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3 years ago

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In a certain game of chance, your chances of winning are 0.3. Assume outcomes are independent and that you will play the game fo

ur times. Q: What is the probability that you win at most once

1 answer:

sergeinik [125]3 years ago

3 0

Answer:

0.6517

Step-by-step explanation:

Given that in a certain game of chance, your chances of winning are 0.3.

We know that each game is independent of the other and hence probability of winning any game = 0.3 (constant)

Also there are only two outcomes

Let X be the number of games you win when you play 4 times

Then X is binomial with p = 0.3 and n =4

Required probability

= Probability that you win at most once

= $P(X\leq 1)\\=P(X=0)+P(X=1)$

We have as per binomial theorem

P(X=r) = $nCr p^r (1-p)^{n-r}$

Using the above the required prob

= 0.6517

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Step2247 [10]

Answer:

2

Step-by-step explanation:

it's literally 6-4 = 2

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3 years ago

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Solve these linear equations in the form y=yn+yp with yn=y(0)e^at.

WINSTONCH [101]

Answer:

a) $y(t) = y_{0}e^{4t} + 2$ . It does not have a steady state

b) $y(t) = y_{0}e^{-4t} + 2$ . It has a steady state.

Step-by-step explanation:

a) $y' -4y = -8$

The first step is finding $y_{n}(t)$ . So:

$y' - 4y = 0$

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

$r - 4 = 0$

$r = 4$

So:

$y_{n}(t) = y_{0}e^{4t}$

Since this differential equation has a positive eigenvalue, it does not have a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

So

$(y_{p})' -4(y_{p}) = -8$

$(C)' - 4C = -8$

C is a constant, so (C)' = 0.

$-4C = -8$

$4C = 8$

$C = 2$

The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{4t} + 2$

b) $y' +4y = 8$

The first step is finding $y_{n}(t)$ . So:

$y' + 4y = 0$

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

$r + 4 =$

$r = -4$

So:

$y_{n}(t) = y_{0}e^{-4t}$

Since this differential equation does not have a positive eigenvalue, it has a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

So

$(y_{p})' +4(y_{p}) = 8$

$(C)' + 4C = 8$

C is a constant, so (C)' = 0.

$4C = 8$

$C = 2$

The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{-4t} + 2$

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3 years ago

Complete the transformations below. Then enter the final coordinates of the figure.

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Answer:

Step-by-step explanation:

If a point (x, y) is translated by 4 units horizontally right and 1 unit upwards, coordinates of the image point will be,

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Therefore, vertices of the image triangle ABC will be,

A(2, 2) → A'(2+4, 2+1)

→ A'(6, 3)

B(5, -1) → B'(5+4, -1+1)

→ B'(9, 0)

C(1, -2) → C'(1+4, -2+1)

→ C'(5, -1)

Then reflected across y-axis.

Rule for the reflection across y-axis will be,

(x, y) → (-x, y)

A'(6, 3) → A"(-6, 3)

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3 years ago

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tankabanditka [31]

X = -1/3 should be it

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Y=2/3x+3,2x-3y=8 determine whether perpendicular or parallel

Studentka2010 [4]

<span>Y=2/3x+3 so slope = 2/3

</span><span>2x-3y=8
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so answer: </span><span>parallel</span>

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3 years ago