I really need help with the last one if you could help it would be awesome! Tysm.

A poker hand consisting of 9 cards is dealt from a standard deck of 52 cards. Find the probability that the hand contains exactl

Andrew [12]

Answer: $\dfrac{^{12}C_{6}\times^{40}C_3}{^{52}C_9}$ or $\dfrac{228}{91885}$ .

Step-by-step explanation:

Given : A poker hand consisting of 9 cards is dealt from a standard deck of 52 cards.

The total number of cards in a deck 52

Number of faces cards in a deck = 12

Number of cards not face cards = 40

The total number of combinations of drawing 9 cards out of 52 cards = $^{52}C_9$

Now , the combination of 9 cards such that exactly 6 of them are face cards = $^{12}C_{6}\times^{40}C_3$

Now , the probability that the hand contains exactly 6 face cards will be :-

$\dfrac{^{12}C_{6}\times^{40}C_3}{^{52}C_9}$

$=\dfrac{\dfrac{12!}{6!6!}\times\dfrac{40!}{3!37!}}{\dfrac{52!}{9!\times43!}}\ \ [\because\ ^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{228}{91885}$

Hence, the probability that the hand contains exactly 6 face cards. is $\dfrac{228}{91885}$ .

6 0

3 years ago

8. You recorded the time in seconds it took for 8 participants to solve a puzzle. The times were: 15.2, 18.8, 19.3, 19.7, 20.2,

kirill115 [55]

Answer:

Xbar = 20.813

Median = 19.95

5 - number summary :

Minimum = 15.2

Q1 = 19.05; Q2 = 19.95 ; Q3 = 21.95 ; maximum = 29.4

Standard deviation, s = 4.068

Step-by-step explanation:

Given the data:

X : 15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1, 29.4

Ordered data:

15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1, 29.4

The mean (xbar) :

Xbar = Σx / n ; n = sample size = 8

Xbar = 166.8 / 8 = 20.8125

Xbar = 20.813

The median :

1/2 *(n+1)th term

1/2(9) = 4.5

(4 + 5)th term / 2

(19.7 + 20.2) / 2 = 19.95

The five number summary :

Minimum = 15.2

Lower quartile (Q1) = 1/4(9) = 2.25 ; (2nd + 3rd) term / 2

(18.8 + 19.3) / 2 = 19.05

Median (Q2) = 19.95

Upper quartile (Q3) :

3/4(9) = 6.75 = (6th + 7th) / 2

(21.8 + 22.1) / 2 = 21.95

Maximum = 29.4

The standard deviation, s = sqrt[(x - xbar)²/ (n-1)]

Using calculator ;

s = 4.068

4 0

3 years ago

Math problem help me to do this

Alla [95]

Answer:

um..

Step-by-step explanation:

6 0

3 years ago

What is y greater then or equal to 2x on a graph

Juliette [100K]

Answer:

The minimal number for the objective function P =20x+16y is: 780

The value of x then is: 15

and the value of y then is : 30

Step-by-step explanation:

We are given a system of inequalities as:

y is less than or equal to 2x

i.e. y ≤ 2x--------(1)

x + y is greater than or equal to 45

i.e. x+y ≥ 45 ------------(2)

and x is less than or equal to 30.

i.e. x ≤ 30 -----------(3)

On plotting these inequalities we get the boundary points as:

(15,30) , (30,60) and (30,15)

( Since, the optimal solution always exist at the boundary point )

The optimal function is given by:

Minimize P = 20x+16y

Hence, at (15,30) we get:

P= 780

at (30,60) we get:

P= 1560

at (30,15) we get:

P= 840

This means that the minimal value of the function is 780

and the value exist at (15,30)

5 0

3 years ago

A water balloon slingshot launches its projectiles essentially from ground level at a speed of 25.5 m/s . (You can ignore air re

lozanna [386]

A) The longest horizontal distance is reached at 45 degrees angle. This is true for any projectile launch.

B) First, calculate fligth time (using the vertical motion) and then calculate the horizontal movement.

Flight time = 2* ascendent time

ascendent time => final vertical velocity, Vy, = 0

sin(45) = Voy / Vo => Voy = Vosin(45) = 25.5 m/s * (√2) / 2 = 18.03 m/s

Vy = Voy - gt = 0 => Voy = gt = t = Voy / g

Use g = 10 m/s^ (it is an aproximation, because the actual value is about 9.81 m/s^2 depending on the latitud)

t = 18.03 m/s / 10 m/s^2 = 1.83 s

This is the ascendant time going upward.

The flight time is 2*1.83 = 3.66 s

Horizontal motion

Horizontal velocity = Vx = constant = Vox = Vo*cos(45) = 18.03 m/s

Vx = x / t => x = Vx*t

Horizontal distance = xmax = 18.03m/s*3.66 s = 65.99 m

c) The time the ballon will be in the air was calculated in the part B, it is 18.03 s

5 0

3 years ago