Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
2) At the Bristol Racket Club tennis courts are rented by the hour. The spreadsheet shows the data for two monthly plans. Plan A involves paying a one time monthly fee of $10 plus $9 per hour for court time. Plan B involves a one time monthly fee of per hour for court time. A B 1 2 3 4 5 C # of hours Plan A ($) 1 19 74 2 28 78 3 37 82 4 46 86 Plan B ($) How many hours would need to be rented during the month to make Plan B the best plan? A) 13 or more hours B) 10 or more hours C) 11 or more hours D) 14 or more hours Solution: Let the number of hours be x 70 + 4x < 10 + 9x 60 < 5x x > 12 Answer: (A) 13 or more hours SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 3) How are the symbols , 0.75, and 75% related? Solution: 0.75 is in decimal form of 3/4 and 75% is in percentage form of 3/4. Use inductive reasoning to predict the next number in the sequence. Explain your reasoning. 4) 21, 18, 15, 12, 9, . . . . Solution: Next number is obtained by subtracting 3 from the previous number. Next numbers will be 9 – 3 = 6. Decide whether the argument is an example of inductive or deductive reasoning. Explain your reasons. 5) 23 + 3 = 26, 29 + 3 = 32, 41 + 41 = 82. The sum of two prime numbers is even. A) Deductive B) Inductive Solution: (B) Inductive reasoning Inductive reasoning is the method of deriving a general rule from a specific cases. Write the statement indicated. 6) Write the negation of the following: The test is difficult. The test is not difficult. Decide whether the argument is an example of inductive or deductive reasoning. Explain your reasons. 7) Practice makes perfect. Therefore, if I practice, I'll be perfect. A) A) Inductive B) Deductive Answer: B) deductive; Deductive reasoning starts with a general case or facts and deduces specific instances. 8) Form a conjunction from the following two statements and determine if the conjunction is true or false. Two is an even number. Two is a prime number. Solution: Two is an even and prime number. Conjunction is true as 2 is prime as well as even number. Solve the problem. 9) A child's coin bank contains $ 2.58 in pennies and nickels. If the number of pennies is 36 less than 2 times the number of nickels, how many pennies are in the bank? Solution: Let the number of nickels be x then number of pennies will be 2x – 36. 5x + 2x – 36 = 258 7x = 258 + 36 = 294 x = 42 Number of pennies = 2*42 – 36 = 84 – 36 = 48 10) A drink and a sandwich together cost $ 5.00. The sandwich costs $ 1.50 more than the drink. How much does the sandwich cost? Solution: Let the cost of sandwich be x then the cost of drink will be x - 1.5 x + x - 1.5 = 5.0 2x = 5.0 + 1.5 = 6.5 x = 3.25 Cost of sandwich = $3.25 List all the subsets of S. 11) S = {Chocolate, Vanilla, Mint} Solution: Subsets = {ø, {Chocolate}, {Vanilla}, {Mint}, {Chocolate, Vanilla} , {Chocolate, Mint}, {Vanilla, Mint}, {Chocolate, Vanilla, Mint}} 12) Explain why the sets {a,b,c} and {1,2,3} are equivalent sets but not equal sets. Solution: Since elements are not same. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 13) Find A ? B, given A = { 6, 15, 3} and B = { 15, 3, 100}. A) { } B) {6, 15, 15, 3, 3, 100} C) {6, 15, 3, 100} D) {15, 3} Answer: symbol did not appear between A and B. But AUB = {6, 15, 3, 100} A n B = {15, 3} 14) Find (A n B) n C, given A = {s, e, t}, B = {m, e}, and C = {f, r, e, e}. A ) {s, e, t, m, e, f, r, e, e} B) {s, e, t, m, f, r} C) {e} D) {} Solution: (A n B) = {e} (A n B) n C = {e} Answer: C) Name the property of addition that has been applied. 15) ( 8 + 2) + 2 = 8 + ( 2 + 2) A) Commutative B) Closure C) Identity D Associative Answer: (D) Associative Use the definition of subtraction to rewrite the subtraction equation as an addition equation. 16) x - 64 = 80 Solution: Add 64 to each side x = 80 + 64 if we solve it, we will get x = 144 17) Use the Associative and Commutative Properties of addition to simplify where a and b are whole numbers and Question did not appear. Use the Distributive Property to find the product. 18) 3 × (10 + 8) = 3 × 10 + 3 × 8 = 30 + 24 = 54 Use the definition of division to rewrite the division equation as a multiplication equation. 19) 85 ÷ 5 = 17 Solution: 85 = 5 × 17 Use the distributive property of multiplication over addition to rewrite the sum as a product of two factors, where one of the factors is a sum. 20) 6yz - 54y Solution: 6yz - 54y Take 6y common out, we will get = 6y(z – 9)