All Answers 356371 Answers

Combinations = 22

Permutations = 286

I wrote them all down and this is what i got:

moor

moot

mort

room

root

rort

roto

toom

toro

torr

trow

worm

wort

I tried, but it doesn't work.

Never mind

             f(x)  =  g(x)

               2x  =  x² - 3

                 0  =   x² - 2x - 3

                 0  =  (x - 3)(x + 1)

       Either  x - 3  =  0     or     x + 1  =  0

                        x  =  3     or           x  =  -1

Let the side length of the equilateral triangle be 3.  Then the points that are closer to the center of the triangle than to X, Y, Z is the circle centered at O with radius 1, so the probability is (pi)/(sqrt(3)/4*9) = (4*pi*sqrt(3))/27.

Thank you! The actual answer was the unsimplified form before you got 0.134

Here's an easy way to  determine if your  solutions are  correct :  just substitute  the  x, y values  you  got  in each case into both equations.....if these make both equations true , you  got the  correct answers  ....

Note that (1,3)  is correct but not ( 3,1)

The other solution is  (3, -1)  

How many 7-digit telephone numbers are possible if the first digit cannot be zero and

a. every other digit is odd

If every other digit is  odd either :

positions 1 - 3 - 5 -7   are odd   or positions 2 - 4 - 6  are odd

Assuming that the other positions must be even we have

(5 odd)(5 even)(5 odd) (5 even) (5 odd) (5 even) (5odd) =  5^7   or

(4 even- we can't have a zero) (5 odd) (5even) ( 5 odd) (5 even) (5 odd)  (5 even) =  4 * 5^6

So....the total number  =    5^7 + 4*5^6 =  140,625

b. the telephone number must start with 226 and end with 5

We have   (10)^3  =  1000  possible  numbers here  [ positions 4, 5, 6 can be even or odd ]

c. no repetitions are allowed

(9 ways to  choose  the  first number - zero is not allowed) (  9 ways to  choose the second number, we can choose 0 or any of the other 8 digits we didn't choose in the first position) * ( 8) * (7) *(6) * (5) * (4) =

(9) (9) (8)(7)(6)(5)(4)  =  544,320

(3,-1)  (1,3)

The area   of  triangle  XYZ   =(1/2)  (product of the leg lengths) =  (1/2) (12 * 6)   =  (1/2) (72)  = 36

So....the probability that the area of triangle XYD is at most 12 =   12 /36  =   1/3

Sample Space  = { 1B, 1R, 2B, 2R, 3B, 3R, 4B, 4R, 5B, 5R, 6B , 6R }

A commercial jetliner with an air speed of 640 mi/hr leaves Chicago and flies due west at the same time that a small single-engine plane with an air speed of 180 mi/hr leaves Chicago and flies due east. Determine the speed of a wind blowing from the west if the jetliner is 1500 mi west of Chicago when the single-engine plane is 550 mi east of Chicago.

Let the wind speed  = W

Note that if the wind is blowing from the west, its direction is toward the  east

So....the wind slows the regular rate of the large plane flying west and  increases the regular rate of the small plane flying east

Here's  a  ( bad)  pic of the situation

640  - W    <      Chicago    > 180 + W                    

Note that    Distance / Rate =   Time

But.....they fly the same time....so...

Distance the large plane has flown            Distance  the small plane has  flown

____________________________  =     _______________________________

 Effective  rate                                                  Effective rate

1500                                550

_______           =           _______       cross-multiply

640 - W                         180 + W

1500 ( 180 + W) =  550 ( 640 - W)     simplify

270000 + 1500 W   =  352000 - 550W             add  550W to both sides, subtract 270000 from both sides

2050W = 82000      divide  both  sides  by   2050

W = 40  (mi /hr)

The area of the inscribed equilateral triangle is 75/4*sqrt(3)​​. Find the perimeter of circumscribing square to the nearest whole number.

The ratio of the area of an equilateral triangle to its circumcircle's area is:   1.299 : pi  or  0.413496

Area of the triangle is        75/4*sqrt(3) = 32.47595 u²

Area of the circle is            32.47595 / 0.413496 = 78.54 u²

Raduis of the circle is        r = sqrt( 78.54 / pi ) = 5

Perimeter of a square is     P = 8r = 40 units  

Let x be the number  of male stars

Let y be the number of  female stars

So  we have that

71.2x  +  50.8 y

_____________  =       60                       multiply both sides  by x + y

      x  +  y 

71.2x  + 50.8y =   60 (x + y)

71.2 x + 50.8 y  = 60x  +  60y      subtract   60x, 50.8 y   from  both sides

11.2 x = 9.2 y           divide both sides by 11.2 , y

 x               9.2              92

__  =         ___    =      ____ =   ratio of males / females

 y              11.2            112

x - .3x =  150,000

.7x = 150,000      divide both sides  by  .7

x ≈   214,285.71

Let PR  =  z    

Let  PQ = y

Let QR  = x

We know from the Pytagorean Theorem  that  QR^2  + PQ^2 = PR^2  →  (x^2 + y^2)   = z^2   (1) 

But we also know that  

(x^2  + y^2)  + z^2  = 338      (2)       sub  (1) into (2)   and we have that

z^2  + z^2  =  338

2z^2 = 338     divide both sides  by 2

z^2 =  169 =  area of largest square

Since he left for lunch, we regard the time as around noon....

If he left at 12:05 and returned at 1:00 the hands are in exchanged places.  I think.   

_.

y = -x^2 -5x -6      (1)

x + y = -3     →    y = -3 -x     (2)

Sub (2)  into (1)  for   y    and we have

-3 - x = -x^2  - 5x   - 6        add  3 , x to  both sides

-x^2 - 4x  - 3   = 0             multiply through  by  -1

x^2 + 4x + 3  =  0    factor

(x + 3)  ( x + 1)  = 0

Set both fctors to 0  and solve for x and we get that

x = -3   and     x = -1

And when x = -3   y  =  0

And when  x =  -1     y = -2

So you are CORRECT  !!!    [ good job  !!! ]

Angle PQR is a right angle. The three quadrilaterals shown are squares. The sum of the areas of the three squares is 338 square centimeters. What is the number of square centimeters in the area of the largest square?
 

Area of the largest square is    A = 338 cm²/ 2 = 169 cm² 

See https://web2.0calc.com/questions/let-triangle-abc-be-equilateral-where-the-side-length#r2

thank you so much!