# What is 43 over 100 as a decimal.

### Solution:

The answer is forty three hundredths, which is written as 0.43.

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Friday, October 1st, 2010

The answer is forty three hundredths, which is written as 0.43.

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Friday, October 1st, 2010

- 1L = 1.057 fl qt
- 1L = 1000 ml
- 1.079 fl qt = 1.079 x 1.057 L = 1.140503 L
- 1.140503 L = 1140.503 ml

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Friday, October 1st, 2010

The APR is 4%, so the semi-annual interest rate is 2%. If you deposit $10,000 in the bank after every six months, you will have $85,829.69 in the bank at the end of 4 years:

- After six months you will have $10,000
- After one year you will have 10,000×1.02+10,000 = $20,200
- After 1.5 years you will have $20,200×1.02+10,000 = $30,604
- After 2 years you will have $30,604×1.02+10,000 = $41,216.08
- After 2.5 years you will have $41,216.08×1.02+10,000 = $52,040.40
- After 3 years you will have $52,040.40×1.02+10,000 = $63,081.21
- After 3.5 years you will have $63,081.21×1.02+10,000 = $74,342.83
- After 4 years you will have $74,342.83×1.02+10,000 = $85,829.69

The present value of that $85,829.69, discounting at 2% is **$73,254.81** (i.e. $85,829.69/(1.02^8)), so if you put this amount in the bank now, and make the payments every six months, there will be nothing left in the account after four years.

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Friday, October 1st, 2010

- Recurrence relation
- Note that 1800/1200 = 1.5.
- Next, take 1.5* 1800 =2700, and that is the next population.
- Now 1.5*2700 = 4050.

- To calculate the number of bats at the 12
^{th}count, take 1200 * 1.5^{11}= 1200 *86.5 = 103,797

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Tuesday, September 7th, 2010

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Tuesday, September 7th, 2010

MUx(x,y) = Derivative of U(x,y), treating y constant.

MUx(64,25) =

MUx(49,36) =

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Tuesday, September 7th, 2010

- First, factorize the numerator using prime numbers: 288 = 2*12*12 = 2*3*4*3*4=2*2*2*2*2*3*
- Second, factorize the denominator: 1155 = 5*231=5*7*33 = 5*7*3*11
- Notice that the numerator and denominator have only one factor in common (3).
- Restate the ratio after removing the common factor
- New numerator = 2*2*2*2*2*3 = 96
- New denominator = 5*7*11 = 385
- Same ratio in lowest terms:

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Tuesday, September 7th, 2010

We can factor the expression as follows:

To figure this out, we used the quadratic formula (see http://en.wikipedia.org/wiki/Quadratic_equation):

w =

We recognized that y= is a quadratic equation in the form of y= where a=2, b=-5 and c=-10.

To confirm that our calculation are right, we decided to plot the graph of y = by plugging in various values of w.

As you can see, there is a root at approximately -1.3 and another root at approximately +3.8. So we know approximately what the values of a and b are. We could use a calculator to get closer and closer to the exact values of a and b. For example, if we try w=3.8, we get a value of y = -0.12. If we try a slightly different value, we can see if we’re getting closer to zero or farther away: w=3.81 produces a value of y=-0.018, so we know that 3.81 is a better approximation than 3.8. If we keep calculating closer approximations of the root, we will arrive at the value of b that we calculated using the quadratic formula:

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Monday, September 6th, 2010

First, let’s make sure we understand what we mean by “mathematical induction”: “Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers. It is done by proving that the first statement in the infinite sequence of statements is true, and then proving that if any one statement in the infinite sequence of statements is true, then so is the next one.” (Wikipedia) We have pasted below another more detailed explanation of how to create a proof using mathematical induction (see “Appendix” below).

Let’s now take the equation you provided: 1*3+2*4+3*5+…+n(n+2)=

We can show that this is true for n=1: 1*3 = = = 3

Now let us assume that the statement is true for n = k. If it is, then we will prove that it has to be true for n=k+1:

WTS è = +

* *

= +

=

=

=

=

= **QED**

In the above proof, WTS means “want to show” and QED means “quod erat demonstratum” (“which was to be demonstrated”).

Here’s another more detailed explanation of how to create a proof using mathematical induction:

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Monday, September 6th, 2010

- A = number of ounces of the first alloy
- B = number of ounces of the second all
- A+B=32
- 0.16 A +0.28 B = 32 x 0.25
- Since A + B = 32, we know that A = 32 – B. You can then re-write the equation above as 0.16 (32-B) + 0.28 B = 32 x 0.25
- This can be simplified to 5.12- 0.16 B + 0.28 B =8
- Or, 0.12 B = 2.88
- Or B = 24
- So A = 8

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