All Answers 358087 Answers

There are 12 face cards......so

The probability of drawing one on the first draw = 12/52

And the probability of drawing a "9" on the second draw  = 4/51

So the probability  = (12/52) * (4/51)  = 4/221

These are dependent events....let A be the probability of drawing a face card and let B be the probabilitiy of drawing "9'....then... 

P (A ∩ B)  = 0      in other words......there is no face card that is also a "9"

So...independent events have the relationship that

P(A ∩ B)  must equal P(A) * P(B)...but

0 ≠  4/221

So...... "A"  is the correct answer

I come up with  "A"  4/221 and they are dependent

Find X, im assuming?

\(2^x*5^{3x} = 4^{2x+1}\)

Lets go ahead and take the natural log of each side

\(ln{2^x}*ln{5^{3x}} =ln{ 4^{2x+1}}\)

Then bring down those exponets and pull out the x's on the left

\(x(ln{2}*(3)ln{5}) = (2x+1)*ln{4}\)

Pull the X's over to the right and natural log's to the left

\(\frac{ln{2}*(3)ln{5}}{ln{4}} = \frac{2x+1}{x}\)

Simplify

(ln(2)+3(ln(5)))/ln(4) = 3.98289

(2x+1)/x

You can split these into 2x/x and 1/x

becomes 2+1/x

3.98289 = 2+1/x

1.98289 = 1/x

1.98289x = 1

x = 1/1.98289 = 0.5043

x = .5043

f(t)  =  1.25t   is linear ....ths slope will be constant   ....however

f(t)  = 1.25^t    is exponential ....the slope increases as "t" increases

Look at the difference in the graphs :

https://www.desmos.com/calculator/girifxfur2

A- too many

B- quite a bit

I got 3/169 or B.

I don't know if they are independent or dependent

2^63 = 9223372036854775808

A- too many

B- quite a bit

Help with what?

What equals X?

x = -5 and -9

2^63 = 9,223,372,036,854,775,808

Just cross multiply

3*12=36

8*5=4

                 36/4

                 simplified to 9

                 3/8*12/5=36/4=9

Part A:

6 in chemistry

11 in algebra

6 in both

6+11+6 = 23

 Part B:

2000/40 = 50

12 in chemistry of a sample of 40

12*50 = 600

600 in chemistry of a school of 2000

12/40 = 3/10

When 3 out of every 10 students are in chemistry simply multiply by 200 to find the total students of the school enrolled so that

600/2000 = 3/10

Thank you so much!

Welp, I had no idea what I was talking about

sin(53)= 125/x

x*sin(53) = 125

x = 125/sin(53)

x = 156.517

square can be a perfect square like 4 is a perfect square because 2 multiplied by itself is 2.Do you get it.

The wheel completes 1 rotation in every 5 seconds...so...in 6 seconds.....it rotates another 1/5 times = (1/5) (360 degrees ) =  72 degrees [ using standard position]

So....the position  after 6 seconds  = 

[r cos θ , r sin θ ] ......using r = 21.5   and  72°  = θ, we have

[ 21.5cos(72) , 21.5 sin (72) ] = about  [ 6.64 , 20.45 ]

TYSM!!!!!!!!

Thanks mom

So the car starts on the circumference? Good

So find the circumference first, we needa use that to determine how far along the thing he went.

21.5*2pi = 135.0884841043611093

I'm not gonna round till the end

12 rounds per minute, and a 6 second ride.

The ride makes a round every 5 seconds, so we needa add one round plus 1/5th a round to get

135.088 + 135.088(1/5) = 162.10618092523333116  -   I shortened the equations after the calculation, so it wouldn't take up so much space. The calculations are completely accurate

So, he rode around for 162.10618092523333116 feet

Nevermind, I'm stupid. Just take 1/5th the round and then move him that far along the circumference to find the coordinates.

135.0884841043611093(1/5) = 27.01769682087222186

Now here is where I need CPhill.... I don't have any clue as to how to calculate coordinates on a circle.

x^3+3x-9 = x-1+2x     simplify  by subtracting  x - 1 + 2x from both sides

x^3 + 3x - 9 - x + 1 - 2x  = 0    simplify further

x^3  -  8   = 0    add 8 to both sides

x^3   = 8        take the cube root of both sides

x = ∛8   =   2

An easy way of multiplying fractions is you set it up like this

5    x     3

6           4

And just multiply across and simplify

5*3 = 15

6*4 = 24

So it is 15/24

Part A: 4 7's ina deck of 52 right?

So it's 4/52 if a 7 gets drawn?

4/52 = 2/26 = 1/13

So it's a 1 in 13 chance of a 7 getting drawn

Do that twice

1/169 chance

Part B: First draw, it's a one in 4 chance of getting a heart, due to 13 cards of each suite in a 52 card deck.

But then it is a 13 in 51 chance for the heart, due to the non-replacement

13/51 * 1/4 = 13/204 chance of getting that combination

Part C: B is a dependent even due to the cards being drawn depending on the cards previously drawn. If you draw a Spade, then instead of a 13/52 chance, you have a 12/51 chance of drawing another spade. And etc. till you get to a 1/40 chance of getting a spade, if you, somehow, get 11 consecutive spades.

169  = x^2      take the positive/neg square roots of both sides

±√169 =  x

± 13  = x

x^3  = 1000    take the cube root of both sides

x = ∛1000

x = 10

16 + x^2  = 41     subtract 16 from both sides

x^2  = 25  take the positive/neg square roots of both sides

x = ±√25

x = ± 5

Sorry, wondergirl.....I don't understand the last one.......