All Answers 356330 Answers

You're right.   I made an incorrect observation.

There are 10 matches with a left-handed player competing against a right-handed player.

The volume of the new parallelepiped is 66.

i need help too please

(a) 10*9*8 = 720

(b) C(10,3) = 120.

The probability is 2/33.

By inclusion-exclusion, there are 6 students who do all three activities.

That's right, the probability is 23/24.  Good job!

tThe volume of tetrahedron ABCF is 40.

p(x) = x^2 + 1.

The sum of the coordinates is 23/2.

So it would be 32*60.62/35 = 55.42

Is that correct?

Your question is incomplete. 

=^._.^=

8 choices for the first 4 digit. 

4 choices for the last digit. (1, 3, 5, 7)

Any idea how you could approach it from here?

=^._.^=

answer is 4 the points are 10 and -6

12 with line = 12/99

321 with line = 321/999

(12/99)/(321/999)

Can you take it from here?

=^._.^=

PQ = CQ = x         ∠PCQ = 45º         ∠PBQ = 30º

tan(45º) * x = tan(30º) * (4 - x)

x = 2(√3 -1) ≈ 1.464

An octagon is inscribed in a square so that the vertices of the octagon trisect the sides of the square. The perimeter of the square is 108 centimeters  What is the perimeter of the octagon?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Square side = 1/4(108) = 27

Octagon perimeter = 8(27/3) = 72

The  quarters  are   (3/13)  of  the  coins

The  dimes are  ( 4/13) of  the  coins

The nickels  are  ( 6/13)  of  the  coins

Call  N the total  number of coins  

So

.25 (3/13)N  + .10 (4/13)N  +  .05 ( 6/13)N  =  2.90

(1/4) (3/13)N +  (1/10) (4/13)N  + (1/20)(6/13)N   =  2.90

(3/52)N  +   (4/130)N  + (3/130)N   = 2.90

(3/52)N   +  (7/130) N   = 2.90

(29/260)N   =  2.90

N  =   (2.9)(260 / 29)      =    (1/10) ( 260)   =     26  coins

i got it nvm ty 

Another  non-Calculus  approach

a^2  -  4a  +  8  will  be  a paraola  (in the  variable a)  that turns  upward

The "a"   coordinate  of  the  vertex =   - (-4 ) / ( 2 * 1)   = 2

This value of a  will produce   a  min on the  graph

So

Since

a -  b    =  4

Then  b =    -2

(2/5)  S =  ( 7/9) J

S  =  (5/2) (7/9)  J

S =  (35/ 18)  J

If Sofia  had  5/11 of  the postcards  at  the  end, then  Jonas  had 6/11  of  them

The total   cards   =  S  +  J  + 6    =      (35/18) J  +  J   +  6  =   (53/18)J  + 6

Sofia   gave  Jonas   (2/7)(35/18)J =  (5/9)J

So.....the total  number  that  Jonas  had  in  the  end   =   J  + (5/9)J  + 6 =   (14/9)J + 6

So

[  (14/9)J   +  6 ]                6

______________ =     ______     cross-multiply

[ (53/18)J  + 6]                11

6 [ (53/18)J  +  6]  =  11 [ (14/9)J  + 6 ]

(53/3)J  +  36    =   (154/9)J  +  66

(53/3)J  -  (154/9)J   =  66  -  36

(5/9)J  =  30

J =  (30) (9/5)   =   54

Jonas  ended  up wiith     (14/9)(54)  +  6     =     90    postcards