CPhill

This evaluates to.....

5^(100⁴) .......which is a REALLY big number.....( I can tell you that the final digit is a "5" )

Sorry, geno....I didn't see that you had already posted.......

If no number recurs in a data set......there is no mode.......

Just hit the"2nd" button on the calculator....you will see the"asec" function button....

(18 x 12 - 16) / 8 x 5 - 25

Working with what you have literally written, we have

(216 - 16)/8  x 5 - 25  =

200/8 x 5 - 25 =

25 x 5 - 25 =

125 - 25 =

100

So we have

[2.2 x 10⁵] x [1.5 x 10³ ] =

3.3 x 10⁸

6(9-4m)+5=-181      start by distributing the "6" on the left side over the terms in the parentheses....so we have...

54 - 24m + 5 = -181     combine like terms

59 - 24m = -181  subtract 59 from both sides

-24m = -240     divide both sides by -24

m = -240/-24 = 10

So we have these ordered pairs (1, 2) (2, 5) (3, 8)...we only need to find the slope between any two and use one of the pairs to write the equation

Using the first two, the slope is

[5 - 2 ]/ [2 - 1 ] = 3/1 = 3

And using this and the first point, we have

y - 2 = 3(x - 1)   simplify

y - 2 = 3x - 3  add 2 to both sides

y = 3x - 1

And that's the equation in y = mx ± b form

Let's call the number of pounds of caramel needed 'x"..so the final mixture will be (2 + x) lbs.   ...so we have.....

(2lbs) popcorn*(.80 lb) + (x lbs.) caramel*(2.30 lb.) = (2 + x)lbs of mixture * (1.80lb)

1.60 + 2.30x = (2 +x)(1.80)

1.60 + 2.30x = 3.60 + 1.80x  subtract 1.80x and 1.60 from both sides

.50x = 2.00   divide each side by .50

x = 4 lbs of caramel

This is a graph of a function that has some form such as y = x + Asin(Bx - C). The "x" part makes the graph an ever-increasing one........the period here is pi....this can be seen easily...note that a "relative minimum" of the function occurs just to the "left" of the y axis  at (-pi/4) and the next "relative minimum" occurs at (3pi)/4. So (3pi/4) - (-pi/4) = (4pi/4) = pi.

(I believe this is correct.......would any other forum members like to add anything - or make corrections??.....)