MTE 210: Section 1-1
1.) 0/# = 2.) #/0 = 3.) 0/0 =
1.) 0 2.) undefined 3.) undefined
Three closed boxes (A, B, C) of fruit arrive as a gift from a friend. Each box is mislabeled. How could you choose only one fruit from one box to decide how the boxes should be labeled?
Choose box B and pull out a fruit. If you pull out an apple, it was probably an apple box because Box A is mislabeled. If an orange is pulled, reasoning is similar.
The distance around the world is approximately 40,000km. Approximately how many people of average size would it take to stretch around the world if they were holding hands?
This is impossible to solve due to the fact that: - People could have their hands higher/lower - Everyone has different handspans - As the measurements would be taken, people would grow. - People would die & be born
Without computing each sum of the arithmetic sequence, find which is greater, O or E, and by how much. O = 1 + 3 + 5 + 7 +... + 97 E = 2 + 4 + 6 + 8 +... + 98
Use hop method 1 2 3 ...... +1 = 49 1 2 3 ...... +1 = 49 ^ ^ ^ ^ ^ ^ O = 1 + 3 + 5 + 7 +... + 97 E = 2 + 4 + 6 + 8 +... + 98 ANSWER: Both have 49 numbers. Each O is smaller when paired against an E. So, E is 49 bigger than O.
Find the value of each letter in the magic square. 17 a 7 12 22 b c d 27
17 42 7 12 22 32 37 2 27
The digits of a credit card are written in the boxes shown. If the sum of any 3 consecutive digits is 20, what is the value of A? A ☐ 7 ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ 7 ☐ 4
7 + 4 + X = 20 11 + X = 20 -11 -11 X = 9
Jamie Kendred has seven and a half feet (7 1/2'') of silver wire. He cut off and used nine and five eights inches (9 5/8''). How much wire did Jaime have left? Express your answer in feet, inches, and fractions of an inch, not decimals.
7 1/2'' -9 5/8'' x12in 90in - 9 5/8'' = (80 3/8'') / ( 12) = 6.69 ft .67 = 2/3 so, 12(2/3) = 8 .69-.67 = .03215 = 1/32 ANSWER: 6' 8 1/32''
How many squares are in the following figure? ☐ ☐☐☐ ☐☐☐☐☐ ☐☐☐ ☐
Break it down. ☐ ☐ ☐ ☐ 1 ☐☐ ☐ ☐☐☐☐☐ 1^2 ☐ ☐ 5 ☐ 5^2 9 9^2 The next (original)has 18 squares ANSWER: 18 squares
Rob says that it is possible to create a magic square with the numbers 1, 3, 4, 5, 6, 7, 8, 9, 10. How do you respond?
It's impossible because the magic square has to have rows/colums that sum up to whole numbers.
John asks why the last step of Polyas four-step problem solving process, looking back, is necessary since he has already given the answer. What could you tell him?
It's necessary because you can check your answer and see if you can apply the strategy you used to another problem later on.
Recall the song "The Twelve days of Christmas" This pattern continues for 9 more days. After 12 days, a. Which gifts did my true love give the most? b. How many total gifts did my try love give to me?
a. geese a laying and swans a swimming b. 1(12) = 12 2(11) = 22 3(10) = 30 4(9) = 36 5(8) = 40 6(7) = 42 7(6) = 42 8(5) =40 9(4) =36 10(3) =30 11(2) = 22 12(1) = 12 Sum of all answers is 364 gifts ANSWER: 364 gifts
Consider a game where you have two distinct piles of objects. Two players alternate moves, each player taking any number of objects desired from a single pile. The player who takes the last object wins. a. Show that the 1st player can win the game. b. Who will win the game? c. Which player will win the games(2,2) (3,3) (4,4)? d. Which games can the first player win?
a. goal of first player is to move till there is one in each pile b. the first player will win c. player 2 d. 2nd player will win if the piles are the same size
a. If 10 people shake hands with one another exactly one, how many handshakes take place? b. Find as many ways possible to do the problem. c. Generalize the solution for n people.
a.) a -b b -c c -d -c -d -e -d -e -f -e -f -g -f -g -h -g -h -i -h -i -j ...... =45 handshakes -i -j -j b.) 9 + 8 + 7 + 6 + 5 + 4 + 3 +2 + 1 = 45 handshakes c.) n-1 + n-2 + n-3 + n-4 +.....
Find the sum 36+37+38+39+...146+147.
n= #terms n= last# - first# + 1 a= 1st term z= last term (n/2)(a + z) (112/2)(36+147) = 10,248 ANSWER: 10,248
