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Shkiper50 [21]
2 years ago
11

involving flipping a fair coin. Assume that the coin is flipped 9 times. What is the probability that both heads and tails occur

?
Mathematics
1 answer:
alexgriva [62]2 years ago
7 0
The probability would occur 9 times
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Solve the following differential equations or initial value problems. In part (a), leave your answer in implicit form. For parts
shepuryov [24]

Answer:

(a) (y^5)/5 + y^4 = (t^3)/3 + 7t + C

(b) y = arctan(t(lnt - 1) + C)

(c) y = -1/ln|0.09(t + 1)²/t|

Step-by-step explanation:

(a) dy/dt = (t^2 + 7)/(y^4 - 4y^3)

Separate the variables

(y^4 - 4y^3)dy = (t^2 + 7)dt

Integrate both sides

(y^5)/5 + y^4 = (t^3)/3 + 7t + C

(b) dy/dt = (cos²y)lnt

Separate the variables

dy/cos²y = lnt dt

Integrate both sides

tany = t(lnt - 1) + C

y = arctan(t(lnt - 1) + C)

(c) (t² + t) dy/dt + y² = ty², y(1) = -1

(t² + t) dy/dt = ty² - y²

(t² + t) dy/dt = y²(t - 1)

(t² + t)/(t - 1)dy/dt = y²

Separating the variables

(t - 1)dt/(t² + t) = dy/y²

tdt/(t² + t) - dt/(t² + t) = dy/y²

dt/(t + 1) - dt/(t(t + 1)) = dy/y²

dt/(t + 1) - dt/t + dt/(t + 1) = dy/y²

Integrate both sides

ln(t + 1) - lnt + ln(t + 1) + lnC = -1/y

2ln(t + 1) - lnt + lnC = -1/y

ln|C(t + 1)²/t| = -1/y

y = -1/ln|C(t + 1)²/t|

Apply y(1) = -1

-1 = ln|C(1 + 1)²/1|

-1 = ln(4C)

4C = e^(-1)

C = (1/4)e^(-1) ≈ 0.09

y = -1/ln|0.09(t + 1)²/t|

8 0
3 years ago
Solve the system of linear equations.
icang [17]

Answer: The set does not have a solution

Step-by-step explanation:

Adding Equations 1 & 3 we get 5x = 7. This gives x = 7/5

Putting this value of x in eq. 2 we get

-2y + 2z = -1-(7/5) or

2y - 2z = 12/5  or  5y - 5z = 6

Multiplying eq. 1 by 2  we get  

4x + 2y - 2z = 6

adding this with eq. 2 we get 5x = 5 or x = 1

As the common solution for x from equations 1&3 does not satisfy eq. 1&2 it comes out that the three equations do not have a common solution.

Same can be verified by using different sets of two equations also.

7 0
3 years ago
Solve for t in scientific formula d=rt
yarga [219]
The problem is: d=rt
you are solving for r

d=rt
--  --
t    t


you divide both sides by r, so your answer is:

d/t=r or r=d/t

I hope this helped! :))
3 0
3 years ago
In the following equation, a and b are both integers. a(3x-8)=b -18x
zaharov [31]
The value of a is -6
The value of b is 48
8 0
3 years ago
Read 2 more answers
The graph represents y as a function of x . Which additional point can be plotted so that the graph continues to represent y as
tester [92]

Answer:

I think it's the last one D

Step-by-step explanation:

I'm not 100% sure, but I think the x can't repeat and 4 is the only number of x that hasn't been plotted yet. Tell me if it was right?

5 0
2 years ago
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