Scale factors please help I'm rlly stuck.

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A deck of 52 cards contains four aces. If the cards are shuffled and distributed in a random manner to four players so that each player receives 13 cards, what is the probability that all four aces will be received by the same player?

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Answer:

The probability that all four aces will be received by the same player is approximately 0.01.

Step-by-step explanation:

Of the 52 cards the four aces can be selected in $52\choose4$ ways.

If any one of the players receives all the four aces then that player can be selected in $4\choose1$ ways.

Now for the selected player to receive all the four aces, the four ace cards must be placed among the 13 cards the player receives. This can be done in $13\choose4$ ways.

Then the total number of ways such that all the four aces is received by one player is $4$ $13\choose4$ .

Then the probability that all four aces will be received by the same player is:

$4*\frac{{13\choose4}}{{52\choose4}}=4*(715)/(270725) =0.01056\approx 0.01$

Thus, the probability that all four aces will be received by the same player is approximately 0.01.

Final answer:

The probability that all four aces will be received by the same player in a game of 52 card deck distributed among four players is given by the formula P(E) = 4 * C(48, 9) / C(52, 13), derived through principles of combinatorics.

Explanation:

This is a probability problem that can be solved using combination and permutation principles in mathematics. Specifically, the subject involves combinatorics.

First, we note that each of the four players is dealt 13 cards from a 52 card deck. Hence, for a single player, the total number of ways 13 cards can be chosen from 52 is given by the combination formula C(n, r) = n! / [(n-r)!r!], where ! denotes factorial. In our case, n=52, and r=13.

The total number of ways to deal these 13 cards is thus C(52, 13).

Next, we need to consider the specific case where all four aces end up with one player. This means this player has 9 other cards that are not aces, from the remaining 48 cards (52 total cards - 4 aces). This can happen in C(48, 9) ways.

Therefore, the probability that a specific player gets all four aces is P(E) = C(48, 9) / C(52, 13).

To find the probability that any of the four players gets all four aces, we multiply this result by 4, because there are four players.

So, the final probability is P(E) = 4 * C(48, 9) / C(52, 13).

Learn more about Probability here:

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The recommended space needed for certain plant is 2 ft.² you want to plant 32 of this plants in a square garden .what is the length of each side of the garden if you follow the recommendation?

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each side should be 32ft because if you do 32 times 2^2 it equals 128 and 128/4=32 so 32 per side

1)What are the first five terms of the sequence given by the formula an=4n+1 ? a. 1,5 ,9,13,17 b. 9,13,17,21,25 c. 5,9,13,17,21 d. 4,8,12,16,20 2)Write a recursive definition for the sequence 8,6,4,2 ... a. a1=8, an=an-1-2 b. a1=2, an=an-1+6 c. a1=8,an=an-1+2 d. a1=2, an=an-1+8

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Hello,

1)
I don't if in USA, we count beginning with 0 or beginning with 1

if you count 0,1,2,3,4,5,6... a(0) being the FIRST term the answer is A
if you count 1,2,3,4,5... a(1) being the first term (in this case how do you call a(0) the zeroth term?) the answer is C

In Europ, the first term is a(0).

2)

a(1)=8 Is it the FIRST term?
a(n)=a(n-1)-2
Answer A

How to solve linear equations by substitution?

5x+2y=9
x+y=-3

Answers

5x+2y=9 x+y=3

change x+y=3 into x=3-y

plug that equation into 5x+2y=9 where x is.

5(3-y)+2y=9

then distribute.

15-5y+2y=9

15-7y=9

minus 15.

-7y=-6

divide both sides by -7.

y is equal to -6/7.

then go back to the first equation and plug in for y.

and then you will get x.

then you will have (y,x)

$\begin{cases} 5x+2y=9 \n x+y=-3\end{cases} \n \n\begin{cases} 5x+2*(-3-x)=9 \n y=-3 -x\end{cases} \n \n\begin{cases} 5x-6-2x =9 \n y=-3 -x\end{cases}\n \n\begin{cases} 3x =9+6 \n y=-3 -x\end{cases}$

$\begin{cases} 3x =15 \ \ /:3 \n y=-3 -x\end{cases} \n \n\begin{cases} x =5 \n y=-3 -5\end{cases} \n \n\begin{cases} x =5 \n y=-8\end{cases}$

Solve the equation 6x +2y = 10 for y in terms of x gives what function?y = -6x +10
y = -3x +5
y = 2x
y = 3x + 5

Answers

The correct equation for y in terms of x would be, y = - 3x + 5

Hence, option 2 is true.

Used the concept of an equation that states that,

An equation is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.

Given that the expression is,

6x + 2y = 10

Now, simplify the equation for y in terms of x as,

6x + 2y = 10

Subtract both sides by 6x,

2y = - 6x + 10

Divide both sides by 2,

y = - 3x + 5

So, The correct equation would be, y = - 3x + 5

Thus, option 2 is true.

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Answer:

y = - 3x + 5

Step-by-step explanation:

Given

6x + 2y = 10 ( subtract 6x from both sides )

2y = - 6x + 10 ( divide all terms by 2 )

y = - 3x + 5

A certain forest covers an area of 2,000 square kilometers. Suppose that each year this area decreases by 6%. What is the function that bestrepresents the area of the forest each year and how much area remains after 12 years? Round your answer to the nearest square kilometer.Hint: Use the formula, f(x) = P(1 + r)x.

Answers

The question gives you the formula to use, but it's printed wrong.
The 'x' is an exponent after the (1 + r).

All you have to do is take the formula, and write the numbers into it
that are also given.

The key thing to spot is that the forest is decreasing, so the 'r' is negative,
just as if you had money in a savings account and every year the bank took
6% out of it.

So the formula to use is    f(x) = P (1 + r) ^x

P = 2000
r = -0.06
      f(x) = 2000 (1 - 0.06)^x
         = 2000 (0.94)^x

The amount left after 12 years is

   2000 (0.94)¹² =

   2000 (0.476) = 951.8 square kilometers.

hope this helps- i did the test :)

Answer:

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