geno3141

If you want to find the mean:  add all the numbers and divide by the number of numbers.

If you want to find the median:  arrange them from smallest to largest and choose the middle number (in this case, since there are an even number of numbers, choose the number halfway between the two middle numbers).

If you want to find the mode:  choose the number that is used most often.

If you want to find the sin(60°) without using a calculator, draw a right triangle with angles of 60°, 30°, and 90°.

From geometny, it can be shown that the length of the side opposite the 60° angle is √3, the side adjacent to the 60° angle is 1, and the hypotenuse is 2 (or multiples of these numbers).

Sin is defined to be the length of the opposite side divided by the length of the hypotenuse:  sin  =  opp / hyp.

sin(60°)  =  √3 / 2

To find the average (the mean) of two numbers, add them together and divide by 2.

The compound interest formula is:  A  = P(1 + r/n)^(n·t)

where          A = final amount          P = amount invested = 100.00        r = rate (as a decimal) = .0217

                   n = number of times compounded per year = 365          t = number of years = 2

Substituting:  A  =  100.00(1 + .0217/365)^(365·2)     --->     A  =  104.44

[I use a dot '.' where you use a comma ','.]

The compound interest formula is:  A  = P(1 + r/n)^(n·t)

where          A = final amount          P = amount invested        r = rate (as a decimal)

                   n = number of times compounded per year          t = number of years

You can choose any number that you want for P; I will choose 1.  (This procedure works for any number that you choose for P.)                 The value of A is twice that of P, so A = 2             r = .028              n = 4

Substituting:  2  =  1(1 + .028/4)^(4t)     --->     2  =  (1.007)^(4t)

Since your unknown is in an exponent, use logs:    log(2)  =  log[(1.007)^4t]

An exponent in a log comes out as a multiplier:      log(2)  =  4t·log(1.007)

                                                                          log(2) / log(1.007)  =  4t

                                                                         t  =  [ log(2) / log(1.007) ] ÷ 4

t  ≈ 24.8 years

To go from the x-intercept (-6, 0) to the y-intercept (0, 4), you have a rise of 4 and a run of 6 (both positive because you are moving to the right and moving upward).

slope  =  rise / run  =  4/6  =  2/3  

This means that the point (2, y) is on the line; it says that x has the value of 2; so substitute 2 in for x:

y  =  3x - 2     --->     y  = 3(2) - 2     --->   y  =  4

There is a point-slope form for a line  y - y1 = m(x - x1)

point = (x1, y1) = (4, 2)

slope = m = 3

Substituting:  y - 2  =  3(x - 4)

                     y - 2  =  3x - 12

                      y       =  3x - 10

The point-slope form is probably the most useful of all the forms; it would save you a lot of time if you could learn it.

2x - 3y  =  11          and         x  =  4y + 9

Substituting the second equation into the first:  2(4y + 9) - 3y  =  11

                                                                        8y + 18 - 3y  =  11

                                                                                 5y + 18  =  11

                                                                                        5y  =  -7

                                                                                          y  =  -7/5

Substituting this into the second equation:  x  =  4(-7/5) + 9  =  -28/5 + 45/5  =  17/5

The slope formula is:  m  =  (y2 - y1) / (x2 - x1).

Choose either point to be the first point; I am choosing (x1, y1) = (5, -4) and (x2, y2) = (-2, -5).

This means that x1 = 5, y1 = -4, x2 = -2, and y2 = -5.

Putting these values into the formula:  m  =  (-5 - -4) /(-2 - 5)  =  (-5 + 4) / (-2 - 5)  =  -1 / -7  =  1/7.

If you are in algebra class, you should memorize this formula.