All Answers 355923 Answers

Good job qualitystreet!

A Yes, they are independent because P(A) ⋅ P(B) = P(A ∩ B)

Ty!!

The answer to the second question is A 4.7%.

3/8*1/8=3/64

3/64*100=4.7%

Tysm ^-^

1.   D  is correct.

2.   (P U R) ∩ Q

First let's find  P U R .

P U R   =   {red, blue, green, yellow, black, purple}

Now find the intersection of   P U R  and   Q

The intersection of  {red, blue, green, yellow, black, purple}  and  {red, green, black}

is   {red, green, black} .  So...

(P U R) ∩ Q   =   {red, green, black}

3.   C  is correct.   

Thank you!

Here is my solution: 

To draw two cards we can do $\binom{52}{2}$, which is 1326. 

Since there are 4 aces in the deck, the number of ways we can choose 2, is $\frac{\binom{4}{3}}{2}$, which is 6. 

6/1326 = 1/221.

So the answer is D, 1/211; no, they are dependent events. 

This is a system of equations problem.  

To easiest way to solve this is first add both equations. 

12x + 21y + 21x + 12y = 51 + 15

So 33 y + 33x = 66 

x + y = 2 

We can use x = 2 - y and plug this in to equation #1.

12 ( 2 - y ) + 21y = 15 

24 - 12y + 21y = 15

y = -1 

x = 3 

The ordered pair you are looking for is (3, -1)

The circle centered at (2, -1) and with radius 4 intersects the circle centered at (2, 5) and with radius sqrt10 at two points A and B. Find (AB)^2

These 2 circles are both centred on the line x=2

The centres are 6 units apart.

formulas

\((x-2)^2+(y+1)^2=16\qquad (1)\\ (x-2)^2+(y-5)^2=10\qquad (2)\\ subtract\\ (y+1)^2-(y-5)^2=6\\ y^2+2y+1-y^2+10y-25=6\\ 12y-24=6\\ 12y=30\\ 2y=5\\ y=2.5 \)

now draw a skech becasue I am going to look at the top triangle. 

\((MB)^2=10-2.5^2=3.75\\ MB=\sqrt{3.75}=\sqrt{\frac{15}{4}}=\frac{\sqrt{15}}{2}\\ AB=2*\frac{\sqrt{15}}{2}\\ AB=\sqrt{15}\\ AB^2=15\) 

there may well have been a much simpler fully algebraic way to do this :)

Hi Juriemagic,

That is good except I am not sure about this bit.

From this we see that: 2a=2, therefore, a=1

                                     3a+b = 3, therefore "b" calculates to 0

                              and a+b+c=T1=5, so "c" calculates to 4

Where did you get 2a=2 from?

I did that subtraction twice and then had all the numbers the same

(all 2 in this case, but the 2 is not relevent, it is that they are all the same on the second subtraction that is relevant)

So I knew I could express this a polynomial of degree 2.    

After that I just looked at n^2 that is     1, 4, 9, 16

and compared it to the sequences      5, 8, 13, 20

and I could just see that I had to add 4.      Denominator = n^2+4

[what you did might be right, but I don't understand it. ]

"I have noticed that guests have a tendency to be ruder than regular users. Im not saying every guest does it, but i have seen a lot of guests say rude things. Maybe it is just one guest, but i dont know."

hypocrite lmao.

Arc Length   =  radius * theta (in rads)

{ 45°  =  pi/ 4 rads }

Arc Length  =  6 *  (pi / 4) in  =  6pi/4 in  =  3/2 pi in  =  1.5 pi inches

volume

That's not a realy hard question. I didn't stretch my brain at all.

Avg Speed  =   Total distance / Total time

So we have

[ 80 * 1  + 60 * 1.5 ]    / [ 1 + 1.5 ]  =

[ 80 + 90 ]  / [ 2.5 ] =

[ 170 ] / [ 2.5 ] =

68 mph

Thanks so much, CPhill! 

the volume of the log is 8817.12 cubic inches

because:

37.68 = 2 * π * r

r = 6 in

V = π * r^2 * h

V = π * 6^2 * 78

V = 8817.12 cubic inches

Thank you!

the answer is low

help please

 no problem any time

https://www.desmos.com/calculator/0mpppuh5ec

no problem any time 

thank you both so much!