geno3141

Do you forget some information?

As stated, no fewer than 0, no more than 27.

If the fifth head occurs on the tenth toss, the previous nine tosses must include 4 heads and 5 tails.

With the probability of getting a head = 0.55, the probability of getting a tail = 0.45.

Thus the probability that the first nine tosses are 4 heads and 5 tails:

              9C4·(0.55)4·(0.45)5  =  0.212757,,,

Following this with a head requires multiplying that answer by 0.55  =  0.117016,,,

Draw XY.

This creates right triangle(WXY).

By the Pythagorean theorem, WY  =  4·sqrt(2).

Since triangle(WXY) is an isosceles right triangle, angle(XYW) = 45^o.

This makes angle(ZYW) = 90^o.

Use the Pythagorean Theorem:  WZ²  =  WY² + YZ².

--->     9²  =  [ 4·sqrt(2) ]² + a²

Finish this to get the answer ...

x = 5

y = 135

To be 5 units away from a point means that it is on a circle with radius = 5 and center = (-1,0).

The equation is:  (y - -1)² + (x - 0)²  =  5²

                                    (y + 1)² + x²  =  25

Placing (2, n) into the equation:  (2 + 1)² + n²  =  25

                                                              9 + n²  =  25

                                                                    n²  =  16

So, either  n = 4  or  n = -4. 

If the first term of an arithmetic sequence is a and the common difference is d,

then the fifth term is:  a + 4d  and the 32nd term is:  a + 31 d.

We have these equations:  a +    4d  =  9

                                            a + 31d  =  84

Solving, we have:                       27d  =  75     --->    d  =  75/27  =  25/9

which makes:                                  a  =  -19/9

To find the 23rd term:  a + 22d  =  -19/9 + 22(25/9)  =  ...

You can find all of them by making the discriminant positive: 

               b² - 4·a·c  >=  0      with a = 8 and b = 45

and solving for c.

Or, you can realize that one of the possible correct answers is 0; making the 

product of all of them also 0.

x² - 8x + 1

First:  separate the squared term and the single x-term from the constant:

         (x² - 8x    ) + 1

Second:  complete the square by dividing the coefficient of the x-term by 2 and

                squaring the result:  -8 / 2  =  -4      (-4)² = 16

Third:  add this result into the set of parentheses and subtract this result after the parentheses.

          (x² - 8x + 16) + 1 - 16

Fourth:  factor the expression within the parentheses and simplify the constants:

          (x - 4)² - 15

Can you take it from here?

The line under the less than sign means "possibly equal."

Therefore, the comparison is between:  2x  <= 10  which means "twice x is either less than or equal to 10"  and  2x  <  10 which means that "twice x is strictly less than 10 (and never equal to 10)."

Since x = 5, 2x = 10 which makes the first inequality true and makes the second inequality false.

You can use this formula:  P·(r/k) / (1 - (1 + r/k)^-N·k)

where:  P = original amount = 2,250,000

             r = interest rate (as a decimal) = 0.12

             k = number of times per year money is taken out = 12

             N = number of years = 40

[notice the negative sign in the exponent]

I believe that the answer is $22,691.25; an unusually large number because the interest rate is quite large.