University:
Carleton College
Course:
MATH 111 | lntroduction to Calculus
Academic year:

2024
Views:

270

Pages:

2
Author:

Alecai8y

Question 1 Find a counterexample to show that each statement is false. The sum of any three odd numbers is even. When an even number is added to the product of two odd numbers, the result will be even. When an odd number is squared and divided by 2, the result will be a whole number. Answer Any three odd integers added together equal even. 1+3+5 = 9, where 1, 3, and 5 are all odd numbers but their addition, 9, is also odd, could serve as a counterexample. The outcome will be even if an even number is added to the product of two odd numbers. A possible counterexample is (3x5) + 2 = 1 where the product of 3 and 5 is 15 (odd) but when 2 (even) is added, the result is 17 which is odd. A whole number is produced when an odd number is squared and divided by 2. 52 2 A possible counterexample is = 12.5 where 5 is odd and when squared and divided by 2, the result is not a whole number. Question 2 Roselle has 2 cups of popcorn and 8 oz of soda for a total of 216 calories. Carmel has 1 cup of popcorn and 12 02 of soda for a total of 204 calories. Determine the number of calories per cup of popcorn and per ounce of soda. Answer Let x be the number of calories per cup of popcorn and y be the number of calories per ounce of soda. 2 cups of popcorn and 8 oz of soda have a total of 216 calories: 2x + 8y = 216(1) 1 cup of popcorn and 12 oz of soda have a total of 204 calories: x+12y = 204(2) Divide (1) by 2 to obtain (3): x + 4y = 108(3) Subtract each side of (2) and (3) to eliminate xx and solve for y: 8y = 96 y = 12 Solve for xx using (2): x+12(12) = 204 x+144 x = 60 204 So, there are 60 calories per cup of popcorn and 12 calories per ounce of soda. Question 3 What is the difference between an expression and an equation? Provide an example of each. Answer An expression is a mathematical sentence that includes at least one operation and a variable while an equation is a mathematical sentence stating that two quantities are equal and written as two expressions separated by an equal sign. Examples of expression: 3x3x, 2y-12y-1, m+n-3m+n-3 Examples of equation: 2x=42x=4, 3p=2q+13p=2q+1, y=-2x+ly=-2x+1 Question 4 Which number is the tenths place for 4,507,612.081 Answer The tenth is to the right of the decimal (be careful, don't confuse with comas). So, it's 0. Question 5 What is -0.45 as a fraction? Answer -0.45 45 100 9 20