course Mth 151 001. `query 1 question 11.1.6 {Andy, Bill, Kathy, David, Evelyn}.
.............................................
Given Solution:: ** Listing possibilities on first then second die you can get 1,4, or 2,3 or 3,2 or 4,1. There are Four ways. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ********************************************* Question: In how many ways can the total of two dice equal 11? ********************************************* Your Solution: Assuming all of the same parameters as the last problem, there are 2 possible answers 5,6/6,5 Confidence Assessment: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Confidence Assessment:
.............................................
Given Solution:: ** STUDENT SOLUTION AND INSTRUCTOR RESPONSE: There is only 1 way the two dice can equal 11 and that is if one lands on 5 and the other on 6 INSTRUCTOR RESPONSE: There's a first die and a second. You could imagine that they are painted different colors to distinguish them. You can get 5 on the first and 6 on the second, or vice versa. So there are two ways. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): question 11.1.36 5-pointed star, number of complete triangles How many complete triangles are there in the star and how did you arrive at this number? ********************************************* Your Solution: The 5 pointed star has 5 points which have 5 triangles within, there are also 5 more triangles within the pentagon hence: 5+5=10 Confidence Assessment: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Confidence Assessment:
.............................................
Given Solution:: ** If you look at the figure you see that it forms a pentagon in the middle (if you are standing at the very center you would be within this pentagon). Each side of the pentagon is the side of a unique triangle; the five triangles formed in this way are the 'spikes' of the star. Each side of the pentagon is also part of a longer segment running from one point of the start to another. This longer segment is part of a larger triangle whose vertices are the two points of the star and the vertex of the pentagon which lies opposite this side of the pentagon. There are no other triangles, so we have 5 + 5 = 10 triangles. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): question 11.1.40 4 x 4 grid of squares, how many squares in the figure? ********************************************* Your Solution: The 4x4 square has 16 1x1 squares, 9 2x2 squares, 4 3x3 squares, and 1 4x4 square. Add these all up and there are 30 complete squares. Confidence Assessment: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Confidence Assessment:
.............................................
Given Solution:: ** I count 16 small 1 x 1 squares, then 9 larger 2 x 2 squares (each would be made up of four of the small squares), 4 even larger 3 x 3 squares (each made up of nin small squares) and one 4 x 4 square (comprising the whole grid), for a total of 30 squares. Do you agree? ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): question 11.1.50 In how many ways can 30 be written as sum of two primes? ********************************************* Your Solution: 30=19+11 30=17+13 30=23+7 all of these solutions are made of prime numbers and all of these equal 30. Confidence Assessment: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Confidence Assessment:
.............................................
Given Solution:: **STUDENT SOLTION AND INSTRUCTOR COMMENT: There are 4 ways 30 can be written as the sum of two prime numbers: · 30 = 29 + 1 (instructor note: this is not a sum of two primes) · 30 = 19 + 11 · 30 = 23 + 7 · 30 = 17 + 13 INSTRUCTOR COMMENT: Good, but 1 isn't a prime number. It only has one divisor. The rest of your answers are correct. All sums give you 30, and 7, 11, 13, 17, 19 and 23 are all prime numbers.** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): question 11.1.60 four adjacent switches; how many settings if no two adj can be off and no two adj can be on ********************************************* Your Solution: If no 2 adj can be off or on at the same time, there are only possible solutions XOXO OXOX Confidence Assessment: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Confidence Assessment:
.............................................
Given Solution:: ** There are a total of 16 settings but only two have the given property of alternating off and on. If the first switch is off then the second is on so the third is off so the fourth is on. If the first is off then the second is on and the third is off so the fourth is on. So the two possibilities are off-on-off-on and on-off-on-off. If we use 0 to represent ‘off’ and 1 to represent ‘on’ these possibilities they are written 0101 and 1010. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): question Add comments on any surprises or insights you experienced as a result of this assignment. ** STUDENT COMMENT: No surprises and it's early so i'm reaching for insight as a child reaches for a warm bottle of milk Your comments or questions: These questions were very much more intuitive and required much more thought and introspection than i had previously thought.