Mathematics in the Modern World 1st Semester SY 2021-2022 Module 2 - Formative Assessment #3 Mathematical Reasoning and Problem-Solving INSTRUCTIONS. Answers can either be: a) Entered directly in the text-entry box in the Assignment link in Canvas, or b) written and saved as a WORD file (maybe converted to PDF file) then uploaded in the appropriate Assignment link in Canvas, or c) handwritten on a piece of paper, captured as a picture and saved as an image file. Then, uploaded in the appropriate Assignment link in Canvas. Determine whether the following statements uses Inductive (1 ) or Deductive (D) reasoning. Write only the letter. 1. It's dangerous to drive on icy streets. The streets are icy now, so it would be dangerous to drive. 2. All cats have a keen sense of smell. Fluffy is a cat, so Fluffy has a keen sense of smell. 3. Every cat that you observed purrs. Therefore, all cats must purr. 4. The cost of goods was $1.00. The cost of labor to manufacture the item was $0.50. The sales price of the item was $5.00. So, the item always provides a good profit for the stores selling it. 5. Cacti are plants and all plants perform photosynthesis, therefore, cacti perform photosynthesis. 6. Every chicken we've seem has been brown. All chickens in this area must be brown. 7. All noble gases are stable. Helium is a noble gas, so helium is stable. 8. John is an excellent swimmer. His family has a swimming pool. John's sister Mary must also be an excellent swimmer. 9. All horses have manes. The Arabian is a horse; therefore, Arabians have manes. 10. All brown dogs in the park today are small dogs. Therefore, all small dogs must be brown. II. Disprove the following statements using counterexample. Explain your answers. 1. |x| > 0 x2 > x 2. Vxl = x 5. x5x 3. Vx2 +4 = x+2 Ill. Solve the following using Polya's four-step problem-solving strategies. Make the necessary conclusion or conjecture. 1. A local furniture store is having a terrific sale. They are marking down every price 45%. If the couch you have eye on is $440 after the markdown, what was the original price? How much will you save if you bought it at this sale? 2. The cost C to produce X number of cd's is C = 50+ 5X. The cd's are sold wholesale for $15 each, so revenue R is given by R = 15X. Find how many cd's the manufacturer need to produce and sell to breakeven. 3. One number is 3 les than another number. If the sum of the two numbers is 177, find the value of each number