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3 years ago

Suppose the 13 inch is aware cost $.78 at the same rate how much (in cents) will 33 inches of wire cost

1 answer:

3 0

When comparing to thing with same rate, set up a proportion:
Inches/cost

13/.78=33/x
(13)(x)=(.78)(33) [cross multiplied]
13x=25.74 [simplified]
13/13x=25.74/13 [division property]
x=1.98

33 inches of wire will cost $1.98.

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A class of 10 students hang up their coats when they arrive at school. Just before recess, the teacher hands one coat selected a

Fittoniya [83]

Answer:

0.1274

Step-by-step explanation:

Let X be the random variable that measures the number of children who get their own coat.

Then, the expected value of X is

E[X] = 1P(X=1) + 2P(X=2)+3P(X=3)+...+10P(X=10)

The probability that a child gets her or his coat is

P(X=1) = 1/10

To compute the probability that 2 children get their own coat, we notice that there are 10! possible permutations of coats. The two children can get their coat in only one way, the other 8 coats can be arranged in 8! different positions, so the probability that 2 children get their own coat is

P(X=2) = 8!/10! = 1/(10*9) and

2P(X=2) = 2/(10*9)

Similarly, we can see that the probability that 3 children get their own coat is

P(X=3) = 7!/10! = 1/(10*9*8) and

3P(X=3) = 3/(10*9*8*7)

and the expected value of X would be

E[X] = 1/10 + 2/(10*9) + 3/(10*9*8)+...+10/10! = 0.1274

6 0

2 years ago

48 lbs. equals how many kilograms?

Dahasolnce [82]

Your answer is 21.7724<span>Kilograms</span>

4 0

3 years ago

Read 2 more answers

Alex applies 350 n of force to move his stalled car 40 m how much work did alex do

Katyanochek1 [597]

Step-by-step explanation:

Work done = Force × displacement

= 350 × 40

=14000J

7 0

3 years ago

How would you solve this problem 2/6×3= would you divide or multiply

Rainbow [258]

In the order of operation, multiplying or dividing don't take preference over the other. So with them, you work from left to right.

This means for this question, you first divide, then multiply.

5 0

3 years ago

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Find a particular solution to the nonhomogeneous differential equation y′′+4y=cos(2x)+sin(2x).

I am Lyosha [343]

Take the homogeneous part and find the roots to the characteristic equation:

$y''+4y=0\implies r^2+4=0\implies r=\pm2i$

This means the characteristic solution is $y_c=C_1\cos2x+C_2\sin2x$ .

Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form $y_p=ax\cos2x+bx\sin2x$ . Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.

With $y_1=\cos2x$ and $y_2=\sin2x$ , you're looking for a particular solution of the form $y_p=u_1y_1+u_2y_2$ . The functions $u_i$ satisfy

$u_1=\displaystyle-\int\frac{y_2(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx$
$u_2=\displaystyle\int\frac{y_1(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx$

where $W(y_1,y_2)$ is the Wronskian determinant of the two characteristic solutions.

$W(\cos2x,\sin2x)=\begin{bmatrix}\cos2x&\sin2x\\-2\cos2x&2\sin2x\end{vmatrix}=2$

So you have

$u_1=\displaystyle-\frac12\int(\sin2x(\cos2x+\sin2x))\,\mathrm dx$
$u_1=-\dfrac x4+\dfrac18\cos^22x+\dfrac1{16}\sin4x$

$u_2=\displaystyle\frac12\int(\cos2x(\cos2x+\sin2x))\,\mathrm dx$
$u_2=\dfrac x4-\dfrac18\cos^22x+\dfrac1{16}\sin4x$

So you end up with a solution

$u_1y_1+u_2y_2=\dfrac18\cos2x-\dfrac14x\cos2x+\dfrac14x\sin2x$

but since $\cos2x$ is already accounted for in the characteristic solution, the particular solution is then

$y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x$

so that the general solution is

$y=C_1\cos2x+C_2\sin2x-\dfrac14x\cos2x+\dfrac14x\sin2x$

7 0

3 years ago