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Your total should be 2022 not 2021 !!

1473 + 473 + 73 + 3 =2022

1 + 4 + 7 + 3==15 sum of the digits.

2+3=5

sin a / cos a = tan a = 2      a = 63.4349 degrees       sin a =.8944

I  think  it is    4/52 *  3/52  * 2/52  * 1/52     = 24 / 7311616  = 0.0000032824480936

If I choose four cards from a standard 52-card deck,with replacement, what is the probability that I will end up with all four Aces?    

I wish the problem hadn't specified the "with replacement" condition.  

What does "with replacement" mean?  Do you draw four cards, keep any aces, replace the non-aces

back into the deck, and just keep on drawing cards until you eventually end up with all four aces?  

Do you draw four cards, and if all four aren't all aces, replace all four back into the deck, and draw again? 

Do you keep going until you do finally get all four aces on the same draw?  

sin A = 1/3.

$z = -2 - \sqrt{3}$, so $\lfloor z \rfloor = \boxed{-4}$.

m = slope   = - 13/3

y = (-13/3) x + b

       b = -8

you can add them ....

x=9     y=8     z=5       take it from here.....

The sum is equal to 481,568,115,648,085,302,456,278.

Thomas's speed is 35 mph.

The other x-axis intercept will be the same disatance from the vertex as the one given EXCEPT on the OTHER SIDE of the vertex at x = -2

(75-63) / 75   * 100% = 16%

x/x+1+x+1/x

Hello Guest!

\(x/x+1+x+1/x{\color{black}=1+1+x+ \dfrac{1}{x}}=\dfrac{x^2+2x+1}{x}\)

  !

Write the equation in exponential form.

B. 4^2 = 16

25% of 288 is 72

(288 +x)*.64 = 72+x

184.32 + .64x = 72 + x

x= 312

Here is the graph of the right triangle formed.....you should be able to calculate the area of the triangle     1/2  b  *  h

Let p and q be the two distinct solutions to the equation x^2 - 2x - 8 = 0. What is (p+1)(p+1)?     

You mean (p+1)(q+1) as EP already said.   

Won't x² – 2x – 8 factor to (x – 4)(x + 2)    

In which case    x = +4  and  x = –2   

So (4 + 1)(–2 + 1)  =  5 • –1  =  –5  

_.

What is (p+1)(q+1)

From Vieta:          p + q = - b/a      =   2

                                 pq = c/a        =   -8

(p+1)(q+1)   =    pq    +     p + q    +       1

                           -8    +        2       +       1   =  -5

Rhombus has 4 equal side lengths    and the    diagonals bisect each other at right angles.....sooooo   see the diagram below:

Angle D = 51.42857143 degrees 

Angle D = 1/2(180 - 3*∠B)

∠B = 1/7(180)

(Read from the bottom up )

Hint:  find the height and then use this formula:  V = 1/3 h (a² + ab + b²)

BP = sqrt(AB² + AP²)

PT = sqrt(BP² - BT²)

BD = sqrt(DC² / 2)

Triangles ABD and BCD are similar!!!

4 / BD = BD / 8

BD = √32  = 4√2