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If the ratio of cats to dogs is 2/3, then the ratio of cats to total animals is 2/5, so if there are 50 animals, 20 of them must be cats.

34  +  34 (3) = total spaces

Volume of a cone    V = 1/3 pi r^2 h

                            15 pi = 1/3 pi r^2  5

                            15/5  * 3  = r^2        solve for 'r'  in feet       

The possible lengths OP are 5, 11.

also to answer your question: water and lots of practice

this website is for math-related questions.   

Done 

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1/5+ 2/5 = 3/5

3/5 of his friends had arrived by 8. 

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-6 + 4x = 2 + 3x

Solve for x :))

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49 boys were present at small tree intermediate school on Friday

Step-by-step explanation:

Given:

Number of Fourth graders at the Small Tree intermediate school =96

Number of Girls= 43

Number of girls absent on Friday= 5

Number of boys absent on Friday= 4

To find:

Number of fourth grade boys on Friday=?

Solution:

Let the number of boys be x

Then 

Total number of students = Number of girls + Number of boys

=>96=  43+ x

=> 96 - 43=x

=> x=53

So, the total  number of fourth grade boys = 53

On Friday, 4 boys were absent

So,

No of boys present on Friday= total number of boys - boys absent on Friday

No of boys present on Friday = 53-4

No of boys present on Friday = 49

No. of  boys   =  96 - 43  =   53

53 - 4  =   49 present  on Friday

Let Melody's rocks  =  M

Let  Chris's rocks =  (3/5)M

So

M - 7  = (3/5)M  +  7           simplify

M - (3/5)M  =  7 + 7

(2/5)M  =  14               multiply  both sides by  5/2

M  =  14 (5/2)  =  35

(3/5)M =  (3/5) (35)  =  21

35  +  21   =    56  all  together

N/2  +  24   =  (3/4)N + N/2            

24  = (3/4)N

24 (4/3)   =  N  =   32 = the  number that Clay had at first

NM  = (1/2)   ( DC + AB)   = (1/2) (  5 + 19)  = (1/2) (24)  =  12

PQ  = (1/2)  ( NM + AB)   =  (1/2)  ( 12  + 5) =  (1/2) (17)   =  17 / 2   =   8.5

f(x) = x^4 - 7x^3 + 13x^2 - 26x + 101.

PQ = 26/7.

Slope   =    ( 8200  - 8850)  / (2 - 1)  =  -650

The point  (1, 8850)   is  on the graph

So....we  have  the following  equation

y  = -650  ( x - 1)  + 8850

y   = -650x  +  650  +  8850

y =  -650x  +  9500

The possible lengths OP are 5, 13.

By similar triangles, the area of the hexagon is 80.

Angle of inclination  = Angle of depression

arctan  ( 5000   / ( 15 *5280) )  = angle of  depression  ≈  3.6°

Tan 20 =  opposite side/ adjacent side  = height/distance

tan 20 = height / 1000

1000 tan 20^o = height      You can finish.......

Rearrange  as

16y^2  -  2y  -   4x^2   =  3           complete  the  square on  y

16  (y^2  - 1/8y  + 1/256)  -  4x^2  =  3  + 1/16

16 ( y  - 1/16)^2  -  4x^2  =   49/16          divide  both sides  by  49/16

16 ( y  -1/16)^2 / ( 49/16)  -  4x^2 / (49/16)   =   1       and we  can  write

(y - 1/16)^2  /  (49/256) - x^2  / ( 49/64)   =  1

a^2  = 49/256      a   =  7/16

b^2  = 49/64        b  =   7 / 8

The  center  is   ( 0, 1/16)

The  slope is     a / b   =   (7/16) / ( 7/8)  =  8/16   =1/2

Equation  of  the  asymptote  with positive slope  :

y =(1/2)x  + 1/16

Here's  a  graph  that confirms this  :  https://www.desmos.com/calculator/9dzysghfat

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