We are drawing a 5-card hand from a standard 52-card deck a. What is the probability that all the cards are spades? (5pts)

Answers

Answer 1

Answer:

0.0005 = 0.05% probability that all the cards are spades.

Step-by-step explanation:

The cards are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

52 cards means that N = 52.

13 of the cards are spades, which means that k = 13.

5 card hand means that n = 5.

What is the probability that all the cards are spades?

This is P(X = 5). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 5) = h(5,52,5,13) = \frac{C_{13,5}*C_{39,0}}{C_{52,5}} = 0.0005[/tex]

0.0005 = 0.05% probability that all the cards are spades.


Related Questions

Rearrange so that there is no zero or negative exponent. 2m^0 n^-4

Answers

Answer:

2/n^4

Step-by-step explanation:

Anything to the zero power will become 1 so the m^0 will be 1 and that leaves just 2 in its place. Anything to a negative exponent is equal to its reciprocal so n^-1= 1/n^4. Then you multiple what remains, (2 x 1/n^4) to get the above answer.

Answer:

Step-by-step explanation:

2m^0*n^-4

=2*1*1/n^4

=2/n^4

Note:Any base that has it's power 0 is always considered as one .

If any base has negative exponent transfer that pase to the denominator then its power will be positive. For exanple:

4^-x

=[tex]\frac{1}{4^x}[/tex]

A car bought for $13,000 despreciates at 12% annually. What will the car be worth after 10 Years ?

Answers

Answer:

I think $3620.51

Step-by-step explanation:

If i did it right, the equation should be something like this?

13,000(.88)^10

Find the area. Round to the nearest hundredths if necessary.

Answers

Answer:

12.25π + 77, or approximately 114.48.

Step-by-step explanation:

We can divide the figure into two semicircles (which equal to one circle) and a rectangle. We know that the diameter of the circles is 7, which means the radius is 3.5. Since all points on the circle are equidistant from the center point, we can subtract 18 - 3.5 - 3.5 = 11. Therefore, the dimensions of the rectangle are 11 x 7, which means the area of the rectangle is 77. The formula for the area of a circle is πr^2. There are two semicircles, which means the sum of them both will equal one circle, since they have the same radius. The sum of the areas of the two semicircles equate to 12.25π. The area of the figure is 12.25 + 77, or approximately 114.48.

The object below is made with six identical cubes. Each cube edge is 3 inches long.
As
3 in.
What is the surface area of the object in square inches?

Answers

Answer:

306 square inches.

Step-by-step explanation:

All surfaces of the cubes are exposed to the outside except 2 ( where 2 of the cubes join).

6 separate cubes have 6 * 6 faces exposed so this object has 36 - 2 = 34 surfaces exposed.

Each face of one cube = 3*3 = 9 in^2.

Therefore the surface area =  9 * 34 = 306 in^2.

i need the answer. (will give brainliest to first answer)

Answers

Answer:

[tex]\overline{PO}\cong \overline{SO}[/tex]

Step-by-step explanation:

SAS (Side-Angle-Side) is a proof of congruence for two triangles. It states that when two triangles share two sides and the angle between them, they are congruent. Therefore, if PO and SO are proven to be congruent, the two triangles in the figure will share two sides and the angle between them, thus being congruent.

Which graph represents the function f(x) = 5x + 3)?
4
4
3
2
1
2
1
-
1 2 3 4
-5-4-3-2-4
2+
-5-4-3-2-4
2
-3
4
2
1
54-3-2-1412

Answers

Answer:

the first one

Step-by-step explanation:

all created functional values must always be negative, because "absolute value" Shays creates only positive numbers, and then the "-" in front makes then sure we have only negative numbers.

that rules out the third and fourth answer option.

to decide between first and second answer, I choose to see, when the function should deliver 0 as functional value.

f(x) is 0, when x+3 is 0. and that is only possible for x=-3.

so, at x=-3, y=0.

and that is only true for the first answer option.

What is the perimeter of the triangle? Units

Answers

Answer:

the area of triangle is the product of the base and height divided by 2

Step-by-step explanation:

follow me

Answer:

Perimeter=a+b+c

Step-by-step explanation:

As perimeter is sum of all sides so,

Let sides of triangle be a, b and c

Perimeter=a+b+c

Mark me as brainliest

Thanks

Please help it's urgent!Need help quick!

Answers

Answer:

The answer is number one, top one.

Step-by-step explanation:

You have no time for an explanation.

Solve for x: log(2x) + log3 = 5

Answers

Answer:2/3

Step-by-step explanation:

Answer:

X=50000/3 for x>0

Step-by-step explanation:

First get rid of log (3), toss it over exuation sign.

Then calculate the formula for double angle (sin 2x = sin²X + sin(X) x cos (X) + cos²X)

After you do that you should be able to divide everything with cos²X and get polynomial exuation which is solved by substitution method (you'll get tan and then switch it for lets say letter: t

what is the suppliment of70​

Answers

Answer:

the supplement of angle 70∘ is 110∘. Two angles are called supplementary angles if their sum is 180 degrees.

Two students are reading a book. Keith reads 6 pages a day. Tameka reads 5 pages a day, but he starts sooner and has already read 15 pages. Write a system of equations to represent the situation, using d for days and p for pages. Will Keith and Tameka ever be on the same page on the same day? Explain.

Answers

Answer:

Keith p = 6d

Tameka p = 5d + 15

p=p so the following is also true:

6d = 5d + 15

let's do the same thing on both sides of the equation, subtract 5d

d = 15

after 15 days the will be on the same page

you could also say that Tameka is slowly catching up with a rate of 1 page per day

what is the answer to this question

Answers

D

Explanation: the b value is the starting point and it starts at positive 2, the graph is positive so the slope is also positive which only leaves answer choice D.

Answer:

[tex]slope = \frac{2 - ( - 1)}{0 - ( - 1)} \\ = 3 \\ y = mx + c \\ 2 = (0 \times 3) + c \\ c = 2 \\ { \boxed{y = 3x + 2}}[/tex]

Ayuda porfas!! Una floricola exporta 35 cajas grandes, cada una con 35 paquetes y cada paquete con 35 rosas. ¿Cuantas rosas exporta en total? El problema es de relacion de las potencias cubicas con volumenes.

Answers

Answer:

42875

Step-by-step explanation:

because I would have 35 roses in each package

35 x 35= 1225

1225 would be multiplied by the 35 boxes

1225 x 35 = 42875

Please help?? I have an exam tomorrow

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

x² - 5xy + 6y² = x² - 3xy - 2xy + 6y²

                      = x(x  - 3y) - 2y(x - 3y)

                      = (x - 3y)(x -2y)

x² - 4xy + 3y² = x² -xy - 3xy + 3y²

                      = x(x - y) - 3y(x - y)

                      = (x - y)(x - 3y)

x² - 3xy + 2y² = x² - xy - 2xy + 2y²

                      = x(x - y) - 2y(x - y)

                     = (x - y)(x - 2y)

Least common denominator = (x-y)(x - 2y)(x - 3y)

[tex]RHS = \frac{1*(x-y)}{(x-3y)(x-2y)*(x-y)}+\frac{a*(x-2y)}{(x-y)(x-3y)*(x-2y)}+\frac{1*(x-3y)}{(x-y)(x-2y)*(z-3y)}\\\\= \frac{x- y + ax - 2ay +x -3y}{(x-y)(x-2y)(x-3y)}\\\\= \frac{2x -4y +ax - 2ay}{ x^{3}-5x^{2}y+8xy^{2}-4y^{3}}[/tex]

Find the median of the following data 8,6,10,12,14

Answers

Answer:

the amswe is 10........

Answer:

10

Step-by-step explanation:

Easiest is to cross off one from the beginning and end until you meet in the middle :D!

Ex:

8, 6, 10, 12, 14

   6, 10, 12

       10

can someone help me pls!!

Answers

Answer:

[tex]a=1[/tex]

Step-by-step explanation:

A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite sides of a parallelogram are equal.

Therefore, set any two opposite sides equal to each other to solve for [tex]a[/tex]:

[tex]a+3=2a+2,\\\\3=a+2,\\a=\boxed{1}[/tex]

Answer:

a+3 = 2a+2

a+6 = 6a+1

-------------

a = -1

5a = -5

a = -1

a = -1

if a car driver fills 10 1/2kg of cng and paid rs 1995 what is cost of 1kg of cng

answer quick pls

Answers

Given:

A car driver fills [tex]10\dfrac{1}{2}\text{ kg}[/tex] of CNG and paid Rs. 1995.

To find:

The cost of 1 kg of CNG.

Solution:

According to the given information,

The cost of [tex]10\dfrac{1}{2}\text{ kg}[/tex] of CNG = 1995 rupees

Using this information, we get

The cost of 1 kg of CNG = [tex]\dfrac{1995}{10\dfrac{1}{2}}[/tex] rupees

                                        = [tex]\dfrac{1995}{\dfrac{20+1}{2}}[/tex] rupees

                                        = [tex]\dfrac{1995}{\dfrac{21}{2}}[/tex] rupees

                                        = [tex]1995\times \dfrac{2}{21}[/tex] rupees

                                        = [tex]190[/tex] rupees

Therefore, the  cost of 1 kg of CNG is 190 rupees.

need help pls. will mark brainliest

Answers

C=6
move the constant to the right c-5=1 now calculate c=1+5

Carlos makes a fruit drink by mixing orange juice and grapefruit juice. The ratio of orange juice to grapefruit juice is 3: 1. He makes 10 litres of the fruit drink.

Work out how much orange juice he uses.

Answers

-7.5 is the answer if that’s a choice.

Answer:

7.5 litres

Step-by-step explanation:

Let the amount of orange juice ve 3x litres and amount of grapefruit juice be 1x. (As they are in ratio of 3:1.)

Now, according to the question,

He makes 10 litres of the fruit drink.

So,

⇒ Amount of orange juice + Amount of grape fruit juice = 10 litres

⇒ 3x + x = 10

⇒ 4x = 10

⇒ x = 10 ÷ 4

x = 2.5

Now,

⇒ Amount of orange juice he used= 3x litres

⇒ Amount of orange juice he used= 3(2.5) litres

Amount of orange juice he used= 7.5 litres

He used 7.5 litres of orange juice.

solve the system of equations below
2x-12y=4
x+12y = 56
Write answer as an ordered pair

Answers

Answer:

x = 20

y = 3

Step-by-step explanation:

2x - 12y + x + 12y = 4 + 56

3x = 4 + 56

3x = 60

3x ÷ 3 = 60 ÷ 3

x = 20

x + 12y = 56

20 + 12y = 56

20 - 20 + 12y = 56 - 20

12y = 36

12y ÷ 12 = 36 ÷ 12

y = 3

Answer:

(-52,-9)

Step-by-step explanation:

Hope this helps

how do you find x in this? I need help asap!!​

Answers

Answer:

Step-by-step explanation:

According to the theorem, the angle measuring 110 is one-half the measure of the arc it intercepts. That means that the major arc (this arc of which I'm speaking) measures 110 * 2 = 220.

Since the outside of a circle, regardless of how big or small the circle is, has a degree measure of 360, then x = 360 - 220 so

x = 140°

solve the equation 4^y = 8​

Answers

Answer:

y = [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

4 = 2² and 8 = 2³ , then

[tex]4^{y}[/tex] = 8, can be written

[tex](2^2)^{y}[/tex] = 2³

[tex]2^{2y}[/tex] = 2³

Since bases on both sides are equal, both 2, then equate exponents

2y = 3 ( divide both sides by 2 )

y = [tex]\frac{3}{2}[/tex]

y = 1.5

Step-by-step explanation:

[tex] {4}^{y} = 8[/tex]

Take the logarithm of both sides and you will get

[tex] \log {4}^{y} = y \log4 = \log8[/tex]

or

[tex]y = \frac{\log8}{ \log4} = 1.5[/tex]

Simplify the expression 3 (9+ 4z - 5) ​

Answers

Answer:

12x+12

Step-by-step explanation:

Multiply 3 to everything in the parenthesis

so it becomes

18+12x-15

=12x+12

Which of these inspires confidence increases purchases and speeds up the flow of investment and wages in the circular flow of the free market system

Answers

Question options:

A. antitrust laws B. the provision of public goods C. consumer-protection regulations D. fractional reserve banking.

Answer:

consumer-protection regulations

Explanation:

Consumer protection regulations are regulations that protect the public or general consumers against consumption of unsafe goods. These regulations hold manufacturers accountable for production of goods that may be harmful to consumers. The Consumer Protection Act of 1987 serves the purpose of penalizing erring manufacturers so that consumers are compensated for goods that brought damage to life or property. This therefore inspires great confidence in purchase of goods and investment as consumers are backed by the law.

Evaluate and reduce:
12 + (12)
Enter the number that belongs in the
green box.
[?]

Answers

Answer:

24

Step-by-step explanation:

12 + (12)

first do for the bracket

12 + 12

24


Math help please show work

Answers

Answer:

the jam requires three qts of raspberry so that would be 12 cups and there are 2 cups to a pint so 6 pints I think

1760 yards per mile
1760 x 3 = 5,280. Pamela ran farther

2 pints equal 1 quart
2 x 3 = 6 pints

1.5 x 4 = 6
4 containers are needed

12 inches per foot
77/12 = 6.416
Rounds to 6.42
6ft 42in

How about Brainliest?

what is the range of the data below​

Answers

You need to provide a picture of the data or else nobody can solve it.

Answer:

u need to provide data where is data

Help please! No links!

Answers

Answer:

It is placed to the left of –2

what is the range of this relation? {(0,5), (2,3), (1, -4), (-3, 3), (-1, -2)}

Answers

Answer:

The Answer is 5,3,-4,3,-2 because they are the points on the y axis

Step-by-step explanation:

the range = { -4, -2, 3, 5}

help help help help help help

Answers

Answer:

A

Step-by-step explanation:

because the intercept on the y axis is 6

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