Yearly Income 0 TV 1 TV 2 TV 3 TV >3 TVs Total Less Than 12,000 10 40 51 11 0 112 12,000 – 19,999 11 70 80 15 1 117 20,000 – 39,999 12 110 130 80 12 344 40,000 – 59,999 10 90 80 60 21 261 60,000 or more 1 32 28 25 20 106 Total 44 342 369 191 54 1000A random sample of 1000 families produced the following data (above). Using this table, find the probability of: Part A) A household earning 12,000 to 19,999 per year and owning exactly 2 TVs. Part B) A household having more than 3 TVs or earning more than 59,999. Part C) A household owning fewer than 3 TVs. 

The winner of a contest can choose any 3 of 7 different prizes. How many choices of 3 prizes are possible? 

A club has 8 females and 12 male members. If a 4-person committee is formed by random drawing from the 20 members, how many ways can a committee be formed with exactly 2 male and 2 female members? 

a. Fill in the sum of two dice table below: sum of dice.png b. Determine the probability that a sum of 3 or a sum of 7 is rolled? c. Determine the probability that you roll an odd sum or a sum of 5?

You purchase a raffle ticket to help charity. The raffle ticket costs $8. The charity is selling 200 tickets. One of them will be drawn and the person holding the ticket will be given a prize worth $350. Compute the expected value for this raffle. 

How many ways can a president, vice-president, secretary and treasurer be chosen from a club with 18 members?

Suppose that the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {2, 4, 5, 7}, B = {1, 3, 5, 7, 9} and C = {2, 4, 6}Part A) Find A∪BPart B) Find A∩BPart C) Find ACPart D) Find (A∪C)C

Word gets around if an officer is _______________ in one’s work, and one’s ability to serve is increased.  

For this quiz, you may use: https://matrixcalc.org/ Show all work, provide justifications when needed. Q1. Let   (6 points) (a) Find a basis for Col(A) (b) Find a basis for Nul(A) (c) Find a basis for Row(A) = Col(AT) Q2. Chose any vector   in Nul(A) and verify (this means compute the product)   (2 points) Q3. Chose any vector in Col(A) and verify  that    (2 points) Q4. Explain why we get the result we do in Q3 (you could state a Theorem if you know one, but I am suggesting use the fact that matrix multiplication is a linear transformation together with properties of linear transformations).  (2 points) Q5. What is the rank of the matrix A?  (1 point) Q6. What is the dimension of Col (A) ? (1 point) Q7. What is the dimension of Nul (A)?  (1 point) Q8. Suppose A is an

*BONUS QUESTIONS* Each point is worth 2 points.  1) Name two relevant facts, statistics, data points, etc. that you learned from chapters 1 – 7 that was not covered on the midterm. (2 quality sentences minimum per point = 4 sentences total as the minimum)