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Mice21 [21]
3 years ago
5

A fair coin is tossed 100 times. What is the probability that more than 55 heads are observed?

Mathematics
2 answers:
xeze [42]3 years ago
8 0
P(A)=\frac{100-55}{100}=\frac{45}{100}=\frac{9}{20}
Snezhnost [94]3 years ago
4 0
Let us say T= probability of head turning up = 1/2  in one toss
H = probability of a tail turning up  = 1/2  in one toss

Then P (56 heads or more) =
           1/2^100 [ C(100,56) + C(100,57) + C(100,58) + ....
                         C(100,98) + C(100,99) + C(100,100) ]

   where C(N, R)  =  N ! / [ (N - R)! R! ]    number of occurrances of R formed from
                             N tosses.


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In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t 2 , 2 + t − 5t 2 , 1 + 2t} to the standard basis of P2.
Serjik [45]

Complete Question:

In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t² , 2+t− 5t² , 1 + 2t} to the standard basis C = {1, t, t²}. Then, write t² as a linear combination of the polynomials in B.

Answer:

The change of coordinate matrix is :

M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right]

U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]

Step-by-step explanation:

Let U =  {D, E, F} be any vector with respect to Basis B

U = D [1 − 3t²] + E [2+t− 5t²] + F[1 + 2t]..............(*)

U = [D+2E+F]+ t[E+2F] + t²[-3D-5E]...................(**)

In Matrix form;

\left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right] \left[\begin{array}{ccc}D\\E\\F\end{array}\right] = \left[\begin{array}{ccc}D+2E+F\\E+2F\\-3D-5E\end{array}\right]

The change of coordinate matrix is therefore,

M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right]

To find D, E, F in (**) such that U = t²

D + 2E + F = 0.................(1)

E + 2F = 0.........................(2)

-3D -5E = 1........................(3)

Substituting eqn (2) into eqn (1 )

D=3F...................................(4)

Substituting equations (2) and (4) into eqn (3)

-9F+10F=1

F = 1

Put the value of F into equations (2) and (4)

E = -2(1) = -2

D = 3(1) = 3

Substituting the values of D, E, and F into (*)

U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]

3 0
2 years ago
If the numbers below were ordered from least to greatest, which number could you use to replace the blank? 0.20,2/5 □ , 3/4,8/10
faust18 [17]
1/2 would work for the blank space

because as shown in the image you could relate it to a whole for each one and put it to 100 to figure out what the blank could be

the 0.20 can be converted to 1/5 so that way you can put everything into the 100 group

8 0
3 years ago
Evaluate the radical.<br><br> 64−−√3
IrinaK [193]
It Wil be 73 U will have to put it ❤
5 0
3 years ago
Read 2 more answers
Salazar is driving 70 miles per hour. At this rate, how long will it take for him to travel 840 miles?
Kisachek [45]

Answer:

12 hours

Step-by-step explanation:

Step 1:

70 : 1             Ratio

Step 2:

70 : 1 = 840 : x       Equation

Step 3:

840 = 70x      Multiply

Step 4:

x = 840 ÷ 70      Divide

Answer:

12 hours

Hope This Helps :)

4 0
3 years ago
PLZZZZZ HELP ME! :) XDDD
Taya2010 [7]
 In order to figure out what the answer is you would have to divide the number of feet it fell by the time. If you do 35.75 divided by 3.25 it would be 11. 
So the answer most likely would be 11
Please correct me if I am wrong
Have a great day!
4 0
3 years ago
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