Three cards are selected one after the other from a standard deck of 52 cards.
What is the probability that all three cards are spades if none of the first two cards is replaced?

Answers

Answer 1

Answer:

[tex]\frac{11}{850}[/tex]

Step-by-step explanation:

Let's see

The probability of the first card being a spade is 13/52 (as there's 13 spades in the deck.

The probability for the second card is 12/51 (because there's 12 spades left in 51 cards total).

The probability for the third is - you guessed it! - 11/50

so the total probability is:

[tex]\frac{13}{52} \cdot \frac{12}{51} \cdot \frac{11}{50} = \frac{1}{4} \cdot \frac{4}{17} \cdot \frac{11}{50} = \frac{1}{17} \cdot \frac{11}{50} = \frac{11}{850}[/tex]

A more generic solution:

Let's use the binomials to find the solution with combinations:

We need to pick 3 cards out of 13. This can be done in

[tex]\binom{13}{3} = \frac{13!}{3!\cdot10!}[/tex] ways.

And the total number of ways to pick 3 cards out of 52 is:

[tex]\binom{52}{3} = \frac{52!}{3!\cdot 49!}[/tex]

So the probability is:

[tex]\frac{ \binom{13}{3} }{ \binom{52}{3} } = \frac{ \frac{13!}{3!\cdot 10!} }{ \frac{52!}{3!\cdot 49!} } = \frac{ \frac{13!}{10!} }{ \frac{52!}{49!} } = \frac{13 \cdot 12 \cdot 11}{52 \cdot 51 \cdot 50}[/tex]

Which again brings us to the result computed before.


Related Questions

A soccer ball is kicked at a velocity of 25 meters per second. The following table shows the horizontal distance (in meters) at different angles of elevation (in degrees), ignoring wind resistance.

Angle of Elevation Distance Traveled
15 31.9
25 48.8
30 55.5
45 63.8
50 62.8
55 59.9
60 55.5
70 41.0
Using a quadratic regression calculator, determine the values of a, b, and c that can be used to write a quadratic function that provides a reasonable fit to the set of data. What is the value of c?

A). 8.5411
B). -8.5411
C). 85.411
D). -85.411

Answers

The answer is D hope this helps your very welcome

Answer:

-8.5411

Step-by-step explanation:

I just did this with the desmos calculator !

37.286 to the nearest hundredth

Answers

Answer:

37.3

Step-by-step explanation:

Answer:

37.29

Step-by-step explanation:

Which properties describe the graph of (x + 5)2 + (y – 10)2 < 169?

a. circle with center at (–5, 10), shading inside the circle
b. circle with center at (5, –10), shading inside the circle
c. circle with center at (5, –10), shading outside the circle
d. circle with center at (–5, 10), shading outside the circle

Answers

Answer:

a. circle with center at (–5, 10), shading inside the circle

Step-by-step explanation:

I have a quizlet for those towards the end of the course aka Cameron its

HELI KADAKIA to study ofc

The graph of (x + 5)² + (y – 10)² < 169. The circle with centre at (5, –10), shading inside the circle. The correct option is B.

What is a circle?

A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The given equation of the graph is f(x + 5)² + (y – 10)² < 169. When we plot the equation we get the circle having an inside shaded part. The coordinates of the circle are (5,-10).

Therefore, the graph of (x + 5)² + (y – 10)² < 169. The circle with centre at (5, –10), shading inside the circle. The correct option is B.

To know more about circles follow

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Which data set could be represented by the box plot shown below?

Answers

Answer:

The answer is C

Step-by-step explanation:

It starts at 25 and then it stops at 38.

I hope this helps!

Answer:

hi

Step-by-step explanation:

val Verde Unified SD
https://my.hrw.cc
& Co my.hrw.com/wwtb/api/viewer.pl
Personal Math Trainer Lesson 6.2 - Homework - Homework
112131415161718
9
10
Gordon types 1,612 words in 26 minutes. Find the unit rate.
Gordon types
words per minute.

Answers

Answer:

nothing to do with your question just need points

Step-by-step explanation:

Answer:

62 Words Per Minute

Step-by-step explanation:

Big brain go thinky-think.

Reina scored twice as many goals at her last field hockey game as she did during the first game of the season. If ff represents the number of goals Reina scored during the first game, which expression represents the number of goals she scored during the last game?


And pls dont say that u put the answer somewhere esle

Answers

Answer:2-f

Step-by-step explanation:

How long is the wire that supports the tree
10
5.6 ft
3.3 ft-

Answers

5.6 ft would be the correct answer

In the figure above, RT = TU. What is
the value of x ?
A) 72
B) 66
C) 64
D) 58

Answers

Answer:

C. 64

Hope that helps you

The value of the angle x is calculated as: ∠x = 64

How to find the value of the missing angle?

Let the intersect of line SV and RT be Y

Sides RTU forms a triangle, and the sum of the interior angles of a triangle is 180.

Since RT = TU, ∠TRU  = ∠TUR = z

114 + z + z = 180

114 + 2z = 180

2z = 180 - 114

2z = 66

z = 66/2

z = 33

Line STU is a straight line and the angle of a straight line is 180. Thus:

114 + ∠STR  = 180

∠STR = 180 - 114

∠STR = 66

Also, sides SYT is forms a triangle and the sum of all interior angles of a triangle is 180. Thus:

66 + 31 + ∠SYT = 180

97 + ∠SYT = 180

∠SYT = 180 - 97

∠SYT = 83

But ∠SYT = angle RYV = 83

sides RYV form a triangle and the sum of all interior angles of a triangle is 180

33 + 83 + ∠x = 180

116 +  ∠x = 180

∠x = 180 - 116

∠x = 64

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6.
Do the following conversions:
a.2 GB = ---------------- Kb

b.
2×10 MB = ------------------- B


please answer the question fastly​

Answers

Answer:

a) 2000000 kilobytes

b)20 000 000 bytes

Helpppppp please look at the picture i added

Answers

just shade in one box as 1/2 divide by 5 is 1/10

What is the area of a circle if the diameter is 9cm?
Round to the nearest hundredth (0.01cm2)

Answers

Answer: A≈63.62

Step-by-step explanation:

9/2= 4.5

A=πr2=π·4.52≈63.61725

Answer:

To find the area of a circle we have [tex]\pir^{2}[/tex] and the radius is half of the diameter so we have 4.5² which gives 16.25π

Division in a given ratio
In a class of 30 pupils the ratio of the number of boys to the number of girls is 7 : 8. How many girls are there?​

Answers

Step-by-step explanation:

let the ratio 7:8 be 7x and 8x.

now

7x+8x=30

or, 15x=30

or, x= 30/ 15

or, x= 2

here

no. of boys = 7x= 7*2 = 14

no. of girls= 8x = 8*2= 16

hope this helps u...

Answer:

16 girls

Step-by-step explanation:

sum the parts of the ratio, 7 + 8 = 15 parts

Divide the number of pupils by 15 to find the value of one part of the ratio.

30 ÷ 15 = 2 pupils ← value of 1 part of the ratio, then

8 parts = 8 × 2 = 16 ← number of girls

A store advertises 15% off an item that regularly sells for $300. what is the sale item? how is a 15% discount similar to a 15% decrease? Explain.

Answers

Answer: $255

Step-by-step explanation:

A store advertises 15% off an item which sells for $300. The sale item will then be calculated as:

= $300 - (15% × $300)

= $300 - (0.15 × $300)

= $300 - $45

= $255

The sales price is $255.

A 15% discount is similar to a 15% decrease because in both cases, one has to subtract the value of 15% from the selling price.

Your friend uses 2 1/2 ounds of dried fruit and 1/2 pound of raisins to make trail mix.How many 1/2 pound packages can he make.

Answers

Answer:

he can make 6 because 2 and 1/2 plus 1/2 = 3 and 3 divided by 2 is 6

Step-by-step explanation:

Factor the expression 8a + 16c

-2(a - 8)
6(a - 3c)
4c(2a - 4)
8(a + 2c)
Part B
Based on your answer to the previous question, evaluate the expression for a=4 and c= 3.

-30
48
80
8

Answers

the answer for this question is 80
92 c 29 x is the right answer

Which fraction is equal to 36%?

Answers

Answer:

[tex] \frac{36}{100} = \frac{9}{25} [/tex]

Step-by-step explanation:

3600%/100% cancel them you will get 36% answer..

If total expenditure of firm is Rs. 1000 i). Price of labour (PL)is Rs 200. ii). |Price of capital (PK) is Rs. 100, then determine the budget line for the firm? (

Answers

Answer:

[tex]L + 2K = 200[/tex]

Step-by-step explanation:

Given

[tex]E=1000[/tex] --- Expenditure

[tex]L=200[/tex] --- Labor

[tex]K = 100[/tex] --- Capital

Required

Determine the budget line

First, we calculate the units of labor

[tex]U_1 = \frac{E}{L}[/tex]

[tex]U_1 = \frac{1000}{200}[/tex]

[tex]U_1 = 5[/tex]

Next, the units of capital

[tex]U_2 = \frac{E}{K}[/tex]

[tex]U_2 = \frac{1000}{100}[/tex]

[tex]U_2 = 10[/tex]

The budget line equation is:

[tex]U_1 * L + U_2 * K = E[/tex]

At this point, we take L and K as variables.

So, the equation becomes

[tex]5* L + 10* K = 1000[/tex]

[tex]5 L + 10K = 1000[/tex]

Divide through by 5

[tex]L + 2K = 200[/tex] -- Budget line equation

The radius of a circle is 8 units.
What is the diameter of the circle?
units

Answers

Answer:

16

Step-by-step explanation:

radius is 1/2 of diameter

Answer:

16 units

Step-by-step explanation:

When a circle is inscribed in a square, the length of each side of the square is equal to the diameter of the circle. That is, the diameter of the inscribed circle is 8 units and therefore the radius is 4 units.

Solve each of these equations.

1. 2(x+5)=3x+1

2. 3y−4=6−2y

3. 3(n+2)=9(6−n)

Answers

Answer:

1. x=9

2. y=2

3. n=4

hello just helping out!

How did you compute sums of dollar amounts that were not whole numbers?

Answers

Answer:

$7.34

Step-by-step explanation:

To compute sum of dollars that are not whole numbers. Using the sum of$5.89 and$1.45 as an illustration :

$5.89 + $1.45

Taking the whole numbers first:

$5 + $1 = $6

Take the sum of the decimals :

$0.89 + $0.45 = $1.34

Sum initial whole + whole of sum of decimal

$6 + $1 = $7

Remaining decimal : $1.34 - $1 = $0.34

$7 + $0.34 = $7.34

Find the area.
2m
2m
3m

Answers

Answer:

5 m²

Step-by-step explanation:

please mark me as brainliest

A father is 28 years older than his daughter. In six years' time, he will be three times her age. Find their present ages.

Please use an algebraic equation to find the answer and show your working out if possible!!

Answers

Answer:

8 and 36

Step-by-step explanation:

let the daughter's age be x then father is x + 28

In 6 years their ages are

x + 6 and x + 28 + 6 = x + 34

Father is 3 times her age , then equation is

x + 34 = 3(x + 6) ← distribute

x + 34 = 3x + 18 ( subtract x from both sides )

34 = 2x + 18 ( subtract 18 from both sides )

16 = 2x ( divide both sides by 2 )

8 = x

Daughter's age is 8 and father's age is 8 + 28 = 36

Give the center and radius of the circle x2+y2=25
A) (2,3)r=5
B) (0,0)r=5
C) (0,0)r=25
D) (3,2)r=25

Answers

Answer:

B) (0,0); r=5

Step-by-step explanation:

A circle's standard form is (x-h)^2+(y-k)^2=r^2

The center is (h, k) and the radius is r.

So, here the center would be (0, 0) and the radius would be square root 25, or 5.

Answer:

(0,0) r=5

Step-by-step explanation:

The guy above me

2 × 10^12 red blood cells have a total mass of 90 grams.
Work out the average mass of 1 red blood cell.
Give your answer in standard form.

Answers

Answer:

2×10¹² cells → 90 g

mass of 1 red blood cell : 90÷(2×10¹²) = 45×10^-12 g = 4.5×10^-11 g

solve the inequality
10 - 6x < 70

Answers

Answer:

x > -10

Step-by-step explanation:

10 - 6x < 70

-10           -10

-6x<60

/-6.   /-6

(flip sign)

x>-10

Answer:

This is the answer x < 5

TRIG HW; find missing side by using trignometry

Answers

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

the above is really helpful if you don't have a brain.  :P

for 7 we only need Pythagoras's theorem, know it?

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]

out of curiosity.. does the above formula seem "impossible" ?  or does it make sense?

[tex]c^{2}[/tex] = [tex]12^{2}[/tex] + [tex]16^{2}[/tex]

[tex]c^{2}[/tex] = 144 + 256

[tex]c^{2}[/tex] = 400

c = [tex]\sqrt{400}[/tex]

c = 20

x= 20

for 8 we do need the above list of trig functions. we want to find the Hyp x and we know an angle and the adjacent side sooo use Cos .. b/c we can see it's got those parts in it

Cos(60) = 18 / x

I'll show you the algebra we need to use to get this formula so that we can find x

A = B / x  ( this is how it looks above )

x = B / A    , now just put in the parts

x = 18 / Cos(60)  now solve it w/ your calculator..  :P Cos(60) happens to be 1/2 so you could have done this w/o your calculator   :/

x = 36

there you go,   :)

Ten friends shared a bag of popcorn. Using p to represent the bag of popcorn, which expression represents the amount each friend received? *
1 point
p / 10
10 - p
10p
10 + p

Answers

It’s the first choice

Find the perimeter and the area of the figure.
6 cm
7 cm
9.5 cm
6.5 cm

Answers

The perimeter and the area of the composite figure are 29 centimeters and 49.5 square centimeters, respectively.

How to determine the perimeter and the area of the figure

In this problem we have the representation of a composite figure, the result of the combination of a rectangle and a triangle. The perimeter of the figure is the sum of the sides and the area of the composite figure is the result of suming the areas of the rectangle and triangle:

Rectangle

A = b · h

Triangle

A = 0.5 · b · h

Where:

b - Baseh - HeightA - Area

And the perimeter and the area of the composite figure are now computed:

Perimeter

p = 6 cm + 7 cm + 6.5 cm + 9.5 cm

p = 29 cm

Area

A = 0.5 · (6 cm) · (2.5 cm) + (6 cm) · (7 cm)

A = 7.5 cm² + 42 cm²

A = 49.5 cm²

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Find the cosine of angle E.
A) 39/80
B) 39/89
C) 80/39
D) 80/89

Answers

Answer:

B) 39/89

Step-by-step explanation:

With reference angle E

hypotenuse (h) = 89

base (b) = 39

cosine angle E

= b /h

= 39/89

Ron and Freddy built structures out of snap cubes. Ron's tower had an 8-inch square base. Freddy had a 6-inch square base. If Ron's tower had a volume of 320 cubic inches and Freddy's had a volume of 180 cubic inches, Whose tower was taller? Explain your reasoning.

Answers

Answer: Ron tower's

Step-by-step explanation:

Given

Ron tower has a base of [tex]A_r=8\ in.^2[/tex]

Freddy tower has a base of [tex]A_f=6\ in.^2[/tex]

Suppose the tower is in the shape of a square prism

The volume of Ron and Freddy tower is [tex]320\ \text{and}\ 180\ in.^3[/tex]

The volume of a square-based prism is  [tex]V=\frac{1}{3}a^2h[/tex]

[tex]\therefore \text{height of Ron tower is}\ h_r=\dfrac{3V}{A_r}\\\\\Rightarrow h_r=\dfrac{3\times 320}{8}=120\ in.[/tex]

The height of Freddy tower is

[tex]\Rightarrow h_f=\dfrac{3V}{A_f}\\\\\Rightarrow h_f=\dfrac{3\times 180}{6}=90\ in.[/tex]

Thus, the height of Ron's tower is  more than Freddy's tower by [tex]30\ in.[/tex]

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