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whats d max. # of 1"*3"*4" blocks that can fit into rectangular prism measuring 9"*10"*14"

If we simply divide the volumes we get 9*10*14/(1*3*4)=1260/12=105. But to do this we would need to split some blocks. However, we know the answer cannot be bigger than 105. The 1" side of a block will fit exactly any side of the prism, so we can reduce the problem to filling an area measuring 9*10, 9*14 or 10*14 with 3*4. 6 of these blocks would exactly fill an area A 9*8, 9 would fill area B 9*12, and 8 would fill area C 8*12. For area A there would be a stack of 14 blocks making 84 blocks in all; area B a stack of 90; area C a stack of 72. Now we look at wastage. How many blocks can we use to fill the gaps for area B? What we have left measures 2*10*9. We can consider areas again because we can only arrange the blocks two blocks deep to make up 2 inches. So the area we have to fill is 10 by 9. We need 6 blocks to fill 8 by 9, and, because there are two layers we can use up 12 blocks. That means in all we use 90+12=102 blocks out of a maximum of 105. The volume remaining is 36 cu in. The 12 blocks are arranged 2 blocks deep by 2 blocks wide (2*4") by 3 blocks long (3*3"), leaving a gap, measuring 2*2*9 into which no more blocks will fit.
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Diego made a castle with small building blocks you use an even number of block the number of blocks is between 700 and 800

It all depends on the shape and size of the castle, and the size of the blocks. More information is needed.  If the castle has a square base, then I would pick 784 as the nearest even square (28*28=784) and start with a square of blocks. Then I would take blocks from the centre and build up the sides (to make walls and ramparts) and corners (to make towers) leaving a vacant courtyard in the centre.
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design 1has one block design two has 4 blocks design has three 9 blocks what comes next?

1, 4, 9...square av 1, 2, 3, ...
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H is 10 ft tall, 10 ft wide, thickness of block will be 2.5 ft?

One side of the H is 10' x 2.5 ft = 25 sq ft. Other side of H is the same = 25 sq ft. H is total 10 ft wide, minus the 2.5 ft, minus 2.5 ft makes the H "bar" 5 ft long by 2.5 ft. wide = 12.5 sq ft. 12.5 + 25 + 25 = 62.5 sq ft. (takes a lot of plywood) 3-- 4 ft x 8 ft sheets of plywood. Might want to consider 8 ft high x 8 ft wide using 2 ft thick block letters. Comes out looking about the same ratio, and would only take 2 sheets of plywood. Generally can legally haul 8 ft wide preassembleld " H" on a truck, but not 10 ft wide "H".
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Discuss at least three applications of graph theory in the field of computer sciences?

Graphs are among the most ubiquitous models of both natural and human-made structures. They can be used to model many types of relations and process dynamics in physical, biological[1] and social systems. Many problems of practical interest can be represented by graphs. In computer science, graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, etc. One practical example: The link structure of a website could be represented by a directed graph. The vertices are the web pages available at the website and a directed edge from page A to page B exists if and only if A contains a link to B. A similar approach can be taken to problems in travel, biology, computer chip design, and many other fields. The development of algorithms to handle graphs is therefore of major interest in computer science. There, the transformation of graphs is often formalized and represented by graph rewrite systems. They are either directly used or properties of the rewrite systems (e.g. confluence) are studied. Complementary to graph transformation systems focussing on rule-based in-memory manipulation of graphs are graph databases geared towards transaction-safe, persistent storing and querying of graph-structured data. Graph-theoretic methods, in various forms, have proven particularly useful in linguistics, since natural language often lends itself well to discrete structure. Traditionally, syntax and compositional semantics follow tree-based structures, whose expressive power lies in the Principle of Compositionality, modeled in a hierarchical graph. More contemporary approaches such as Head-driven phrase structure grammar (HPSG) model syntactic constructions via the unification of typed feature structures, which are directed acyclic graphs. Within lexical semantics, especially as applied to computers, modeling word meaning is easier when a given word is understood in terms of related words; semantic networks are therefore important in computational linguistics. Still other methods in phonology (e.g. Optimality Theory, which uses lattice graphs) and morphology (e.g. finite-state morphology, using finite-state transducers) are common in the analysis of language as a graph. Indeed, the usefulness of this area of mathematics to linguistics has borne organizations such as TextGraphs, as well as various 'Net' projects, such as WordNet, VerbNet, and others. Graph theory is also used to study molecules in chemistry and physics. In condensed matter physics, the three dimensional structure of complicated simulated atomic structures can be studied quantitatively by gathering statistics on graph-theoretic properties related to the topology of the atoms. For example, Franzblau's shortest-path (SP) rings. In chemistry a graph makes a natural model for a molecule, where vertices represent atoms and edges bonds. This approach is especially used in computer processing of molecular structures, ranging from chemical editors to database searching. In statistical physics, graphs can represent local connections between interacting parts of a system, as well as the dynamics of a physical process on such systems. Graph theory is also widely used in sociology as a way, for example, to measure actors' prestige or to explore diffusion mechanisms, notably through the use of social network analysis software. Under the umbrella of Social Network graphs there are many different types of graphs: Starting with the Acquaintanceship and Friendship Graphs, these graphs are useful for representing whether n people know each other. next there is the influence graph. This graph is used to model whether certain people can influence the behavior of others. Finally there's a collaboration graph which models whether two people work together in a particular way. The measure of an actors' prestige mentioned above is an example of this, other popular examples include the Erdős number and Six Degrees Of Separation Likewise, graph theory is useful in biology and conservation efforts where a vertex can represent regions where certain species exist (or habitats) and the edges represent migration paths, or movement between the regions. This information is important when looking at breeding patterns or tracking the spread of disease, parasites or how changes to the movement can affect other species. In mathematics, graphs are useful in geometry and certain parts of topology, e.g. Knot Theory. Algebraic graph theory has close links with group theory. A graph structure can be extended by assigning a weight to each edge of the graph. Graphs with weights, or weighted graphs, are used to represent structures in which pairwise connections have some numerical values. For example if a graph represents a road network, the weights could represent the length of each road. A digraph with weighted edges in the context of graph theory is called a network. Network analysis have many practical applications, for example, to model and analyze traffic networks. Applications of network analysis split broadly into three categories: First, analysis to determine structural properties of a network, such as the distribution of vertex degrees and the diameter of the graph. A vast number of graph measures exist, and the production of useful ones for various domains remains an active area of research. Second, analysis to find a measurable quantity within the network, for example, for a transportation network, the level of vehicular flow within any portion of it. Third, analysis of dynamical properties of networks.
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which is larger 2/3 or 3/2 ?use words and pictures to explain your answer.

The answer can be found by turning the fractions into blocks. We need a big supply of blocks from which we take 6. A third of 6 blocks is 2 blocks. We need two thirds=4 blocks. Half of 6 blocks is 3 blocks. We need three times this many blocks=9 blocks. So we need take extra blocks from the supply. Which of the two sets of blocks is larger? The set of 9. So since this came from 3/2, 3/2 must be bigger than 2/3.
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how we do this 113-29=84

That's right. 113=100+10+3 and 29=20+9. So when we subtract we are actually doing: 100+10+3-20-9. This can be arranged by grouping the numbers to make the subtraction easier: (100-20)+(10+3-9)=80+13-9=80+4=84. Or 100-20+10-9+3=80+1+3=84. So, the 10 has been removed from 113 and used in the subtraction because we can't subtract 9 from 3 in the ones position without help from the tens. Here's another way of thinking about it. Imagine a set of three drawers. In the top drawer we have the hundreds, the middle drawer the tens and the bottom drawer the ones. We replace the digits with blocks. In this case a block in the top two drawers and 3 in the bottom drawer. But these blocks are boxes. The top drawer box contains 10 smaller boxes which are the same size as the blocks in the middle drawer. And the middle drawer contains 10 even smaller boxes the size of those in the bottom drawer. We come along and we want to take 29 away from what we have in the drawers. Let's start with the bottom drawer with just 3 boxes or blocks. We can't take away 9! So we go to the next drawer and take out the only box in it, leaving the middle drawer empty, and empty all the blocks in it into the bottom drawer so we now have 13 blocks and we can easily take away 9 leaving 4 blocks. Close the bottom drawer. The middle drawer is empty! We need to take 2 blocks or boxes and there aren't any! So we take the box out of the top drawer and empty it into the middle drawer so we have 10 boxes in it. So we remove 2 leaving 8. We are left with nothing in the top drawer, 8 blocks/boxes in the middle drawer and 4 in the bottom. That represents the number 84.  
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how many base ten blocks to use to make 725,300?

725,300=7253*100=7253*10^2 . . . .
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7x+2y=5 and 3y=16-2x

7x+2y=5 and 3y=16-2x  solve each of the following systems using the method of youre choice. However, you must show an organize work. We could solve both equations, but what would we have? We would still have two equations. Each would show y in terms of x, or x in terms of y. We still wouldn't know the values of x or y. E.g., y = 16/3 - 2/3 x (the second equation) When you are given two equations in the same problem, you can be sure that you are supposed to solve them simultaneously, to find the one unique pair of x,y values that will solve both equations. Let's proceed with that thought in mind. 7x+2y=5   3y=16-2x -> rewrite the second:  2x + 3y = 16 We'll eliminate the y terms by subtracting one equation from the other. To do that, the y terms must be the same. 3 * (7x+2y) = 3 * 5           21x + 6y = 15 2 * (2x + 3y) = 2 * 16      (  4x + 6y = 32)                                     ----------------------- Subtract and get---->       17x         = -17 17x = -17 x = -1 We will substitute that x value into the first equation. 7*(-1) +2y = 5 -7 + 2y = 5 2y = 12 y = 6 Finally, substitute both values, x and y, into the second equation. 3 * 6 = 16 - (2 * -1) 18 = 16 - (-2) 18 = 18 Now, you know that x=-1 and y=6 solves both equations at the same time. This tells you that if you plot the two equations on the same graph, you will have two lines that intersect at (-1, 6).  
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