MHF What is the difference between the number of solutions for a trigonometric linear equation and a non-trigonometric linear equation? What type of solution would you expect for each and what techniques would you use to solve each equation? Worksheet Questions MCV Q- Let y = x/x+1 Find the first, second and third derivative (1:3)

5. My character in the classic Xbox game, Knights of the Old Republic, wants to create a new lightsaber. I have decided that the following attributes (and what percent of my decision they represent) will determine which crystal I choose: Cost (15%), Attack Modifier (32%), Damage (34%), Regeneration Force Points (19%). The following table lists the crystals I will consider, and their ratings (out of 10). Which crystal is the best fit for my character's lightsaber? Crystal Cost Rubat Damind Eralam Sapith -1 -2 -3 -4 Attack Modifier 1 4 5 5 Damage 1 1 5 7 Regeneration Force Points 3 2 0 0

14. Toss a coin 10 times and record how many times you tossed heads. a) What is your experimental probability of tossing heads? b) What is the theoretical probability of tossing heads? c) Compare the two probabilities and determine if you are considered to be "lucky" at tossing heads.

4. In each of the following examples, identify the sampling method used. a. Instructors are interested in knowing what eating techniques their students are utilizing. Rather than assessing all students, the researchers randomly select one specific class to comprise their sample. b. National Geographic collects data on its readers by asking them to fill out and send in a survey from the March issue. c. A psychologist is studying the sleep patterns of the 3960 students in her basement. She decides to start by asking a random sample of 30 students how many hours of sleep they get weekday nights. The psychologist assigns each student a number from 0001 to 3960 and uses a computer to randomly generate a list of 30 numbers to select the students for the sample.

14. Toss a coin 10 times and record how many times you tossed heads. a) What is your experimental probability of tossing heads? b) What is the theoretical probability of tossing heads? c) Compare the two probabilities and determine if you are considered to be "lucky" at tossing heads. d) If you were to toss the coin 100 times, what would you expect the experimental probability of heads to be? Defend your answer.

4. Consider the linear system x + 3y = 2 3x + hy = k. Determine all values of h and k so that the linear system has (a) no solution. (b) a unique solution. (c) infinitely many solutions. 5 The network in the figure below shows the traffic flow (in vehicles per hour) over sever

3. Leo is a self-employed plumber. One month, Leo's plumbing business had three contracts for $2500.00, $7000.00, and $275.00. The cost of Leo's expenses and materials to complete these contracts was $7200.00. a) How much did Leo earn an hour based on a 40-hour work week?

6. (1 point) In how many ways can 12 (identical) cookies be distributed among four friends so that the tallest friend gets either none or just three of them? 7. (2 points)

1. (2 points) How many ways can you form a four-person relay team from 10 available runners? How many of these teams would include both the fastest and the slowest runners?

Q3 Let S = R² with addition and multiplication in S defined by (a, b) + (x, y) = (a + x, b+y), (a, b) x (x, y) = (ax, by). Throughout this question you may assume that R is a field. (i) Show that (x, y) is an additive identity element in S if and only if (x, y) = (0,0). (ii) Show that (x, y) is a multiplicative identity element in S if and only if (x, y) = (1, 1). (iii) Verify that the distributive law holds in S. (iv) By considering the element (1,0), or otherwise, show that S is not a field.