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7. The coin is tossed twice. Which of the following is the correct representation of the sample space for this experiment? a. HH, TT, HT, TH b. HH, TT, HT, HH c. HT, TH, HT, TH d. TT, HT, TH, TT 8. A pair of dice is rolled once. How many possible outcomes are there? b. 18 c. 6 a. 12 d. 36

7. The coin is tossed twice. Which of the following is the correct representation of the sample space for this experiment? a. HH, TT, HT, TH b. HH, TT, HT, HH c. HT, TH, HT, TH d. TT, HT, TH, TT 8. A pair of dice is rolled once. How many possible outcomes are there? b. 18 c. 6 a. 12 d. 36

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Describing a Mathematical System I. Directions: Write the letter of the correct answer on the space provided before the number. 1. Which of the following defines a probability. a. It is a chance that will something will happen. b. It is a set of all the possible outcomes. c. It is just one of the possible outcomes. d. It is a result of a single trial of an experiment. 2. Is it possible to draw a triangle with the sides 1 cm, 3 cm and 5 cm? b. No a. Yes c. Cannot be determined d. None of the above 3. In the figure below, which is the external angle? a. ZABC c. ZDCB b. ZCBA d. ZACB D 4. If the lengths of two sides of a triangle are 12 cm and 6 cm, what is the possible length of the third side? a. 18 cm b. 16 cm c. 20 cm d. 36 cm 5-6. Complete the following proof by supplying the missing statement or reason. Given: AACD; BD bisects ZCDA Prove that DC > CB Statements Reasons AACD; BD bisects ZCDA Given 23=26 An angle bisector divides and angle into congruent parts m24 = mz1 +mz3 The exterior angle is equal to the sum of the two nonadjacent interior angles of the triangle BD DB 5. m24 < mz6 Transitive Property DC > CB 6. 5. What is the reason for no.5? c. Transitive Property d. Distributive Property a. Reflexive Property b. Commutative Property 6. What is the reason for no.6? a. The longest side is opposite the largest angle b. The shortest side is adjacent to the longest side. c. The longest side is opposite to the longest side d. The shortest side is opposite to the smaller angle 7. The coin is tossed twice. Which of the following is the correct representation of the sample space for this experiment? a. HH, TT, HT, TH b. HH, TT, HT, HH c. HT, TH, HT, TH d. TT, HT, TH, TT 8. A pair of dice is rolled once. How many possible outcomes are there? b. 18 a. 12 c. 6 a. cross roads 9. Which of the following does not represent a perpendicular line? c. the clock striking 3:00 a.m 10. In rolling a dice, what is the probability of getting 5? b. straight road a. 5 6 b./ C. 11. Which of the following statement shows a theoretical probability? a. Tossing a coin four times and getting a head thrice. b. Tossing a coin and getting a head or a tail is 1 out of 2 sides. c. Spinning a wheel twenty times and landing on yellow twice. d. Rolling a dice ten times and getting 5 thrice. d. 36 d. window pane 1.13
Transcribed Image Text:Describing a Mathematical System I. Directions: Write the letter of the correct answer on the space provided before the number. 1. Which of the following defines a probability. a. It is a chance that will something will happen. b. It is a set of all the possible outcomes. c. It is just one of the possible outcomes. d. It is a result of a single trial of an experiment. 2. Is it possible to draw a triangle with the sides 1 cm, 3 cm and 5 cm? b. No a. Yes c. Cannot be determined d. None of the above 3. In the figure below, which is the external angle? a. ZABC c. ZDCB b. ZCBA d. ZACB D 4. If the lengths of two sides of a triangle are 12 cm and 6 cm, what is the possible length of the third side? a. 18 cm b. 16 cm c. 20 cm d. 36 cm 5-6. Complete the following proof by supplying the missing statement or reason. Given: AACD; BD bisects ZCDA Prove that DC > CB Statements Reasons AACD; BD bisects ZCDA Given 23=26 An angle bisector divides and angle into congruent parts m24 = mz1 +mz3 The exterior angle is equal to the sum of the two nonadjacent interior angles of the triangle BD DB 5. m24 < mz6 Transitive Property DC > CB 6. 5. What is the reason for no.5? c. Transitive Property d. Distributive Property a. Reflexive Property b. Commutative Property 6. What is the reason for no.6? a. The longest side is opposite the largest angle b. The shortest side is adjacent to the longest side. c. The longest side is opposite to the longest side d. The shortest side is opposite to the smaller angle 7. The coin is tossed twice. Which of the following is the correct representation of the sample space for this experiment? a. HH, TT, HT, TH b. HH, TT, HT, HH c. HT, TH, HT, TH d. TT, HT, TH, TT 8. A pair of dice is rolled once. How many possible outcomes are there? b. 18 a. 12 c. 6 a. cross roads 9. Which of the following does not represent a perpendicular line? c. the clock striking 3:00 a.m 10. In rolling a dice, what is the probability of getting 5? b. straight road a. 5 6 b./ C. 11. Which of the following statement shows a theoretical probability? a. Tossing a coin four times and getting a head thrice. b. Tossing a coin and getting a head or a tail is 1 out of 2 sides. c. Spinning a wheel twenty times and landing on yellow twice. d. Rolling a dice ten times and getting 5 thrice. d. 36 d. window pane 1.13
12. Is it possible to draw a triangle with the sides 3 cm, 4 cm and 5 cm? c. Cannot be determined d. None of the above b. No 13. Given the figure below, find the mZE. (5y+12)° a. 21° b. 20° 120°/2° E c. 36° d. 80° N 14. Which of the following describes an outcome if the experiment? a. tossing a coin twice c. getting a head b. taking a test d. spinning a wheel 15. You are choosing a password that has 3 letters followed by two digits. How many passwords are possible if letters and digits can be repeated? a. 1, 757, 000 b. 1,560 c. 1, 757, 600 d. 15, 600 16. What is the probability of getting all heads if you flip 4 coins? 1 a. b. = C. 16 17. What is the probability of randomly picking a number from 1 to 10 that is even? 1 a. b. = C. d. 2 10 10 18. Janice and his husband is fond of collecting mugs. They group the mugs base in its color and patterns. As per grouping, Janice counts that there are 3 yellow, 4 pink, 2 blue, 5 white, 1 black, 4 plain and 2 striped. If Janice's husband chose a mug at random. What is the probability that the mug would be blue? a. b. 1 c./17 d. ²/ 19. Which of the following does not describes an experimental probability. a. A probability found by repeating an experiment. b. can be computed by dividing the number of times an event occurs by the total number of trials c. in an experiment in which all outcomes are equally likely to happen. d. none of the above For items 20-22, determine the relationship of each pair of angles. 4 6 20. 21 and 28 c. corresponding angles a. alternate interior angles b. alternate interior angles d. supplementary angles 21. 24 and 28 a. alternate interior angles b. alternate interior angles 22. 23 and 26 c. corresponding angles d. supplementary angles a. alternate interior angles c. corresponding angles b. alternate interior angles d. supplementary angles 23. A pedestrian lane is an example of a. intersecting lines c. perpendicular lines d. none of these b. parallel lines 24. Vincenzo is in a rush to set out tons of gold found in the basement of Geumga Plaza however being careful not to be caught by Geumga tenants he put 5 bars of gold and a guillotine file inside his briefcase. What is the probability that Vincenzo will pick the guillotine file? a 4.5 b. 1 C. 25. Which of the following illustration below shows a perpendicular line? C. 4 a. Yes Xi a.
Transcribed Image Text:12. Is it possible to draw a triangle with the sides 3 cm, 4 cm and 5 cm? c. Cannot be determined d. None of the above b. No 13. Given the figure below, find the mZE. (5y+12)° a. 21° b. 20° 120°/2° E c. 36° d. 80° N 14. Which of the following describes an outcome if the experiment? a. tossing a coin twice c. getting a head b. taking a test d. spinning a wheel 15. You are choosing a password that has 3 letters followed by two digits. How many passwords are possible if letters and digits can be repeated? a. 1, 757, 000 b. 1,560 c. 1, 757, 600 d. 15, 600 16. What is the probability of getting all heads if you flip 4 coins? 1 a. b. = C. 16 17. What is the probability of randomly picking a number from 1 to 10 that is even? 1 a. b. = C. d. 2 10 10 18. Janice and his husband is fond of collecting mugs. They group the mugs base in its color and patterns. As per grouping, Janice counts that there are 3 yellow, 4 pink, 2 blue, 5 white, 1 black, 4 plain and 2 striped. If Janice's husband chose a mug at random. What is the probability that the mug would be blue? a. b. 1 c./17 d. ²/ 19. Which of the following does not describes an experimental probability. a. A probability found by repeating an experiment. b. can be computed by dividing the number of times an event occurs by the total number of trials c. in an experiment in which all outcomes are equally likely to happen. d. none of the above For items 20-22, determine the relationship of each pair of angles. 4 6 20. 21 and 28 c. corresponding angles a. alternate interior angles b. alternate interior angles d. supplementary angles 21. 24 and 28 a. alternate interior angles b. alternate interior angles 22. 23 and 26 c. corresponding angles d. supplementary angles a. alternate interior angles c. corresponding angles b. alternate interior angles d. supplementary angles 23. A pedestrian lane is an example of a. intersecting lines c. perpendicular lines d. none of these b. parallel lines 24. Vincenzo is in a rush to set out tons of gold found in the basement of Geumga Plaza however being careful not to be caught by Geumga tenants he put 5 bars of gold and a guillotine file inside his briefcase. What is the probability that Vincenzo will pick the guillotine file? a 4.5 b. 1 C. 25. Which of the following illustration below shows a perpendicular line? C. 4 a. Yes Xi a.
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