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Lina20 [59]
3 years ago
8

Suppose that 3 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 3 are diamonds?

Mathematics
1 answer:
Marat540 [252]3 years ago
5 0

There are 13 diamonds in the deck, so \dbinom{13}3 ways of drawing 3 diamonds.

There is a total of \dbinom{52}3 ways of drawing any 3 cards from the deck.

So the probability of drawing 3 diamonds is

\dfrac{\binom{13}3}{\binom{52}3}=\dfrac{11}{850}\approx0.012941

where \dbinom nk=\dfrac{n!}{k!(n-k)!}.

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PLZZZZZZ HELPPPPP! <br> Question 8
tankabanditka [31]
X=2t
y=1-t
t=x/2
y=1-x/2
y=(-1/2)x+1
7 0
3 years ago
If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2
Oksanka [162]

If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2 times the area of the rectangle, what is the the length and the width

Solution:

Let the length of rectangle=x

Width of rectangle=x/10

Perimeter is 2(Length+Width)

= 2(x+x/10)

Area of Rectangle= Length* Width=x*x/10

As, Perimeter=2(Area)

So,2(x+x/10)=2(x*x/10)

Multiplying the equation with 10, we get,

2(10x+x)=2x²

Adding Like terms, 10x+x=11x

2(11x)=2x^2

22x=2x²

2x²-22x=0

2x(x-11)=0

By Zero Product property, either x=0

or, x-11=0

or, x=11

So, Width=x/10=11/10=1.1

Checking:

So, Perimeter=2(Length +Width)=2(11+1.1)=2*(12.1)=24.2

Area=Length*Width=11*1.1=12.1

Hence, Perimeter= 2 Area

As,24.2=2*12.1=24.2

So, Perimeter=2 Area

So, Answer:Length of Rectangle=11 units

Width of Rectangle=1.1 units

7 0
3 years ago
Read 2 more answers
Each day for 12 consecutive days, Ricardo jogged for 1 2/3 hours at an average rate of 6 1/4 miles per hour. Find the total dist
kirill115 [55]

Answer:

Your answer is 125 miles

Step-by-step explanation:

1 \frac{2}{3} ×6 \frac{1}{4} = 10 \frac{5}{12}

10 \frac{5}{12} × 12 = 125

8 0
3 years ago
Find the area<br><br> A: 54.94 cm<br> B: 40.59 cm<br> C: 33.165 cm<br> D: 27.47 cm
aleksandrvk [35]
D: 27.47 cm. A=b×h÷2

6.7×8.2=54.94
54.94÷2=27.47 cm

hey what can I say except your welcome.
8 0
3 years ago
Read 2 more answers
Find all the missing elements:
pentagon [3]

Answer:

B = 34.2°

C = 58.2° or 121.8°

c= 10.6

Step-by-step explanation:

Step 1

Finding c

We calculate c using Pythagoras Theorem

c²= a² + b²

c = √a² + b²

a= 8, b = 7

c = √8² + 7²

c = √64 + 49

c = √(113)

c = 10.630145813

Approximately c = 10.6

Step 2

Find B

We solve this using Sine rule

a/sin A = b/sin B

A = 40°

a = 8

b = 7

Hence,

8/sin 40° = 7/sin B

8 × sin B = sin 40° × 7

sin B = sin 40° × 7/8

B = arc sin (sin 40° × 7/8)

B ≈34.22465°

Approximately = 34.2°

Step 3

We find C

Find B

We solve this using Sine rule

b/sin B = c/sin C

B = 34.2°

b = 7

c = 10.6

C = ?

Hence,

7/sin 34.2° = 10.6/sin C

7 × sin C = sin 34.2 × 10.6

sin C = sin 34.2° × 10.6/7

C = arc sin (sin 34.2° × 10.6/7)

C = arcsin(0.85)

C= 58.211669383

Approximately C = 58.2°

Or = 180 - 58.2

C = 121.8°

5 0
2 years ago
Read 2 more answers
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