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Anarel [89]
3 years ago
6

If u have 3 dice what is the probability that they will all land on the same number

Mathematics
1 answer:
Sveta_85 [38]3 years ago
6 0

Answer:(1/6)3

or 1/216

Step-by-step explanation:

You have a 1/6      chance of getting the first number.1/6  

chance of the second and so on. Is it just        

(16)3

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Assume V and W are​ finite-dimensional vector spaces and T is a linear transformation from V to​ W, T: Upper V right arrow Upper
scZoUnD [109]

Answer:

Thus for the vectors v_1, v_2, v_p there are scalars c_1, c_2, c_p not all zeros, such that c_1v_1 +c_2v_2+... +c_pv_p = 0. It means that the vectors v_1, v_2, v_p are linearly dependent in contradiction with the fact that the vectors form a basis for H. So the assumption that T(v_1), T(v_2),..., T(v_p) are linearly dependent is false, proving the required.  

Step-by-step explanation:

Let B = {v_1 ,v_2,..., v_p} be a basis of H, that is dim H = p and for any v ∈ H there are scalars c_1 , c_2, c_p, such that v = c_1*v_1 + c_2*v_2 +....+ C_p*V_p It follows that  

T(v) = T(c_1*v_1 + c_2v_2 + ••• + c_pV_p) = c_1T(v_1) +c_2T(v_2) + c_pT(v_p)

so T(H) is spanned by p vectors T(v_1),T(v_2), T(v_p). It is enough to prove that these vectors are linearly independent. It will imply that the vectors form a basis of T(H), and thus dim T(H) = p = dim H.  

Assume in contrary that T(v_1 ), T(v_2), T(v_p) are linearly dependent, that is there are scalars c_1, c_2, c_p not all zeros, such that  

c_1T(v_1) + c_2T(v_2) +.... + c_pT(v_p) = 0

T(c_1v_1) + T(c_2v_2) +.... + T(c_pv_p) = 0

T(c_1v_1+ c_2v_2 ... c_pv_p) = 0  

But also T(0) = 0 and since T is one-to-one, it follows that c_1v_1 + c_2v_2 +.... + c_pv_p = O.

Thus for the vectors v_1, v_2, v_p there are scalars c_1, c_2, c_p not all zeros, such that c_1v_1 +c_2v_2+... +c_pv_p = 0. It means that the vectors v_1, v_2, v_p are linearly dependent in contradiction with the fact that the vectors form a basis for H. So the assumption that T(v_1), T(v_2),..., T(v_p) are linearly dependent is false, proving the required.  

8 0
2 years ago
Solve each system of equations using the elimination method<br><br> 3x+8y=2<br> 4x-2y=-10
LenaWriter [7]

x = -2

y = 1

let's multiply second equation by 4 to get a common coefficient of y variable.

16x-8y=-40

add the equations

3×+8y=2

16x-8y=-40

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

3x+16x = -38

19x = -38

x = -2

substitute x

3×-2 + 8y = 2

-6 + 8y = 2

8y = 2+6

y = 1

check the answer

-6+8 = 2

-8-2= -20

8 0
2 years ago
Use red and yellow and a ten frame.show both addends. Draw to make a ten then write the new fact
NISA [10]

Let us fill the blank squares in the 10-frame by the yellow circles below to make 10s.

1.  Fill the 3 blank squares with 3 yellow circles below to make a 10 and form a new fact 10 + 2. Now, we can easily add 10 and 2 to get 12.

2.  Fill the 1 blank square with 1 yellow circle below to make a 10 and form a new fact 10 + 4. Now, we can easily add 10 and 4 to get 14.

Please refer attached figures for better understanding.


3 0
3 years ago
Read 2 more answers
Write an equation for the line that passes through E(4, -3) and is parallel to the line
GarryVolchara [31]

Answer:

make y the subject first

Step-by-step explanation:

y=5/7(x) -27/7

parallel lines have equal gradient m1=m2

y-y1=m(x-x1)

y-(-3)=5/7(x-4))

y=5/7(x) -20/7 -3

final answer

y=5/7(x) -41/7

3 0
2 years ago
The March family go out for dinner, and their bill comes to $118.40. If they leave a 20% tip, how much is the tip they leave?
erica [24]

Answer:

tip amount = $23.68

Step-by-step explanation:

t = tip percentage (as decimal, so 5% would be 0.05)

c = cost

tip amount = c * t

tip amount = (118.40) * (0.20) = $23.68

hope this helps :)

6 0
2 years ago
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