Matthew Fonda
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B.S. in Applied and Computational Mathematics. Developer at eNotes.com.
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Recent Activity

Answered a Question in Math
There are no four odd integers with a sum of 19. This is because the sum of four odd numbers is always going to be even. Using the following rules, we can see why this is true: 1. The sum of... 
Answered a Question in Math
2+3=5 
Answered a Question in Math
This problem is know as the Birthday Problem or Birthday Paradox. Note: the above answer answers a slightly different questionit answers the probability that anyone has the same... 
Answered a Question in Math
First start by simplifying the right hand side: (3x + 2)  2(x+4) = 3x + 2  2x  8 (multiply through second part by 2) = x  6 (combine like terms) Now we just have to solve: x  6 = 7 x =... 
Answered a Question in Reference
Most computer related majors will include some amount of programming. A major in Information Technology will generally include much less programming than a major in Computer Science. The exact... 
Answered a Question in Math
The key here is to remember the rule for dividing with exponents: `x^a / x^b = x^(ab)` Applying this rule here, we find: `a^7/a^4 = a^(74) = a^3` Another way of solving this problem is by... 
Answered a Question in Math
We have 11 different members we can choose from, and we want to count the number of committes consisting of 4 members. To solve this sort of problem, we use combinations: `11C4 = ((11),(4)) = (11!)... 
Answered a Question in Math
We are interested in the number of ways to choose 2 items from a set of 15 items. We use combinations for this: 15C2 = `((15),(2)) = (15!) / (2!*13!) = (15*14) / 2 = 105` Therefore there are... 
Answered a Question in Math
In my opinion it depends on how confident you feel in your algebra ability. PreCalculus is likely to be the more advanced version of College Algerbra, so if you feel confident then I would go with... 
Answered a Question in Math
The important thing to remember here is the order of operations PEMDAS: parentheses, exponentiation, multiplication, addition, subtraction. (99*99) + (99) / (99)  (1) * (0) + (20*20) / (400)... 
Answered a Question in Math
We can expand` (x+y)^11` using the binomial theorem: `(x+y)^11 = sum_{k=0}^11 ((11),(k))x^k y^(11k)` We see that a term will contain` x^10` only when k=10. So we can let k=10 to find the full term... 
Answered a Question in Math
We must simplify `(10n^7) / (15n^7)` . The first thing to notice is that we have `n^7` in both the numerator, and denominator, so these terms cancel out: `(10n^7) / (15n^7) = 10/15` We next need to... 
Answered a Question in Math
When asking for the value of n, I assume you are asking for number of tests Alfred has taken, including the last one. Let's recall the definition of average (also known as the mean): mean = `... 
Answered a Question in Math
We must solve the differential equation: `x^3 dy/dx = 2` The first step is to notice that this is a separable equation, so we will separate: `dy = 2/x^3 dx` Next, we can integrate both sides: `int... 
Answered a Question in Math
To solve this, we'll rewrite the inequality in terms of y, then graph it to visually see the points. Subtract y from each side: ==> 2x <= y Multiply each side by 1. Note that this flips the... 
Answered a Question in Math
When working on word problems, one of the trickiest parts can be transforming the words into a math equation you can proceed to solve. A good strategy is to start by listing what numbers we know... 
Answered a Question in Math
This expression cannot be expressed in the form nPr. Recall the definition of nPr: nPr = n * (n  1) * ... * (n  r + 1) The given expression, (27*26*25*24) / (4*3*2*1) is not in this form.... 
Answered a Question in Math
We use the Extended Pigeonhole Principle. We assume there are 365 days in a year, 24 hours in a day, and 60 minutes in an hour, therefore 525,600 minutes in a year. Since the maximum age is 120... 
Answered a Question in Math
To show that R is an equivalence relation, we must show that it is symmetric, reflexive, and transitive. Let A = P({a,b,c}) and let xRy iff x = y for all x, y in A. Symmetric: Let x, y be let... 
Answered a Question in Math
I think your answers for a and b are correct. For c, this is asking for the expected value of your random variable X. Recall that expected value of a random variable X is given by E[x] = x1*p1 +... 
Answered a Question in Math
For this problem, a direct proof is the way to go. Start by defining set difference and subsets, then use these definitions to reach the conclusion. Set difference: `AB = {x \in A  x \notin B}`... 
Answered a Question in Math
There are four different binary numbers with the first digit 1 and the last two digits zero We have 1 possible choice for the first digit, 2 for the second, 2 for the third, and 1 for the fourth... 
Answered a Question in Math
Given the equation `x^2 + y = 2` , we want to solve for y. All we need to do here is subtract `x^2` from both sides of the equation: `\implies x^2 + y  x^2 = 2  x^2` `\implies y = 2  x^2` 
Answered a Question in Math
This was proven by Euler (1736) in his famous solution to the Seven Bridges of Königsberg problem. This same work is also considered to be the origin of graph theory. I will give an overview... 
Answered a Question in Math
Recall that the formula for choosing k people from a group of n people is `((n),(k)) = (n!) / (k!(nk)!)` The answer to your question follows directly from this formula. In both cases, the n=12. In... 
Answered a Question in Math
We have one choice for the first digit, and two choices for the second, third, fourth, and fifth digits, so the total number of possible five digit binary numbers with 1 as the first digit is:... 
Answered a Question in Math
The sum of the interior angles of a pentagon must add up to 540 degrees. We know three of the angles already, so the other two angles (we will call them A and B), must make the sum of all angles be... 
Answered a Question in Math
You can also prove this with a direct algebraic proof: Definiton: An integer n is said to be odd if it can be written as n = 2k + 1 for some integer k. Proof: Let n be the product of three... 
Answered a Question in Math
Our goal is to write 234.32 octal (base 8) in decimal. In octal, instead of having a ones place, tens places, hundreds place, etc. like you do in decimal, you have a 1's place, 8's place, 64's... 
Answered a Question in Math
The first step here is to recognize that each part of this expression looks a lot like a factorial. Recall that `27! = 27*26*25*...*2*1` If we divide 27! by 23!, the result is 27*26*25*24, which is... 
Answered a Question in Math
Suppose that g is the inverse of f. Let's think for a moment about what this means. In order for this to be the case, it must be true that if for all x in the domain of f, if y = f(x), then x =... 
Answered a Question in Math
To solve this problem, we'll translate the words into equations, then solve the equations. Let j represent Jill's current age, and let b represent Bill's current age. 1.) "Jill is 6 years less than... 
Answered a Question in Math
Multiplication is associative, which means that the order in which you do the multplication does not matterthe result will be the same no matter what order you multilply. So you are... 
Answered a Question in Math
We are looking for a polynomial with roots 1, 2, and 5. If we find functions with each of these as roots, and multiply them together, then the resulting function will have all three as roots. This... 
Answered a Question in Math
One way to solve this problem is to count the total number of ways the total can add up to 16, then count the total number of possible outcomes. First, we'll count the total number of possible... 
Answered a Question in Math
Given an equation in the form of `y = mx + b` the slope is given by m, and the yintercept is given by b. We'll transform the given equation into that form: `y = 3(x  4) + 1` Multiply each term in... 
Answered a Question in Math
Since f is continuous and differentiable on the interval [1,4], the mean value theorem states that there exists a c such that: `f'(c) = (f(4)  f(1)) / (4  1)` Note that `f'(x) = 3x^2` Therefore,... 
Answered a Question in Student Study Tips
I agree with all the ideas, and especially with #5. I think this advice also extends further than just reading. Attempting to take on anything above your current skill level is a great way to... 
Answered a Question in Math
The idea infinity and infinitely plus one being the same quantity is very counterintuitive. This idea is actually known as "Hilbert's paradox of the Grand Hotel." The page on Wikipedia does a... 
Answered a Question in Math
I disgree. Where is it shown that one can do standard calculations making use of an infinite number of decimal places? Moreover, where is it proven that one can use such calculations... 
Answered a Question in Math
I just figured out the fallacy of the proof given by number 2. It is incorrect as follows: if you let x = 0.999 then 10x = 9.99 (not 9.999) 10x  x = 9.990.999 = 8.991 9x = 8.991 x =... 
Answered a Question in Math
This is a question best asked to the teachers in your school. The topics covered in these courses vary from school to school. I imagine the teachers at your school would be very excited that you... 
Answered a Question in Math
There are a few different proofs for this. I think the easiest to understand is a simple algebraic proof: Let x = 0.99... 10x = 9.99... 10x  x = 9.99...  0.99... = 9 9x = 9 x = 1 For more... 
Answered a Question in Math
When dividing 1,000,000 seconds by the number of seconds in a day (86,400), we must consider the remainder. (1,000,000 sec) / (86,400 sec/day) =11.574 days We now find the remainder: (11... 
Answered a Question in Math
To divide fractions, flip one of them, then multiply across: ` ` `2 / 5 : 2 / 8= 2 / 5 * 8 / 2 = 16 / 10` We then simplify, arriving at our answer: `8/5` 
Answered a Question in Math
I want to elaborate a bit more on how to find this. When working on a problem involving a sequence, a good first step is to look at the numbers and see if anything stands out. For this sequence, we... 
Answered a Question in Math
AB is a line segment that we know the start point and end point of. We know from the Pythagorean theorem that the length of the hypotenuse of triangle is given by `c = sqrt(a^2 + b^2)` Using our... 
Answered a Question in Math
I don't think you've provided us with enough information to answer this question. What is the starting position of the object? Was it launched with some specific velocity at some specific angle?... 
Answered a Question in Math
This question is difficult to answer without knowing what [[x]] means. The closest thing I can think of is this might be the nearest integer function, which is sometimes written as [x], x, or... 
Answered a Question in Math
Use the pointslope equation: `y  y_1 = m(x  x_1)` We're given x = 3, y = 6, and m = 4/3. Let's plug them into the pointslop equation: `y  6 = 4/3(x  3)` We then simplify: `y + 6 = 4/3 x...
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