geno3141

If tan(x)  =  260/360, to find the value of x, use invTan:  x  =  invTan(260/360).

If you use the F-test to compare variances, then if you reject the assumption that σ1² = σ2², you will use one formula, while if you don't reject the assumption, you will use a different formula.

My suggestion is to use a calculator to solve this; the one at this site will give you a good approximation.

To test whether or not it is a true proportion, cross multiply:

3/11  =  12/33                 -->  Is 3 x 33 equal to 11 x 12? If so, it is a true statement, if not, it is incorrect.

Find 10% of 2008  by turning 10% into a decimal and multiplying times 2008:  0.10 x 2008  =  the answer

arg  refers to the size of the angle of a complex number placed in polar coordinates. I believe that this is a mistype in this question.

arc cos  is the size of the angle whose cos is .47.

If you want to find arc cos(θ) = .47, then use a calculator to find the invCos(.47); usually done by pressing (2nd) (cos) and entering .47. If you wish your answer to be in degrees, it is approximately 62 degrees.

A number to a negative exponent can be written as the same number to a positive exponent if you place it in the denominator:

10^-2  =  1 / 10^2  =  1 / 100

9850  =  8060(1 + x)^4

Remove the multiplier of 8060 by dividing both sides by 8060:

     9850 / 8060  =  (1 + x)^4

Remove the exponent of 4 by finding the 4th root of both sides:

    (9850 / 8060) ^ (1/4)  =  1 + x

Now, subtract the 1:

    (9850 / 8060) ^ (1/4)  -1  =  x

To turn x into a percentage, multiply by 100.

If you can't use the calculator:

If you use Pascal's triangle to get the coefficients:

Row 0:                                1

Row 1:                             1     1

Row 2:                         1      2       1

Row 3:                     1      3      3       1

Row 4:                  1     4       6      4      1                      

(a + b) ^ 4  =  1a^4  +  4a^3b  +  6a^2b^2  +  4ab^3  + 1b^4

In (x² + 2/x)^4,  a = x²   and   b = 2/x

                       1(x²)^4  +  4(x²)^3(2/x)  +  6(x²)^2(2/x)^2  +  4(x²)(2/x)^3  +  1(2/x)^4

                            x^8  +  4(x^6)(2/x)  +  6(x^4)(4/x²)  +  4(x²)(8/x^3)  + 16/x^4

                            x^8  +  8/x^5  +  24x^2  +  32/x  +  16/x^4

A procedure that isn't as easy as doing it by calculator, and a way in which more mistakes can be made!

If you must do it by hand and if you know combinations (nCr) you don't need to use Pascal's triangle to find the coefficients: the coefficients of row 4 are:   4C0,  4C1,   4C2,   4C3,   4C4

a/b  =  5/7

a/9  =  5/7

cross multiply:               7·a  =  9·5

                                      7a  =  45

divide both sides by 7:       a  =  45 / 7