The probability that a police officer is physically assaulted on the job can be estimated as 560/14,000 = 0.04 or 4%. But what does this have to do with postal workers and the probability of one of them being assaulted on the job? Comparing pears to apples
here. Also, over what period of time...
This problem can be done by hand, of course, but it requires a lot of computations as you have a multiple regression. Are you allowed to use a calculator such as the TI-83 or higher graphing calculator? If you are, the answers are not too difficult to
1) Put the data in L1, L2,...
Yousaf, you need to compare how much John is going to pay under either alternative:
1) 3.2% simple interest rate. What John pays to borrow $500,000 for 3 years is equal to
$500,000*3.2%*3 = $48,000
2) 1.6% compound interest rate, compounded semi-annually.
Suppose that the statement is true for n, i.e., 2n >= n+1 (inductive assumption)
Then, for n+1, one finds using the inductive assumption, that
2(n+1) = 2n+2 >= (n+1)+2 > (n+1)+1.
Since the statement obviously holds for n=1 (2*1=1+1) and n=2 (2*2> 2+1), you are done!...
You have 15 freshmen, 15 sophomores, 15 juniors, and 15 seniors available.
We assume that the order in which the students are chosen within each "standing" is irrelevant, i.e., we only care about who they are and not the position they were picked.
So, there are 15C4 ways (combinations)...
I assume that you are supposed to perform this calculation without a calculator. Well, the point to start from is to recognize that
13.568/.4 does not change if you multiply both 13.568 and .4 by 10 or by 100 or even by 1000 and so on.
13.568/.4 = 135.68/4 =...
Eme, something is missing in the expression you wrote above. In any case, let's assume that we had
3c3(5c+2cq) where q is any integer (or even just any real number as a matter of fact). Then you would have
3c3*5c + 3c3*2cq where we used the distributive property of multiplication with...
xsin(x)[cos(x)ln(x) + sin(x)/x].
You can write the function y =xsin(x) as
y = exp(log(xsin(x)))= esinx*log(x),
then dy/dx = [sin(x)/x + ln(x)cos(x)]esin(x)log(x) = [sin(x)/x + ln(x)cos(x)]xsin(x) .
In case of continuously compounded interest, the relevant formula is
A = Pert.
In this case you want to achieve A=225,500, r=8.15% or 0.0815 and t = 8+145/365 =8.39726 years.
So, you can find the amount of money that you want to invest today, P, to achieve A in 8 years and 145 days...
Sun, I am afraid that this is not a "simple" inverse Laplace transform problem. it is not terribly difficult, but it requires quite a bit of calculations.....
The answer is e(1-i)t[(2-i)+(2+i)e2it]
and it requires that you use complex numbers. Note that the solutions of s2-2s+2 = 0 are...
Jerri, you are given a polynomial, x3-14x2+49, and that is "what it is", but what are you exactly asked to do with it? What do they mean by "what is?"
Maira, if I am reading this right, you are given the following binomial:
16x4 - 1
and you are asked to factor it.
Well, you should recall that, in general, if you are given something like
you can factor it as follows
a4-b4 = (a2+b2)(a2-b2).
Now the first term, (a2+b2),...
Laplace transforms are used to solve initial-value problems given b n-th order linear differential equations with constant coefficients. In your case n=2. If L indicates the Laplace transform operator, we can write the assigned equation as
L(y'') - L(y') -6L(y) = L(0).
I am sure...
This problem is very easy. Start with the formula given, i.e., n=3m-2l. Now, use the fact that you are told that l = m+2 and rewrite your original formula as
n = 3m -2(m+2).
Simple algebraic manipulations give n = 3m-2m - 4 = m-4. So the answer is (A).
If you start with 7x - 8a = 3x+24a, we can subtract 3x from both sides of the equation. This yields:
4x-8a = 24a. Now add 8a to both side of the equation we just wrote. This gives:
4x = 32a.
Finally, divide both sides by 4 which gives x = 8a. So your answer is (b)....
Robert gave you the right answer in terms of solutions for x and y.
The matrix that your problem is asking for is given by
| 7/9 -6/9|
|-2/9 3/9 |
i.e. your answer is (C)
The first matrix is 2x3, the second is 3x2, hence we know that the matrix we get from the multiplication is a 2x2. To compute it, multiply the first row of the first matrix by the first column of the second matrix, then the first row of the first matrix
by the second row of the second matrix,...
The problem is fairly simple: you have a system of linear equations given in matrix form
Az = b
where A= |2 3 | b = |12| z = | x |
|4 -1| |8 | | y |
So, the general solution is given by z = A-1 b where A-1 is the inverse of the matrix A we wrote...
The answer is altitude = 2*rainfall -6
You can check that this answer works for all your numbers. For instance, if rainfall = 9, then altitude = 2*9-6=12 and so on.
The other relationship is given by
rainfall = 0.5*altitude + 3.
To explain how to get these equations,...
So, you have the following simple polynomial: 3x2y - 6xy2 + 12xy.
What is the GFC all all the expression's terms ? I assume you can see that the GFC is 3xy.
Hence, divide each term of your polynomial by 3xy, i.e.
3x2y/3xy = x
and 3xy(x-2y+4) is...