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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The answer is forty three hundredths, which is written as 0.43.
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:
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.
MUx(x,y) = Derivative of U(x,y), treating y constant.
MUx(64,25) =
MUx(49,36) =
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:
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: