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3 years ago

What is the probability that a randomly dropped marker will fall in the unshaded region?

Mathematics

2 answers:

statuscvo [17]3 years ago

7 0

The correct answer is 14 by 15

Natasha2012 [34]3 years ago

7 0

It would be 4 out of 64 because thats how many squares there are. If you simplify it, it will be 1/16.

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An electronics store receives a shipment of 35 graphing calculators including 7 that are defective. eight calculators are chosen

spin [16.1K]

There are 23535820 combinations that can be made of 35 calculators taken 8 at a time.

$_{35}C_8=\frac{35!}{8!27!}=23535820$

8 0

3 years ago

Find a particular solution to <img src="https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%20%5Cfrac%7B%20d%5E%7B2%7Dy%20%7D%7Bd%20x%5E%7

Digiron [165]

$y=x^r$
$\implies r(r-1)x^r+6rx^r+4x^r=0$
$\implies r^2+5r+4=(r+1)(r+4)=0$
$\implies r=-1,r=-4$

so the characteristic solution is

$y_c=\dfrac{C_1}x+\dfrac{C_2}{x^4}$

As a guess for the particular solution, let's back up a bit. The reason the choice of $y=x^r$ works for the characteristic solution is that, in the background, we're employing the substitution $t=\ln x$ , so that $y(x)$ is getting replaced with a new function $z(t)$ . Differentiating yields

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac1x\dfrac{\mathrm dz}{\mathrm dt}$
$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac1{x^2}\left(\dfrac{\mathrm d^2z}{\mathrm dt^2}-\dfrac{\mathrm dz}{\mathrm dt}\right)$

Now the ODE in terms of $t$ is linear with constant coefficients, since the coefficients $x^2$ and $x$ will cancel, resulting in the ODE

$\dfrac{\mathrm d^2z}{\mathrm dt^2}+5\dfrac{\mathrm dz}{\mathrm dt}+4z=e^{2t}\sin e^t$

Of coursesin, the characteristic equation will be $r^2+6r+4=0$ , which leads to solutions $C_1e^{-t}+C_2e^{-4t}=C_1x^{-1}+C_2x^{-4}$ , as before.

Now that we have two linearly independent solutions, we can easily find more via variation of parameters. If $z_1,z_2$ are the solutions to the characteristic equation of the ODE in terms of $z$ , then we can find another of the form $z_p=u_1z_1+u_2z_2$ where

$u_1=-\displaystyle\int\frac{z_2e^{2t}\sin e^t}{W(z_1,z_2)}\,\mathrm dt$
$u_2=\displaystyle\int\frac{z_1e^{2t}\sin e^t}{W(z_1,z_2)}\,\mathrm dt$

where $W(z_1,z_2)$ is the Wronskian of the two characteristic solutions. We have

$u_1=-\displaystyle\int\frac{e^{-2t}\sin e^t}{-3e^{-5t}}\,\mathrm dt$
$u_1=\dfrac23(1-2e^{2t})\cos e^t+\dfrac23e^t\sin e^t$

$u_2=\displaystyle\int\frac{e^t\sin e^t}{-3e^{-5t}}\,\mathrm dt$
$u_2=\dfrac13(120-20e^{2t}+e^{4t})e^t\cos e^t-\dfrac13(120-60e^{2t}+5e^{4t})\sin e^t$

$\implies z_p=u_1z_1+u_2z_2$
$\implies z_p=(40e^{-4t}-6)e^{-t}\cos e^t-(1-20e^{-2t}+40e^{-4t})\sin e^t$

and recalling that $t=\ln x\iff e^t=x$ , we have

$\implies y_p=\left(\dfrac{40}{x^3}-\dfrac6x\right)\cos x-\left(1-\dfrac{20}{x^2}+\dfrac{40}{x^4}\right)\sin x$

4 0

3 years ago

A prism is filled with 48 cubes with a side length of 1/2 unit. What is the volume of the prism in cubic units? Please I need he

Aleksandr [31]

Answer:

The volume of the prism is 6 unit³

Step-by-step explanation:

In order to calculate the volume of the prism we first need to calculate the volume of each cube. The volume of a cube is given by the formula below:

volume cube = a³

Where a is the length of the side of the cube. So each cube has a volume of:

volume cube = (1/2)³ = 1/8 unit³

Since the cubes are filling the prism, the volume of the prism is the sum of the volume of all the cubes, in this case 48. Since all the cubes are equal, we can multiply the number of cubes by the volume of one cube in order to calculate the volume of the prism. We have:

volume prism = 48*volume cube

volume prism = 48*(1/8) = 6 unit³

5 0

3 years ago

Solve the formula C=πd for π.

guajiro [1.7K]

Answer:

That means Circumference = PI * diameter

Therefore,

PI = Circumference / diameter

Step-by-step explanation:

4 0

3 years ago

one video rental club charges $25 to become a member and 2.50 to rent each video another charges no membership fee but charges $

ladessa [460]

The total charges for the first club as a function of the number of rentals (x) are

... f1 = 25 + 2.50x

The total charges for the second club are

... f2 = 3.25x

We want to find x so that f1 < f2.

... f1 < f2

... 25 + 2.50x < 3.25x

.. 25 < 0.75x . . . . . . . . . . subtract 2.50x

... 25/0.75 < x . . . . . . . . . divide by the coefficient of x

... 33 1/3 < x

You must rent 34 videos or more to make the first club more economical.

8 0

3 years ago