5a. Write the equation of the polynomial with leading coefficient 3 that has degree 4, with x-intercepts at -2 and 1, both having a multiplicity of 2.

b. Write the equation of the polynomial which goes through the following points. (-2,0),(-1,0),(5,0), and (0,10).

c. (1+i) is a zero of f(x)=x^4 - 2x^3 - x^2+ 6x - 6. Find the other zeros

Please show all the work. Expert and correct answers only.

Bobby rolls 2 fair 6-sided dice and considers it a "success" if the sum of the die results is 5 or 6. He performs 4 trials.  

Martha tosses 2 fair coins and considers it a "success" if both coins land on "heads." She performs 3 trials.

Heather rolls 1 fair 4-sided die and considers it a "success" if he rolls a "1." He performs 5 trials.

What is the probability that exactly 2 success occur in all of the combined trials above?

Researchers interested in determining if there is a relationship between anxiety and religiosity conducted the following study. Subjects completed a 5 point anxiety item (high score = high anxiety) and also completed a 15 item checklist designed to measure an individual’s degree of religiosity (belief in a particular religion, regular attendance at religious services, etc). A high score indicates greater religiosity. Sample data from 10 subjects are provided below. Can you predict anxiety (y) from religiosity (x)? First determine the correlation coefficient and test if that correlation coefficient is statistically significant or not. Second determine and plot the best fitting line. And third, determine if the best fitting line is --- good enough.

Religiosity Anxiety

4 4

3 4

1 3

5 3

9 2

6 1

14 2

9 2

12 1

11 2

The hospital has acquired medical diagnostic equipment that cost $2,000,000 total. In addition, the hospital had to pay $45,000 to have the equipment shipped to it from the manufacturer, and $60,000 to install the equipment. It is expected that the equipment has a 7-year useful life, and a $200,000 salvage value. Calculate the ten years of depreciation using straight line, double declining balance, and sum-of-the-years digits.

1

2

3

4

5

6

7

1

2

3

4

5

6

7

1

2

3

4

5

6

7

A machine costing $213,600 with a four-year life and an estimated $16,000 salvage value is installed in Tonys Company’s factory on January 1. The factory manager estimates the machine will produce 494,000 units of product during its life. It actually produces the following units: 121,800 in Year 1, 123,500 in Year 2, 121,100 in Year 3, 137,600 in Year 4. The total number of units produced by the end of Year 4 exceeds the original estimate—this difference was not predicted. (The machine cannot be depreciated below its estimated salvage value.)

Compute depreciation for each year (and total depreciation of all years combined) for the machine under each depreciation method.

1A. Compute depreciation for each year (and total depreciation of all years combined) for the machine under the Straight-line depreciation.

1B. Compute depreciation for each year (and total depreciation of all years combined) for the machine under the Units of production.

1C. Compute depreciation for each year (and total depreciation of all years combined) for the machine under the Double-declining-balance.

Question 1 (20pts):

Create a dictionary of the form {“Jordan”: “Basketball”, “Federer”: “Tennis”, “Ronaldo”: “Football”} and perform the following actions

• Print all the keys in the dictionary
• Print all the values in the dictionary
• Iterate through the dictionary and print the value only if the key is “Federer”
• Iterate through the dictionary and print the key only if the value is “Football”

Question 2 (15pts):

List1 = [3, 4, 5, 20, 5]

List2 = [4, 9, 6, 2, 10].

Using list comprehensions, print the output if you multiply the i-th element of each list

Question 3 (15pts):¶

Dic1 = {"John":10, "Joe":15}

• Check whether “John” is one of the keys
• Remove the key “Joe” along with its associated value
• Add another key and value pair - “Jean”: 40

Question 4 (15pts):

• Write a user defined function to find the highest of the three numbers: 30, 10 and 20. The highest number should be printed. Note: The function has to be user defined.

• With a given integral number n, write a program to generate a dictionary that contains key value pairs such as i: 2^i, and i takes values between 1 and n (both included). Then print the dictionary.

Suppose the following input is supplied to the program:

4

Then, the output should be:

{1: 2, 2: 4, 3: 8, 4: 16}

Question 5 (20pts):

• Using list comprehensions, print all the values between 1 and 10 that are divisible by 2. The output should be [2, 4, 6, 8].

• By using list comprehension, please write a program to print the list after removing the value 24 in [12,24,35,24,88,120,155].

Question 6 (15pts):

Remove the last value in [12,24,35,24,88,120,155] consecutively and print the removed value in each removal.

   Find the derivative of the function
   f(t)=arccsc⁡〖(-t^2)〗
   f(x)=arccot⁡√x
   y=ln⁡〖t^2 〗-arctan⁡〖t/2〗
   f(x)=arcsec⁡x+arccsc⁡x
   y=arctan⁡〖x/2〗+1/(2(x^2+4))

   Use implicit differentiation to find an equation of the tangent line the graph of the equation at the given point.
arctan⁡(x+y)=y^2+π/4, (1,0)

A congressional committee of three is to be chosen from a set of 4 Democrats, 4 Republicans, and 3 Independents.

1) find p(all 3 are from different groups)

2) find p(at least 1 democrat)

3) find p(the majority are independents)

Task : Input this data into the SPSS and do the regression analysis as discussed today in the class.

For questions 1, 2, and 3, walk through each question by hand, then use the “disp” command in your MATLAB script to display your answer to the screen.
1. What is the final value of x? x = 10; if round(x/5) == x/5 x = 2 * x + 4; elseif x == 10 x = 4 * x; else x = 0; end
2. What is the final value of x? x = 10; if round(x/3) == x/3 x = 2 * x + 4; elseif x == 10 x = 4 * x; else x = 0; end
3. What is the final value of x? x = 9; if round(x/4) == x/4 x = 2 * x + 4; elseif x == 4 x = 4 * x; else x = 0; end
4. Write a MATLAB script that calculates the total cost for Giant Slinkys: • Ask the user to input the quantity of Giant Slinkys they wish to have shipped. • Make sure the user's input is a positive integer. • 10 or fewer Giant Slinkys cost $21.99 each. • 11 to 50 Giant Slinkys are $19.99 each • 51 to 100 Giant Slinkys are $17.99 each • More than 100 Giant Slinkys cost $15 each. • Sales tax is 9.5% • Shipping is $10 for each group of 10 Giant Slinkys. For example: ◦ Shipping for 1 Giant Slinky is $10; Shipping for 8 is also $0; Shipping for 10: $10. ◦ Shipping for 11 Giant Slinkys is $20; Shipping for 15, also $20; Shipping for 20: $20. • Shipping is free for orders of 50 or more Giant Slinkys