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You are welcome    

Note: my answer was changed a bit.

Thanks Melody!

Well it looks like you have got a sphere, radius 1 inside a cube, sidelength 2

The volume of the cube is 8 unit cubed

the volume of the sphere is      \(\frac{4}{3}\pi r^3 = \frac{4}{3}\pi\)

So the probability that you choose a point inside the cube that is also inside the sphere   \(\frac{4\pi}{3}\div 8=\frac{4\pi}{24}=\frac{\pi}{6}\approx0.52\)

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Always check for reasonableness.

I expected the prob to be a bit higher than that but I guess it sounds feasible.

Oh btw, I didn't mean to use the virus as a joke. I understand its harshness. I won't ever make that mistake ever again.

So, you are looking for a ration of 5 to 7. So there are 5/12 boys in the whole classroom/school. 5/12 of 540 is 225 boys.

Patricia's investment: FV =$50,000 x 1.01^(2*4)

                                        FV =$50,000 x  1.0828567056280801

                                        FV =$54,142.84

Jose's investment:   FV =$50,000 x 1.04^2

                                    FV =$50,000  x  1.0816

                                    FV = $54,080.00

The difference between Patricia's and Jose's investments =54,142.84  -  $54,080.00 =$62.84.

Thank you!!

https://www.quora.com/For-a-given-positive-integer-n-is-there-a-method-for-finding-the-smallest-positive-integer-with-exactly-n-factors-1

FV=$82,000; R=0.06/12; N=12 *12;PMT = FV*(((1 + R)^N - 1)^-1* R)

 PMT =$ 390.20 - Monthly payment required.

Note: I compounded your 6% APR on a monthly basis.

The cat's speed is    17-12  ft/s = 5 ft/s faster thsn the mouse and will cover the 4 feet difference in    4 ft / 5 ft/sec = .8 sec

      bye-bye mouse

20 000 = 12 500 (1+.035)ⁿ    solve for'n'

20 000/12500 = 1.035ⁿ

1.6 = 1.035ⁿ

log 1.6 / log 1.035 = n = 13.66 yrs ~~ 14 years   

OK, TacoBell....!!!!

After Sue  gives Tony  x of her sweets.....she has  18  - x   and he has  18 + x

When  she  eats  5 of her sweets after she gives Tony x sweets,  she  has  18 - x  - 5   =  (13   - x )  left    

And when Tony eats (1/2)  of what he has, he  has  [ 18 + x ]  / 2  left

So....the total  number that they have  combined =   (13 - x)  +  [ 18 + x ]  / 2

Sue has   18 - x - 5

Tony has   (18 + x)/2

The total arrangements are

Choose one of the  girls * Choose one of the  boys * Choose one of the remaining  boys * Choose one of the remaining  girls =  

C(6,1) * C(5,1) * C(4,1) * C(5,1)  =   6 * 5 *  4  * 5  =    600

Thx for the help

A 270°  clockwise rotation   is the  same as  a  -90°  counter-clockwise  rotation

Let ( x, y)  be  the original   point  = ( -7, 5)

A 90°  counter-clockwise  rotation  gives  us  (-y, x)   =   (-5, -7)

Here's the  graph  : 

Let  the  number  of green fish  = G

Then the  number of yellow fish =  G - 6

The total  fish in the tank =   G + G  - 6 =   2G  - 6

And 40% of these are  yellow ....so....

Yellow fish                     G - 6

 ________   =               ______  =  .40                 multiply  both  sides  by  2G - 6

  Total fish                      2G - 6

G - 6  =  .40 (2G - 6)  simplify

G  - 6  =   .8G  -  2.4          add6 to  both sides.....subtract     .8G  from  both  sides

.2G = 3.6     divide  both  sides  by  .2

G = 18    fish are  green           

Amouunt of 50% solution +  amount of 35% solution  =   total amount at  40%

So wwe have

.50x  + .35 (10)  =  .40 (x + 10)    simplify

.50x + 3.5   =  .40x  + 4       subtract  ,40x , 3.5  from  both sides

.10x =  .5     divide  both  sides  by  .10

x  = 5   gallons of the 50%  solution

Sue   sews  1/3  of the  dress in one  hour

Helen  sews   1/2  of the  dress in one hour

So.....the portion that they  can sew in one hour  working together  is   

1/3  +  1/2  =       5/6              

The reciprocal of this  tells us how long  it will take them working together to  complete the  dress  =  6/5 =   1.2  hours

This is a  binomial  probability

The probability of  at least  5  hits = 

P(5 hits) =  C (7,5)(.224)^5 (1-.224)^2

P(6 hits) =  C (6,5) (.224)^6 ( 1 - .224)

P(7 hits )  =  (.224)^7

Adding these we have

C (7,5)(.224)^5*(1-.224)^2  +  C (6,5) (.224)^6 *( 1 - .224)  + (.224)^7   ≈ .0077  ≈  0.77 %

X Squared by 2 subtract x subtract 12 equals 0