Question

use the following statement to answer question 14 - 15: if you can download 6 songs for $5.94, then each song costs $0.99. 14. what is the converse of this statement? a if you cannot download 6 songs for $5.94, then each song isnt $0.99. b you can download 6 songs for $5.94 if and only if each song is $0.99. c if each song costs $0.99, then you can download 6 songs costs $5.94. d if each song isnt $0.99, then you cannot download 6 songs for $5.94. 15. what is the biconditional of this statement? a if you cannot download 6 songs for $5.94, then each song isnt $0.99. b you can download 6 songs for $5.94 if and only if each song is $0.99. c if each song costs $0.99, then you can download 6 songs for $5.94. d if each song isnt $0.99, then you cannot download 6 songs for $5.94. use the following statement to answer question 16 - 17: if a figure has 10 sides, then it is a decagon. 16. what is the converse of this statement? a a figure has 10 sides if and only if it is a decagon. b if a figure does not have 10 sides, then it is not a decagon. c if a figure is not a decagon, then it does not have 10 sides. d if a figure is a decagon, then it has 10 sides. 17. what is the biconditional of this statement? a a figure has 10 sides if and only if it is a decagon. b if a figure does not have 10 sides, then it is not a decagon. c if a figure is not a decagon, then it does not have 10 sides. d if a figure is a decagon, then it has 10 sides. use the following statement to answer questions 18 - 19. students perform during halftime at the football games if and only if they are in the high school band. 18. true or false? 19. if the statement is true, choose choice d. if the statement is false, choose a counterexample that proves it. a false; the band does not perform at halftime. b false; the band performs after the game. c false; cheerleaders also perform at the game. d true use the following statement to answer questions 20 - 21. an angle in a triangle measures 90° if and only if the triangle is a right triangle. 20. true or false? 21. if the statement is true, choose choice d. if the statement is false, choose a counterexample that proves it. a false; right angles are not 90°. b false; 90° angles cannot be in triangles. c false; right triangles have two right angles. d true

Explanation:

1. The converse of a conditional statement "if p then q" is "if q then p". Here, p is "you can download 6 songs for $5.94" and q is "each song costs $0.99". So the converse is "If each song costs $0.99, then you can download 6 songs for $5.94".
2. A biconditional statement is of the form "p if and only if q". So for the given statement, the biconditional is "You can download 6 songs for $5.94 if and only if each song is $0.99".
3. For the statement "if p then q" where p is "a figure has 10 sides" and q is "it is a decagon", the converse is "if q then p" which is "If a figure is a decagon, then it has 10 sides".
4. The biconditional is "p if and only if q", so it is "A figure has 10 sides if and only if it is a decagon".
5. The statement "Students perform during halftime at the football games if and only if they are in the high - school band" is false because cheerleaders also perform at the game, so there are other groups that perform at halftime.
6. Since the statement is false, the counter - example is that cheerleaders also perform at the game.
7. An angle in a triangle measures 90° if and only if the triangle is a right triangle is a true statement based on the definition of a right triangle.
8. Since the statement is true, we choose D.

Answer:

1. C. If each song costs $0.99, then you can download 6 songs for $5.94
2. B. You can download 6 songs for $5.94 if and only if each song is $0.99
3. D. If a figure is a decagon, then it has 10 sides
4. A. A figure has 10 sides if and only if it is a decagon
5. C. False; Cheerleaders also perform at the game.
6. C. False; Cheerleaders also perform at the game.
7. D. True
8. D. True