BMAD

If a -' b is defined as the inverse of the +' operation, such that a +' b -' b = a = a -' b +' b, then (Using Common Notion 2: "If equals be added to equals, the wholes are equal.") Note that the second comports with the notion that a -' a should equal the identity element: 1. (This is why I favor the second.) 2. If x' is defined as repeated addition (via +'), such that 2 x' 4 = 4 +'4, then Note that the ordering is that implied by the old-fashioned reading of 2 x 4 as "twice four," or "two fours." This definition has the interesting, and possible undesirable consequence that 1 is a left-identity but not a right-identity: 1 x' 4 = 4, but 4 x' 1 = 3. (All multiplications not containing a one commute.) Lack of universal commutivity can be remedied by defining 1 x' 4 as 4 +' 0; i.e. multiplying by one is adding nothing to 4, which then requires the final counting of interstices. In this case 1 x' 4 = 3 = 4 x' 1, all multiplication commutes, but there is no multiplicative identity. I'd be interested to hear opinions on which definition of 1 x' a is preferable. The second, containing some appeal, leads to a breakdown in distributivity when 1's are involved. The first, I believe, allows for distributivity in all cases. (I've not rigorously proven it, though.) 3. Properly speaking, I'd say However, we don't really want that result, do we? So, let's clean up our definitions by dropping the notion of items-and-spaces, and just go with a +' b = a + b -1 (where " + " is the usual addition operator), a x' b = a x b -1 (ditto). Note that a +' 1 = a, and a +' b = b +' a. Good so far. a x' b = b x' a, but we still have no (and have no hope of a) multiplicitave identity element. This has grave consequences for the idea of division, but we forge ahead blindly... Defining division as the inverse of the multiplication operation, such that a x' b /' b = a = a /' b x' b, we can use the above to determine that 4. Using the most-recent definition of " x' ", and assuming that sqrt'(a) is the inverse of a x' a, we see that Very well thought out answer. I am curious as to how you resolve the following identity for square roots This is using the traditional sense of computation symbols b= a + 1 b^2 = a^2 +2a+1 sqRoot(b^2)=sqRoot(a^2+2a+1) sqRoot(b^2)=sqRoot((a+1)^2) Using the new definitions of the number system with the above identity 36 = (a+1)^2 how would the solution proceed?

"Sale price" is the price you pay to buy a stock "Market Purchase Price" is the price the market would pay to get the stock back "projected sale price" is the price that the market is trending to become (the next sale price). However it is not guaranteed, completely dependent on the market remaining stable. This projection rarely happens so consider it a guide.

here is a snapshot of what i mean starting at number 91. The columns that have no number above them (the nothing space) should be shifted up so that each of the three columns start at a number.

From now on, the "+" symbol no longer means to combine the count of objects (e.g. 3 things plus 4 things make 7 total things would not be modeled as 3 + 4 = 7). Instead, the use of the + symbol is to show 5 + 3 = 7 to resolve the question of "how many spaces between objects are created when you line up five things and three things" (ex: t _ t _ t _ t _ t _ t _ t _ t ) and this is now to be considered addition If the other basic computational symbols maintained the same relationship to addition as they had before this new convention what would be the answers to the following problems? 4 - 3 = ? 3 x 3 = ? 9 / 3 = ? sqrt (36) = ?

List out the numbers from 1 to 150 in a vertical column. Left align all of the numbers to where the leading digit of the number is directly on top of the next number's leading digit (e.g. for the numbers 9, 10, and 11. 9 would be above 1 and that above 1 where zero would have nothing above it and 1 below it ex. ... 9 10 11 ... ) remove the nothing space above all the numbers to where the numbers are shifted up until they are at the top creating a list of new numbers. With this new list of numbers what is the probability of randomly selecting 322? 99? and 140?

close. if you revisit your approach, you might find your mistake

If three circles are mutually tangent where one has a radius of 3cm, another has a radius of 4cm, and the last has a radius of 5cm. What is the area of the region bounded between the three circles?

A reporter on New Year's Eve 1993 wanted to know, from Pat and Chris, how old they were, but felt (correctly, it turns out) that one would lie. So the reporter asked them both, "Write down your age now, your age at the end of next year, add these together, then multiply the result by 5," quickly followed by: "now add the last digit of the year you were born." They had no time to fake that last digit; Pat answered 281, while Chris announced 229. Who was lying, and what were their real ages at the time?

Every day, Ellie takes the commuter train and arrives at the station 8:30 AM, where she's immediately picked up by a car and driven to work. One day she takes the early train, arrives at the station at 7:00 AM, and begins to walk towards work. The car picks her up along the way and she gets to work 10 minutes earlier than usual. When did Ellie meet the car on this day?

What is the maximum number of Friday-the-13ths that there can be in a single year? What is the minimum number?

The people living on Sesame Street all decide to buy new house numbers, so they line up at the store in order of their addresses: 1, 2, 3, . . . . If the store has 100 of each digit, what is the first address that won't be able to buy its house numbers?

crawl

That is the way the simulation worked this time. either sell, trade with someone, or just wait and see what happens next time?

day 7

Are you sure that you want to? It costs 4.12 a share to buy Hoty and the market will only give you $1.00 per share you own so you will lose $3.12 per share.

crowd

Day 6 is now up and available.

Here's my try your solution produces revenue of 6450.

This quick selling strategy, though effective, is often risky and very selfish.

It depends. :-P

Like any stock market purchase, there is no gurantee of increase but typically decreasing supply with a steady demand does increase its value. But consider what it means to have a steady demand.

The latter

Two circles are drawn with five inches between the centers. A line is drawn tangent to the bottom of one circle and the top of the other. The circumference of one circle is 6.28 inches. The area of the other circle is 12.56 inches squared, Angle x is formed by the tangent line and the line between the centers. Determine angle x. (assume that pi = 3.14)

frown

grown