O Question 1 10 pts [10 points] 1. Construct a truth table for the following proposition and determine whether the proposition is a contingency, tautology, or ons contradiction. tics (p * - P) - (q " - 9) p pap qa-g [p * - p) - 19 4 - Browser T T lance T oring F F F Report Upload Choose a FileDue by Sunday Oct 1 X + urses/92915/quizzes/375 177/take?preview.= 1 J K L M N O P Q R S 10 11 12 13 14 15 16 17 18 19 T U V W X Y Z 20 21 22 23 24 25 26 Encode the message "ONE IF BY LAND AND TWO IF BY SEA" using matrix C: 10101 01 10 3 C= 2 1 1 1 1 0 0 10 2 1 1 12 1 Upload Choose a File 67"F M O H 8 9Test 1 Due by Sunday Oct X + W/courses/92915/quizzes/375177/take?preview =1 D Question 9 10 pts This is an extra-credit question. [Extra 10 points] 9. The technology matrix for an economy based on energy (E) and transportation (T) is E T M= 0.25 0.25 T 0.4 0.2 Find the output for each sector that is needed to satisfy a final demand of $50 million for energy and $50 million for transportation. Upload Choose a FileED6030 70650 Mat X Quiz Test 1 Due by Sunday Oct 1 X + northeastern.instructure.com/courses/92915/quizzes/375177/take?preview=1 - OX Accessibility Report Settings Upload Choose a File D Question 2 10 pts [10 points] 2. Solve the following problems. 2.1 How many 4-digit opening combinations are possible on a combination lock with 12 digits if the digits cannot be repeated? 2.2 Six tennis players have made the finals. If each of the 6 players is to play every other player exactly once, how many games must be scheduled? 2.3 How many 5-letter code words are possible using the first 10 letters of the alphabet if letters can be repeated? Upload Choose a File 7:52 PM 0 # @ 8 9 67'F Mostly sunny ~ ( 10/6/2021 earchcan be repeated? Upload Choose a File Back D For Question 3 15 pts Relo Save Print Cast [15 points] 3. An experiment consists of rolling four fair dice and adding E Crea the dots on the four sides facing up. Compute the probability of obtaining Tran the following: View Insp 3.1 The sum is15 3.2 The sum is not 6 3.3 The sum is 5 or 6 3.4 The sum is 5 and 6 Upload Choose a File O 9 67"FQuestion 4 15 pts [15 points] 4. Two fair dice are each numbered with a 3 on one side, a 2 on two sides, and a 1 on three sides. The dice are rolled, and the numbers on the two up faces are added. If X is the random variable associated with the sample space S = (2, 3, 4, 5, 6]: 4.1 Find the probability distribution of X. 4.2 Find the expected number of X. 4.3 Find the standard deviation of X. Upload Choose a FileQuin Test 1 Due by Sunday Qu ] X + e.com/courses/92915/quizzes/375177/take?preview=1 O Upload Choose a File D Question 5 15 pts [15 points] 5. The data in the following table were obtained in a study to determine the frequency and dependency of IQ ranges relative to males and females. 1,000 people were chosen at random and the following results were recorded: 1Q Below 90 90-120 Above 120 Totals Female 150 300 50 500 Male 140 280 80 500 Totals 290 580 130 1000 5 1 What is the probability of a person having an IO below 90 given that 67'F Mostly ODue by Sunday Oct ? X + urses/92915/quizzes/375177/take?preview= 1 Below 90 90-120 Above 120 Totals Female 50 300 50 500 Male 140 280 80 500 Totals 290 580 130 1000 5.1 What is the probability of a person having an IQ below 90, given that the person is a female? 5.2 What is the probability of a person having an IQ above 120, given that the person is a male? 5.3 What is the probability of a person being a female, given that the person has an IQ 90-120? Upload Choose a FileTest 1 Due by Sunday Oct 1 X + com/courses/92915/quizzes/375177/take?preview=1 0 - 0 Q 1 2 Upload Choose a File D Question 6 10 pts [10 points] 6. In the U.S., records show that of the registered voters, 50% are Democrats, 40% are Republican, and 10% are Independents. In an election, 90% of the Democrats, 20% of the Republicans, and 60% of the Independents voted in favor of an environment protection bill proposal. If a registered voter chosen at random is found to have voted in favor of the bill: 6.1 what is the probability that the voter is a Democrat? 6.2 what is the probability that the voter is a Republican? 6.3 what is the probability that the voter is an Independent? Upload Choose a File 67'F Mostly sunny1 Due by Sunday Oct | X + courses/92915/quizzes/375 177/take? preview= 1 D Question 7 10 pts [10 points] 7. Write the following system as a matrix equation and solve using the inverse coefficient matrix. Note: You need to show how to get the inverse matrix. X1 - X3 = 2 241 - X2 = 3 X1 + X2 - 2X3 = 4 Upload Choose a File 15 pts D Question 8 [15 points] 8. The numbers 1-26 were assigned to the letters in the alphabet as shown below. ODue by Sunday Oct 1 X + urses/92915/quizzes/375177/take?preview=1 [15 points] 8. The numbers 1-26 were assigned to the letters in the alphabet as shown below. Blank A B C D E F G H 1 2 3 4 5 6 7 8 9 L M N O P Q R S 10 11 12 13 14 15 16 17 18 19 T U V W X Y Z 20 21 22 23 24 25 26 Encode the message "ONE IF BY LAND AND TWO IF BY SEA" using matrix C: 10101 1 103 67'F Mos O H O N 9