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Assuming a quadratic, we have that

y  = ax^2 + bx + c  

Since (0,5) is on the graph, c  =5

And we have the remaining  system

a(9)^2 + b(9)  + 5  =  -11

a(6)^2  + b(6) + 5  =  13     simplify

81a + 9b  =  -16     multiply through by  6 ⇒  486a  + 54b  =  - 96   (1)

36a + 6b   =   8      multiply through by  -9 ⇒  -324a  -54b  =  -72     (2)

Add (1)  and (2)

162a  =  -168

a  = -28/27

To  find b we have

36 (-28/27) + 6b  =  8   

-112/3 + 6b  = 8 

⇒  b  =  68/9

The function is

y  =  - (28/27)x^2  + (68/9)x  + 5

Here's a graph  with the included points  :

https://www.desmos.com/calculator/z4qpjyxpic

The probability should be:

1 - [1/5 + 1/2] = 3 / 10, or d.

Thanks!

Actually, I think that it is n/2 = 20?

Thanks, Cphill for the help though, I couldn't figure M at first.

That isn't right, sorry. 5 and 1 dont multiply to 10

What is the government jobs and what are the three branches of the gorvernment

Being that there is 4 red, 2 blue, 6 green, 8 white, that means there is 20 marbles, with 8 success, 8/20. Since the marble is not replaced, that drops it to 7/19 for the second pull. Multiply these together and you get 14.7%.

(8/20)*(7/19)=.147

.147*100=14.7

N(Spanish or History)  = N(Spanish)  + N(History)  - N(Spanish and History)

N(Spanish or History) =       26          +    38              -   16

N(Spanish or History )  =    48

Prob  =  (48  / 88)      =   6 / 11

Thanks!

Divide x4-3x3+6x2-3x+5 by x2+1

Step by Step would be nice, but not nessesary.

How do I graph y = tan((x/2) - (π/4)) +1?

Number that liked movie  =  26

Of these.....12  are in the 18-34 age group

So

12 /26   =   6/13  ≈  46%

OK...RP!!!!

24 use text messaging

Of these, 17  also use  e-mail....so....

The probability is  17/24 =   70.83   ≈    71%

2x^2 - mx + n

The sum of the roots is given by

m / 2  = 6   multiply both sides by 2

m  = 12

The product of the roots  is given by

n/2  = 10      multiply both sides by 2

n  =  20

So....

m + n  =  12  + 20   = 32

EDIT TO CORRECT AN ERROR.....

5^x  = 80

Log Form

log₅ 80   = x

b   = 5

x  = x

n  = 80

the answer is D

a) Not replaced

Yelllow marker First - Then Blue Marker  =

(1/10)(1/9)  =  1/90

b) Replaced

(1/10) (1/10)  = 1/100

Answer   "C"

Circumference= 2*pi*r

So, we need the radius to solve this. Since we know that the area is 50.24

r=√A/pi so 50.24/3.14=√16=4

Our radius is 4, let's plug in! 2*3.14*4= 25.12 

(a) the first marker is not replaced?

1/10 x 1/9 = 1/90

(b) the first marker is replaced?

1/10 x 1/10 = 1/100

ln32 = x

   e^x = 32

b = e

x = x

n = 32

Thanks Tiggsy :)

Nice, heureka!!!....one question....what is the  intercept theorem???.....I've seen you refer to this several times in the past.....

Let the number of brown counters  = B....so....the number of purple counters is 4B

So....the total number of counters is 5B

So.....

The probability of taking a brown one on the 1st draw is   B / [B + 4B]  = B / 5B  = 1/5

The probability that a brown one is taken on the second draw is  [ B -1]  / [ 5B - 1]

So....the total probability is

[1/5 ]  * [ B - 1 ] / [ 5B - 1]  = 17/ 445

[ B- 1] / [ 5B - 1]  = 17/89   cross multiply

89 [ B - 1 ]  =  17 [ 5B - 1]

89B - 89  = 85B - 17       add/subtract  89, 85B to/from  both sides

4B = 72     divide both sides by 4

B = 18  =  the original number of brown  counters

4B  = 72  =   the original number of purple counters