I think this is correct

68% of the players fall within one standard deviation.....a player weighing ≤ 170 pounds would lie in the part of the curve to the right of this......so, because of the symmetric nature of the curve, this probability =  

[ 100 - 68 ] / 2  =  32 / 2   =   16%

cos a = adjacent / hypotenuse

cos a = 10/35

a = arccos(10/35)

a ≈ 73.398º

\((63)6\div65 \\~\\ =\frac{63*6}{65} \\~\\ =\frac{378}{65}\\~\\ \approx 5.815\)

tan^2 (x)  - 1  = 0     factor this as a difference of squares

[ tan x  - 1 ]  [ tan x  +  1  ]   = 0

Set each factor to 0   and solve for x

tan x  -  1   =   0      add 1 to both sides

tan x   =   1         and this occurs at    pi/4 +  pi*n   where n is an integer

And

tan x  +  1  = 0      subtract 1 from both sides

tan x  =  - 1      and this occurs at  (3pi)/4   +  pi*n    where n is an integer

radius = diameter / 2

r   =   6/2   =   3

volume of toy = volume of hemisphere + volume of cylinder + volume of cone

volume of toy = ( \(\frac12*\frac43*\pi*r^3\) ) + ( \(\pi*r^2*\text{cylinder height}\) ) + ( \(\frac13*\pi*r^2*\text{cone height}\) )

volume of toy = ( \(\frac12*\frac43*\pi*3^3\) ) + ( \(\pi*3^2*10\) ) + ( \(\frac13*\pi*3^2*8\) )

volume of toy = ( \(\frac12*\frac43*\pi*27\) ) + ( \(\pi*9*10\) ) + ( \(\frac13*\pi*9*8\) )

volume of toy = ( \(18\pi\) ) + ( \(90\pi\) ) + ( \(24\pi\) )

volume of toy = 132π   cubic centimeters               ≈ 414.69 cubic cm

You started off correctly, Guest, but series impedances don't add algebraically, they add according to Pythagoras.

So impedance Z = [(X_L )² + R² ]^½

★★★★★★★★★★★★★★

Good job, Gwendolyn....!!!!

We have a right triangle.....

One leg is the radius of the Earth.....   and the hypotenuse =  Earth's radius + 3.1 miles

The distance to the horizon forms the other leg and is given by

sqrt [  ( 3959 + 3.1)^2   - 3959^2  ]   ≈  156.7 miles

I think they want to know this :

[ 1 + 1/2 ]  / [3 / 16]   =

[3/2] / [ 3/16]      invert the second fraction and multiply

[ 3/2]  *  [ 16/ 3]      swap denominators

[3 / 3 ]  *  [  16 / 2  ]   =

1 * 8  =

8

Density   =  Mass of Liquid / Volume of tank

The problem here is that the liquid isn't identified.....so.....determining its mass is impossible

However...assuming that we have water.....its mass is almost exactly 1kg  per L

So   8314.5 L   ≈  8314.5 kg

So.....the density  is

8314.5 kg  /  [ 5 * 2 * 23 ] dm^3   ≈   8314.5 kg / 230 dm^3   ≈  36.15 kg / dm^3

2^38 = 274877906944

1 whole divided by 3/16 is: 5 1/3

1/2 divided by 3/16 is: 2 2/3

I'm guessing this is what you were asking? The question was a bit unclear.

The  tank can hold  55692 cm^3     (1)

The volume of the log  plus the volume of the water in the tank  =

pi ( 5)^2 * 44  +  55692 (.95)   ≈  56363.2  cm^3     (2)

So   the approximate volume that spills out  =    (2)  - (1)  ≈ 671.152  cm^3

Our answers differ probably due to rounding......but.....close enough  !!!!

Solve for p:
40 p^3 - 8 p^2 + 5 p - 1 = 0

The left hand side factors into a product with two terms:
(5 p - 1) (8 p^2 + 1) = 0

Split into two equations:
5 p - 1 = 0 or 8 p^2 + 1 = 0

Add 1 to both sides:
5 p = 1 or 8 p^2 + 1 = 0

Divide both sides by 5:
p = 1/5 or 8 p^2 + 1 = 0

Subtract 1 from both sides:
p = 1/5 or 8 p^2 = -1

Divide both sides by 8:
p = 1/5 or p^2 = -1/8

Take the square root of both sides:
Answer: | | p = 1/5         or    p = i/(2 sqrt(2))         or     p = -i/(2 sqrt(2))

Thank youuu!! I really appreciate your help!

Population /  Density  =  Area   ....so....

186,440  /  1678   ≈  111.1  square miles

3x-4x+7y-2 = 45    simplify

-1x +  7y - 2  =  45   add 2 to both sides

-1x + 7y  = 47

This is the equation of a line.....see the graph, here :

https://www.desmos.com/calculator/awwi8jf2ej

(-5/8)   /  (-3/4)     invert the second fraction and multiply

(-5/8) * (-4/3)   =

20 / 24   =

5 / 6

Do you mean what does x and y equal?

um... 45....

128z

What is the unstopable force?

If it was wind, the wind would break into two paths, going around the object.

Well, suppose you needed to type in 1 over 8. You would type it out like this:  1/8

Yes.

well, what does x and y equal?