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jeka94
3 years ago
7

How many 5-card hands can be formed that include exactly 2 pairs? (example 2 queens, 2 kings)

Mathematics
1 answer:
iVinArrow [24]3 years ago
3 0
10. Here's why:
K,K,K,K,QQ,Q,Q,J,JJ,J,10,10,1010,9,9,9,98,8,8,8,77,7,7,6,66,6,5,5,55,4,4,4,43,3,3,3,22,2,2,A,AA,A
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The Corectttttt Answerrrrr is C
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Does anyone know the quitent of 83/4
igomit [66]

Answer:

20.75

Step-by-step explanation:

The quotient of 83/4 is 20.75

6 0
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lyudmila [28]

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Step-by-step explanation:

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3 years ago
What are all the values of x, for which the square of x is equal to the value of x increased by 2?
Sedbober [7]
=±22
x
=
±
2
x
2


Using the fact that 2=ln2
2
=
e
ln
⁡
2
:

=±ln22
x
=
±
e
x
ln
⁡
2
2


−ln22=±1
x
e
−
x
ln
⁡
2
2
=
±
1


−ln22−ln22=∓ln22
−
x
ln
⁡
2
2
e
−
x
ln
⁡
2
2
=
∓
ln
⁡
2
2


Here we can apply a function known as the Lambert W function. If =
x
e
x
=
a
, then =()
x
=
W
(
a
)
.

−ln22=(∓ln22)
−
x
ln
⁡
2
2
=
W
(
∓
ln
⁡
2
2
)


=−2(∓ln22)ln2
x
=
−
2
W
(
∓
ln
⁡
2
2
)
ln
⁡
2


For negative values of
x
, ()
W
(
x
)
has 2 real solutions for −−1<<0
−
e
−
1
<
x
<
0
.

−ln22
−
ln
⁡
2
2
satisfies that condition, so we have 3 real solutions overall. One real solution for the positive input, and 2 real solutions for the negative input.

I used python to calculate the values. The dps property is the level of decimal precision, because the mpmath library does arbitrary precision math. For the 3rd output line, the -1 parameter gives us the second real solution for small negative inputs. If you are interested in complex solutions, you can change that second parameter to other integer values. 0 is the default number for that parameter.
8 0
3 years ago
Tanya wants to test the theory that the exterior angles of a
PilotLPTM [1.2K]

Answer:

f + e + d = 360^o

Step-by-step explanation:

The question is incomplete, as what is required is not stated and the triangle is not given.

So, I will solve generally.

The proof is as follows (see attachment for triangle)

From the attachment, we have:

a + f = 180

b + e = 180

c + d = 180

Make f, e and d the subject

f = 180 - a

e = 180 - b

d = 180 - c

Add up the equations

f + e + d = 180 -a + 180 - b + 180- c

Collect like terms

f + e + d = 180 + 180+ 180-a- b - c

f + e + d = 540-a- b - c

We have:

f + e + d = 540-(a+ b + c)

a + b + c \to 180 --- angles in a triangle

So, we have:

f + e + d = 540-180

f + e + d = 360^o --- proved

6 0
3 years ago
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