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b.  Look at the y values for A   and we have  2, 5, 8, 11, 14, 17, 20

This is arithmetic.....common difference =3   and first term = 2

So....

an  = 2 + 3(n - 1)   =  3n - 1

c. Look at the y values for B and we have     1/2, 1, 2, 4, 8, 16

This is geometric.....common ratio  =1/(1/2)  =  2   and the first term = 1/2

So....

an  = (1/2)(2)^(n - 1)

d.  See c.....we have a common ratio.....this always indicates a geometric progression

If independent

P(A and B )  = P(A) * P(B)

0.2     =     (0.6) * (0.55)     ???

0. 2  =   0.33   ...so....not independent

This means that

P(A l B)   not equal to P(A)  and P(B l A)  not equal  to P(B)

Independent.....dice rolls are independent....so....C

2. sin^2 x + sinx  = 1

sin^2 x + sin x - 1  =  0

Let a = sin x

a^2 + a - 1  = 0

a^2 + a= 1       complete the square on a

a^2 + a + 1/4  = 1 + 1/4

(a + 1/2)^2  =  5/4

Take both roots  

a + 1/2 = √5/2

a =  √5 - 1

        _____

           2

sin x = √5 - 1

            _____    take the arcsin and x  ≈ 38.17°   and (180 - 38.17) ≈ 141.8°

               2

Or

a  =   -√5 + 1

        ______      

             2

sin (x)  =  - √5  - 1

                _______      this answer is < -1....so no answer for sin x  

                      2

1.  4 sin^2 x – 1 = 0    add 1 to both sides

4sin^2x  = 1       divide both sides by 4

sin^2 x   = 1/4          take both roots and we have that

sin x = √[1/2 ]  and this happens at  45 degrees and  135 degrees    

And

sin x = - √[1/2]   and this happens at   225 degrees and 315 degrees

See answer here, FA :  https://web2.0calc.com/questions/help-please_29047

[ Age  -  Mean ]

____________   = z score     .....fill in what we know

    Std Dev

[ Age - 35 ]

________     =  -2.1              multiply both sides by  8.2

     8.2

Age  - 35  =  -17.22         add 35 to both sides

Age  =  17.8  years 

[ 105 - 103 ] 

_________      =  z score  ≈  0.74  

    2.7

They are the same thing.....but....since they want two decimal places....try either 0.50  or .50

thank you for my answer do i put in 0.5 or 0.50

We're just sticking each number into the function and evaluating, GM....for example

f(3)  =  2(3) - 7  =  6 - 7  =  -1

And

g(3)  = 5^3  =  125

Pretty easy, huh  ????

First one....good job on both parts  !!!!

a.  This looks to be arithmetic.....common difference between terms =2

And the first term = 2

So

a_n  = 2 + 2(n - 1)   which we can simplify as   a_n = 2_n

b. Also arithmetic .....common difference = 2 ....first term = 3

a_n  = 3 + 2(n - 1)     which we can simplify as   a_n  = 2n + 1

c. Arithmetic....common difference = -25  and the first term is 50

a_n  = 50 - 25(n - 1)    =   75 - 25n  

4. Geometric.....common ratio  = 1 / (1/3)  = 3....first term = 1/3

a_n  = (1/3)*3^(n - 1)

That's a nice approach, Melody   !!!

See here, flanspawn  :  https://web2.0calc.com/questions/one-of-my-questions-i-couldnt-get

FYI....picture:

Integers between 20 and 40  =  19  = B

We have 4 primes  from 20 to 40  = A

So  P ( A l B)   =   4 / 19  ≈  0.21 

Here's my attempt

Possible letter combos

Choose any letter  and let this also be the repeated letter = 26 ways

But....we have 4C2 = 6  positions for the two identical letters to occupy.....

And we have (25)(24) ways to choose the other two letters

So...I believe that the total number of "words"  = 4C2 * 26 *25*24  = 93600

And since the digits cannot be repeated  = 10 * 9  =  90

So...the total possibilities  =  93600 * 90  =  8,424,000

Hmm... Not math, but interesting!

I'm not so good at these types of problems, please forgive me if this isn't the answer that you wanted (I messed up super bad on another problem!)

Here we go:

I believe that the sample is biased because it does not represent the population - The City did not get random coaches, so it isn't random.

I also believe that the question is not biased - because both water and the sports drink are given equal opportunity. UNLESS you count in the order, where drinking water is presented first as an option, and therefore has a slight psychological effect upon the participant's mind. :)

My own thoughts -- probabaly not professional. :)

Thanks, tertre and EP.....!!!!

Here's a way to do this

Find the distance^2 between both points.....we have

D^2  =  (-1 - 3)^2  + (-1 - 1)^2   =  4^2 + 2^2  =  20

Now.....construct two  circles   with centers at the two points and a radius of D^2

So.....we have

(x + 1)^2 + (y + 1)^2  = 20

(x - 3)^2 + ( y - 1)^2  = 20

Set these equal

(x + 1)^2  + (y + 1)^2  = (x - 3)^2 + ( y - 1)^2   simplify

x^2 + 2x + 1 + y^2 + 2y + 1  = x^2 - 6x + 9 + y^2 - 2y + 1

2x + 2y + 2  =   -6x - 2y + 10     divide through by 2

x + y + 1  =  -3x - y + 5

2y = - 4x + 4    divide through by 2

y  =  -2x + 2

y = 2 - 2x         (1)

Sub this into the equation for either circle for y

(x+ 1)^2  + ( 2 - 2x + 1)^2  = 20

(x+ 1)^2 + (3 - 2x)^2  = 20

x^2 + 2x + 1 + 4x^2 - 12x + 9  = 20

5x^2 - 10x + 10 = 20       divide through by 5

x^2 - 2x + 2 = 4

x^2  - 2x  = 2        complete the square on x   [ you can also use the quadratic formula ]

x^2 - 2x + 1  = 3

(x - 1)^2  = 3      take both roots

x - 1  = ±√3   add 1 to both sides

x  =  1±√3

So   

x  = 1+ √3      or x  = 1  - √3

And using (1)....we can find y as either

2 - 2 [ 1+ √3]   =   -2√3    and    2 - 2 [ 1 - √3]  = 2√3

So....the two other possible points are

( 1 +√3, -2√3 )   and  ( 1 - √3,  2√3 )

Strong Work so far!    I will use your results to proceed:

The didstance between the 2 given pionts is  sqrt 20

set up a circle centered at  -1, -1  with radius  sqrt 20

(x+1)^2 + (y+1)^2 = r^2 = 20     

to find the point(s) on the given perpindicular line, sub in y = -2x+2 into the circle equation

(x+1)^2 + (-2x+2 + 1)^2 = 20    expand and simplify to get

5x^2 - 10x -10 = 0     Quadratic fomula gives   x = 1 +- sqrt(3)      use these values to sub into the perpindicular line equation to find the correspondine 'y' values ....

My fault! Sorry! :(

1.

First term  =  510

Common ratio  = 1.12

Recursive Rule     a_n  =  a_n-1 * (1.12),   a₁  = 510

2.   Explicit Rule

a_n  = 510 * (1.12)^(n - 1)

3. Phones sold in week 3

a₃  = 510 * (1.12)^(3 - 1)  =  510 * (1.12)^2  ≈ 640 phones

4. Phones sold in first year  =

510 * [ 1 - 1.12^52] / [ 1 - 1.12]  ≈  1,536,478   phones