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(68-44.20)/68  x 100% = 35% markdown

25 x 1.35 = $ 33.75

x = 10 dollar shirts

661 - x = 12 dollar shirts

10x + 12 (661-x)  + 378 = 12x + 10(661-x)

10x +7932 - 12x + 378 = 12x +6610 -10x

x = 425    shirts @ $10

Let AX = M

Let BX = 24 - M

Since  ACB is bisected, we have this relationship

M / 30 = (24 - M) / 27     cross-multiply

27M =  30( 24 - M)     simplify

27M = 720 - 30M     add 30M to both side

57M = 720

M =  720 / 57   =   240 / 19   = AX

Then     24 - M   =    24 - 240/19  =   216/19  =   BX

Since each triangle is under the same height, the ratio of their areas is just the ratio of their bases

So

area BCX / Area ACX  =  ( 216 /19) / (240 / 19)   =  216 /240  = 9 / 10

But the line should be through B

Notice that after 5! every number will end in 0. So, we are just looking for 1!+2!+3!+4! which ends in a 3. 

A guess.

6 axes of symmetry

\(\frac{7*5!}{6}\)

Here's an image :

Note that

BAC + ABC + BCA   = 180     .....   so  ......

BAC/2  + ABC/2 + BCA/2   = 90   ⇒   [90 - BCA/2  =  BAC/2 + ABC/2]   (1)

And by the Exterior Angle Theorem.....

XIB =  BAC/2 + ABC/2     (2)

Sub (1) into (2)   and we have that

XIB =  90 - BCA/2

We set up equations. a+b+c=221, a=b+8, a=c+5

yes i meant it to be like that @echofire 

CPhill: There is a minor typo in the answer. $3 x 0.07 =0.21 cents for 1 full year.

So, for 4 months or 1/3 of a year =$3 + 0.21/3 =$3.07 - principal + interest for 4 months.

No.....I used to be a tutor at a Junior College....

Here's my best attempt :

When each player has an even number of cards, there will only be 1 equal sum between the players....to see this....let's suppose that we have  cards 1 - 4

The  possible outcomes between two players are

(1, 2)  <    (3,4)

(1, 3)   <   (2,4)

(2, 3)   =   (1,4)      

Note that the number of "winning"   scores is     C(4,2)/ 2 - 1  =  3 - 1  =  2

When each player has an odd number, n,  of cards, the number of winning scores is just C(2n, n) / 2

Suppose we have cards 1- 6

The outcomes are

(1,2, 3)  <  (4, 5, 6)

(1,2,4)  <   (3, 5, 6)

(1, 2, 5) <  (3, 4, 6)

(1, 2, 6) <  (3, 4, 5)

(1, 3, 4) < ( 2, 5, 6)

(1,3, 5) < ( 2, 4, 6)

(1, 3, 6) < ( 2, 4, 5)

(1, 4, 5) > (2, 3, 6)

(1, 4, 6) >( 2, 3, 5)

(1, 5, 6) > ( 2, 3, 4)

Note that the number of winninig scores is just   C(6,3)/2  = 20/2 =  10

This implies....that.....for 14 cards....each player holds 7  and  the number of winning hands =

C(14, 7) / 2   =    1716 winning hands

Solve the following system:
{19 = 6 A + F | (equation 1)
71 = 19 A + F | (equation 2)

Express the system in standard form:
{-F - 6 A = -19 | (equation 1)
-F - 19 A = -71 | (equation 2)

Subtract equation 1 from equation 2:
{-F - 6 A = -19 | (equation 1)
0 F - 13 A = -52 | (equation 2)

Multiply equation 1 by -1:
{F + 6 A = 19 | (equation 1)
0 F - 13 A = -52 | (equation 2)

Divide equation 2 by -13:
{F + 6 A = 19 | (equation 1)
0 F+A = 4 | (equation 2)

Subtract 6 × (equation 2) from equation 1:
{F+0 A = -5 | (equation 1)
0 F+A = 4 | (equation 2)

 F = -5 - First term         and A =4 - Common difference

Connections Academy 

JUst count the final results. Thus, we have 3*2=6 values. 

What is that? 

Count how many three digit numbers you can form, then add all of them up, and divide by how the number of numbers. 

In LaTeX: \(18=\frac{3}{4}(2w-1)\). Solving this, we get \(\frac{6w}{4}-\frac{3}{4}=18, \frac{6w}{4}=18\frac{3}{4}\) . Now, multiplying both sides by \(4\) , we attain       \(​​​​​​6w=75, \boxed{x=12.5}.\)

1.  495  * pi / 180  =  (495/ 180)pi  =  (99/36)pi = (11/4)pi

2.  (5)^4−2(5)^3+5(5)^2-7(5)+4  =  469    (remainder)

3.     x^3−x^2−4x+4  = 0     factor as

         x^2 ( x - 1) - 4(x - 1) = 0

       (x - 1) (  x^2 - 4) = 0

       (x - 1) ( x - 2) (x + 2)  = 0

Set each factor to 0 and solve for x and we get that

      x = 1    x =  2    x = -2

4.  (x^4y^7)^2/3  =   (x^4)^(2/3) * (y^7)^(2/3)  =   x^(8/3) * y^(14/ 3)  =

x^( 2 + 2/3)  * y^(4 + 2/3)  =

{ The whole number of the mixed number tells us how many powers of the variable are taken outside the radical....the numerator of the mxed mixed number fraction tells us how many powers of the variable are inside the radical......so we have }

x²y⁴ ∛[ x² y² ]

5.   (1/4)(5/12x−3/4)>x+(1/12)      multiply through by 12

3 [ (5/12) x - 3/4 ]  > 12x + 1     simplify

(15/12)x - 9/4  > 12x  +  1

(5/4)x - 9/4  > 12 x + 1         multiply through by 4

5x - 9 > 48x + 4      subtract 48x from both sides, add 9 to both sides

-43x  > 13               divide both sides by -43...reverse he inequality sign

x < -13/43

Here are the distributions of all 10 digits 0 - 9 between 1809 and 2019:

(0=62, 1=242, 2=61, 3=41, 4=41, 5=41, 6=41, 7=41, 8=132, 9=142)Total = 844

As you can see, 1 occurs 242 times between 1809 and 2019 inclusive.

theres nothing there....

Hey CPhill are you a teacher?

Oh okay thank you!!

We know the opposite side to the angle  and the adjacent side

Make SURE that your calculator is set to DEGREE mode  [ that may be your problem ]

So....the trig function that relates   opp/ adj  is the tangent

So

tan x = ( 38/ 53)      take the tangent inverse to find the angle

tan^-1 ( 38/63) = x  ≈  35.64°