] $ b. $ \square $ Two $ \left[\begin{array}{rrr|r}1 & -7 & -5 & 6 \\ 0 & 0 & 0 & 0\end{array}\right] $ c. $ \square $ $ \left[\begin{array}{rr|r}1 & 3 & -5 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right] $ d. $ \square $ $ \left[\begin{array}{ll|l}1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 0\end{array}\right] $

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Select all that apply Information gathered from epidemiological studies _____. (Select all that apply.) Multiple select question. can be used to test hypotheses about why people are at higher risk are not subject to the third variable problem as correlational studies are can give us important clues as to who is at highest risk for a disorder

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In the Amish community, who takes care of notifying others of a death? Multiple Choice ◻ neighbors ◻ hospital ◻ funeral home ◻ family In the Amish community, who takes care of notifying others of a death? Multiple Choice ◻ neighbors ◻ hospital ◻ funeral home ◻ family

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During a recession, the Federal Reserve is most likely to sell government bonds to the public. True False

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Which feature of Gram-positive cells is responsible for positive Gram staining?

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vee Singh MS st May) Instructions of Questions: 10 arks: 5 mit: 45 minutes ?s: Contact sessions- 4,5,6,7,8 and 9 Question 2 0.5 pts If the probability of defective items made by a factory is 0.004, then the probability that less than 2 items are defective in the sample of 1000 items is 4e-1/4 5e-4 4e-6

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(25 pts) The thermodynamic dissociate constant of formic acid is 7.1 x10?? at 25.0 °C. The molar ionic conductivities at infinite dilution for H? and formate ion are 349.65 S cm² mol?¹ and 55.5 S cm² mol?¹, respectively. Calculate the resistance of of 0.500 M aqueous solution of formic acid in a cell having cell constant of 0.367 cm?¹. (Assume DHLL applies with one iteration)

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NAME: HW6P2 (15 points): PERSON #: LAB SECTION: The Pascal's triangle can be displayed as elements in a lower-triangular matrix as shown below for 6 rows of Pascal's triangular matrix. Write a MATLAB program that creates a nxn matrix that displays n rows of Pascal's triangle. The program must prompt the user to enter the number n of rows in the lower triangular matrix and then create the matrix. (One way to calculate the value of the elements in the lower portion of the matrix is $C_{ij} = \frac{(i-1)!}{(j-1)!(i-j)!}$ $\begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0\\ 1 & 1 & 0 & 0 & 0 & 0\\ 1 & 2 & 1 & 0 & 0 & 0\\ 1 & 3 & 3 & 1 & 0 & 0\\ 1 & 4 & 6 & 4 & 1 & 0\\ 1 & 5 & 10 & 10 & 5 & 1 \end{bmatrix}$ Use the program to create 4 and 7 rows Pascal's triangles. You can use the built-in function factorial () in MATLAB. Only the Pascal's triangular matrix (PT) must be displayed in the Command Window. Do Not Use disp or fprintf in your program.

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yolanda s.