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3 years ago

You roll a fair 6-sided die.What is P(not 5)?

Mathematics

1 answer:

VLD [36.1K]3 years ago

3 0

5/6 chance not to roll a 5 or 0.833333333

Step-by-step explanation:

a 6 sided die shows 5 once the chance to roll is is 1/6 the change not to roll it is 5/6

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Plz use Differential equation method to solve this:

Oduvanchick [21]

Answer:

Step-by-step explanation:

We have the differential equation $y' = y + \frac{x}{y}$ with initial conditions $y(0)=1$ .

First, notice that the equation can be rewritten as

$y'-y =xy^{-1}$ ,

which is a Bernoulli equation. Once we have recognized the type of the equation we know how to continue. Recall that a Bernoulli equation has the general form

$y'+p(x)y=q(x)y^n$ .

In this particular case we have $n=-1$ . This kind of equation is solved by the change of variable $z=y^{1-n}$ . In our exercise we get $z=y^{1-(-1)}=y^2$ . Now we take derivatives and get

$z'=2yy'$ which es equivalent to $\frac{z'}{2y}=y'$ .

Then, we substitute the value of $y'$ we have obtained in the original equation:

$\frac{z'}{2y}-y = xy^{-1}$ .

The next step is to multiply the whole equation by $2y$ , in order to eliminate the denominator of $z'$ . Thus,

$z' -2y^2=2x$ .

Recall that $y^2=z$ , then

$z' -2z=2x$ .

This last equation is a linear equation, which has general solution

$z(x) = \exp\left(-\int(-2)dx\right)\left(\int 2x \exp\left(\int(-2)dx + C\right)\right)$ .

So, let us calculate the integral that appear in the formula:

$\int(-2)dx = -2x$

$\int 2x e^{-2x}dx = -\frac{\left(2x+1\right)e^{-2x}}{2}$ .

Then, the solution for $z$ is

$z(x) = e^{2x}\left(-\frac{\left(2x+1\right)e^{-2x}}{2} + C\right) = -\frac{\left(2x+1\right)}{2} + Ce^{2x}$ .

Now, we return the change of variable:

$(y(x))^2 =-\frac{\left(2x+1\right)}{2} + Ce^{2x}$ .

The last step is to find the value of the constant $C$ . In order to do this, substitute the initial value:

$(y(0))^2 = 1 =\frac{\left(2\cdot 0+1\right)}{2} + Ce^{2\cdot 0} = -\frac{1}{2} + C$ .

Thus, we have the equation

$1=-\frac{1}{2} + C$ that gives $C=\frac{3}{2}$ .

Therefore,

$(y(x))^2 = -\frac{\left(2x+1\right)}{2} + \frac{3}{2}e^{2x}$ .

8 0

4 years ago

The perimeter of a rectangle is 24cm. The length is two times the width. Write an equation and solve to find the length and widt

stich3 [128]

Idk how to write the equation but I know that the length is 8 and the width is 4 and when you add all these together you get 24cm. AREA: Length x width (8 x 4) and then that would equal 32. Hope that helps sorry if it doesn’t :)

8 0

4 years ago

Alfred has a 30 dollar gift voucher.He plans to buy as many video games as he can.The cost of each game is 10 dollars.There is a

kotykmax [81]

10+2=12 30 divided by 12 = 2.5

5 0

3 years ago

Julian is itemizing deductions on his federal income tax return had 1300 in non reimbursed work expenses last year if his AGE wa

GarryVolchara [31]

Answer: 420

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Need help with this math problem

AysviL [449]

Answer:

CAB = 54

ABC = 21

ACB = 105

DCB = 75

Step-by-step explanation:

18x - 15 = (13x - 11) + (4x + 1)

18x - 15 = 17x - 10

x = 5

CAB = 13x - 11 = 13(5) - 11 = 65 - 11 = 54

ABC = 4x + 1 = 4(5) + 1 = 20 + 1 = 21

ACB = 180 - (CAB + ABC) = 180 - (54 + 21) = 180 - 75 = 105

DCB = 180 - ACB = 180 - 105 = 75

3 0

4 years ago