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That's pretty neat, Bertie....!!!!

This is a probability problem that uses combinations:

Formula:  _nC_r·p^r·(1-p)^n-r  =  ₂₀C₁·(.15)¹·(.85)¹⁹

I believe that this is correct.....the probability is given by...

C(20,1) (.15)(.85)^19  = about 13.7%

Use the formula:  A = P(1 - r)^t

where A = final amount; P = beginning amount = 34000; r = rate = 0.15; t = time = 5:

     A  =  34000(1 - 0.15)⁵

Now, it's calculator time!

Folding a parabola on the line of symmetry will have one wing of the parabola lying exactly upon the other wing of the parabols.

The slope of this line is 1/5.

The slope of a line perpendicular to this has a negative reciprocal slope:  slope = -5.

Now, you know the slope of the new line and a point that it passes through, so use the slope-intercept form:

     y - y₁  =  m(x - x₁)   where m = -5, x₁ = 9, and y₁ = 5.

Substitute and simplify.

 (x^4)^5/(x^3)^3=  x^20 / x^9  = x^11

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 (a^2b^3/ab^2)....I'm going to assume this is  (a^2b^3)/(ab^2).... if so, we have

(a^2)/(a) * (b^3)/(b^2) =

a * b  =

ab

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(2/3)^-3×(a^3/b)^-2.......notice that we can use this"trick' to get rid of the negative exponents.....

(3/2)^3 * (b/a^3)^2    ....so we have...

(27/8) * (b^2 / a^6) =

(27b^2)/(8a^6)

Use the formula:  A = P(1 + r)^t   --->   A  =  800(1 + 0.05)⁷

  Calculator time!

If there can be only one computer connect to one peripheral graphics device (leaving 4 graphics devices unconnected) then:  

the first computer can be connected to 23 devices;

the second computer can be connected to 22 devices;

the third computer can be connected to 21 devices;

etc;

the nineteenth computer can be connected to 5 devices;

so 23 x 22 x 21 x ... x 5  or 23! / 4!

Thank you very much!

If you want to find the inverse of a cmmon log, use the 10^x key.

If you want to find the inverse of a natural log, use the e^x key.

The easiest formula is:  Area = base x height.

If you know the base and the height of the triangle, use the formula:  Area = 1/2 · base · height.

If you know two sides of the triangle and the size of the included angle, use the formula:  

     Area = 1/2 · a · b · sin(C).

If you know the lengths of the three sides of the triangle, first find the semiperimeter:  s = (a + b + c) / 2,

then use the formula:  Area  =  √( s · (s - a) · (s - b) ·(s - c) ).

.421875 is the decimal form

2+2=5 ;))))))))))))

The square root is easy it's just 60

Usually you are dealing with a right triangle. In this case you can use the Pythagorean Theorem, which equates the sum of the squares of the "legs" of the triangle with the square of the hypotenuse.

Submit an example if a question you would like to solve.

sqrt(40)=sqrt(4*10)=2sqrt(10)

(no comment)

you sir are a genius

I really like Chris's answer to this question, using the graph plotter makes life so much easier.

Here's the 'on paper' method that we had to use before these sophisticated plotters were available.

Let

$$7\cos12t+6\sin12t\equiv R\cos(12t-\alpha)=R\cos12t\cos\alpha+R\sin12t\sin\alpha,$$

then

$$R\cos\alpha=7 \text{ and } R\sin\alpha=6.$$

Squaring and adding,       $$R^{2}=7^{2}+6^{2}=85, \text{ so }R=\sqrt{85}.$$

Dividing,                         $$\tan\alpha = 6/7, \text{ so }\alpha = 0.7086 \text{ rad}.$$

We have then                 $$7\cos12t+6\sin12t=\sqrt{85}\cos(12t-0.7086)>9.$$

The maximum for the cosine occurs when 12t - 0.7086 = 0, that is, when t = 0.0591 (4dp, but I kept greater accuracy for all decimal values during the calculation).

For equality with the 9,           $$12t - 0.7086 = \cos^{-1}(9/\sqrt{85}),\quad t=0.0773.$$

It follows that the wave is greater than 9 for the time span 2(0.0773 - 0.0591) = 0.0364.

Since the period of the wave is 2pi/12, the proportion of the time that the wave is greater than 9 is

0.0364/(pi/6) = 0.0696, that is, about 7% (agreeing with Chris).

As an alternative, the form    $$R\sin(12t+\beta)$$    could have been chosen rather than the cosine.

3

the answer is three

-0.00212916666

4x - [6/y] = 15

4x - [6/(-2)]  = 15

4x - [- 3 ]  = 15    

4x + 3 = 15     subtract 3 from both sides

4x  = 12          divide both sides by 4

x = 3

lol yea yea. i confess. haha