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Stels [109]
3 years ago
7

Two cards are selected at random without replacement from a well-shuffled deck of 52 playing cards. Find the probability of the

given event. (Round your answer to four decimal places.)
Two cards of the same suit are drawn.
Mathematics
2 answers:
Ne4ueva [31]3 years ago
6 0
The probability of drawing, say, two clubs is:
\frac{1}{4}\times\frac{12}{51}=0.058824
The probabilities of drawing two hearts, two spades or two diamonds is also 0.058824 for each event. The four events are mutually exclusive, therefore the probability of drawing two cards of the same suit is:
0.058824\times 4=0.2353
solmaris [256]3 years ago
4 0

There are 52 cards in a deck of cards. In the first try, the probability of getting any card is 1/52. In the second try, there are already 51 cards because there is no replacement, hence the probability on the second try is 1/51. Hence the probavility of the two events is 1/52*1/51 equal to  1/2652.
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You have a wire that is 20 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The o
Aleksandr [31]

Answer:

Therefore the circumference of the circle is =\frac{20\pi}{4+\pi}

Step-by-step explanation:

Let the side of the square be s

and the radius of the circle be r

The perimeter of the square is = 4s

The circumference of the circle is =2πr

Given that the length of the wire is 20 cm.

According to the problem,

4s + 2πr =20

⇒2s+πr =10

\Rightarrow s=\frac{10-\pi r}{2}

The area of the circle is = πr²

The area of the square is = s²

A represent the total area of the square and circle.

A=πr²+s²

Putting the value of s

A=\pi r^2+ (\frac{10-\pi r}{2})^2

\Rightarrow A= \pi r^2+(\frac{10}{2})^2-2.\frac{10}{2}.\frac{\pi r}{2}+ (\frac{\pi r}{2})^2

\Rightarrow A=\pi r^2 +25-5 \pi r +\frac{\pi^2r^2}{4}

\Rightarrow A=\pi r^2\frac{4+\pi}{4} -5\pi r +25

For maximum or minimum \frac{dA}{dr}=0

Differentiating with respect to r

\frac{dA}{dr}= \frac{2\pi r(4+\pi)}{4} -5\pi

Again differentiating with respect to r

\frac{d^2A}{dr^2}=\frac{2\pi (4+\pi)}{4}    > 0

For maximum or minimum

\frac{dA}{dr}=0

\Rightarrow \frac{2\pi r(4+\pi)}{4} -5\pi=0

\Rightarrow r = \frac{10\pi }{\pi(4+\pi)}

\Rightarrow r=\frac{10}{4+\pi}

\frac{d^2A}{dr^2}|_{ r=\frac{10}{4+\pi}}=\frac{2\pi (4+\pi)}{4}>0

Therefore at r=\frac{10}{4+\pi}  , A is minimum.

Therefore the circumference of the circle is

=2 \pi \frac{10}{4+\pi}

=\frac{20\pi}{4+\pi}

4 0
2 years ago
Step by step explanation please
galina1969 [7]

Two equal triangles

2(1/2×b×h)

=2(1/2×8×10)

= 80 {cm}^{2}

Three rectangles

=3(l×h)

=3(18×8)

=3(144)

432 {cm}^{2}

Total Surface area

80 {cm}^{2}   +  432 {cm}^{2} \\ 512 {cm}^{2}

8 0
3 years ago
What is 25/30 in simplest form
telo118 [61]
5/6 all you do is divide by 5
5 0
3 years ago
Read 2 more answers
I need to know the steps
vaieri [72.5K]

YES. She is correct.

\dfrac{x}{16}=4\qquad\text{multiply both sides by 4}\\\\\not\!4^1\cdot\dfrac{x}{16\!\!\!\!\!\diagup_4}=4\cdot4\\\\\dfrac{x}{4}=16

Equations are equivalent

Their solutions:

\dfrac{x}{16}=4\qquad\text{multiply both sides by 16}\\\\x=4\cdot16\\\\\boxed{x=64}\\----------\\\\\dfrac{x}{4}=16\qquad\text{multiply both sides by 4}\\\\x=16\cdot4\\\\\boxed{x=64}


3 0
3 years ago
What is the value of x?
OLga [1]

Answer:

x = 24

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

<em>a</em> = a leg

<em>b</em> = another leg

<em>c</em> = hypotenuse

Step 1: Plug in known variables

x² + 10² = 26²

Step 2: Evaluate

x² + 100 = 676

Step 3: Isolate <em>x </em>term

x² = 576

Step 4: Isolate <em>x</em>

√x² = √576

x = 24

5 0
3 years ago
Read 2 more answers
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