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Artist 52 [7]
2 years ago
10

The increasing annual cost (including tuition, room, board, books and fees) to attend college ) to attend college has been widel

y discussed in many publications including Money magazine. The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars. Click on the datafile logo to reference the data. Round degrees of freedom to the preceding whole number.
Private Colleges
52.8 43.2 45.0 33.3 44.0
30.6 45.8 37.8 50.5 42.0
Public Colleges
20.3 22.0 28.2 15.6 24.1 28.5
22.8 25.8 18.5 25.6 14.4 21.8
(a) Compute the sample mean and sample standard deviation for private and public colleges. Round your answers to two decimal places.
ample mean $ thousand sample standard deviation $ thousand
Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for public colleges. (Round the standard deviation to two decimal places.)
sample mean $ thousand sample standard deviation $ thousand
(b) What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private − Public.)
$ thousand
Interpret this value in terms of the annual cost (in dollars) of attending private and public colleges.
We estimate that the mean annual cost to attend private colleges is $ more than the mean annual cost to attend public college
(c) Develop a 95% confidence interval (in thousand dollars) of the difference between the mean annual cost of attending private and public colleges. (Use Private − Public. Round your answers to one decimal place.)
$ thousand to $ thousand
Mathematics
1 answer:
Karolina [17]2 years ago
4 0
I think it’s a carrot
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Find dy/dx by implicit differentiation for ysin(y) = xcos(x)
tatyana61 [14]

Answer:

\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}

Step-by-step explanation:

So we have:

y\sin(y)=x\cos(x)

And we want to find dy/dx.

So, let's take the derivative of both sides with respect to x:

\frac{d}{dx}[y\sin(y)]=\frac{d}{dx}[x\cos(x)]

Let's do each side individually.

Left Side:

We have:

\frac{d}{dx}[y\sin(y)]

We can use the product rule:

(uv)'=u'v+uv'

So, our derivative is:

=\frac{d}{dx}[y]\sin(y)+y\frac{d}{dx}[\sin(y)]

We must implicitly differentiate for y. This gives us:

=\frac{dy}{dx}\sin(y)+y\frac{d}{dx}[\sin(y)]

For the sin(y), we need to use the chain rule:

u(v(x))'=u'(v(x))\cdot v'(x)

Our u(x) is sin(x) and our v(x) is y. So, u'(x) is cos(x) and v'(x) is dy/dx.

So, our derivative is:

=\frac{dy}{dx}\sin(y)+y(\cos(y)\cdot\frac{dy}{dx}})

Simplify:

=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}

And we are done for the right.

Right Side:

We have:

\frac{d}{dx}[x\cos(x)]

This will be significantly easier since it's just x like normal.

Again, let's use the product rule:

=\frac{d}{dx}[x]\cos(x)+x\frac{d}{dx}[\cos(x)]

Differentiate:

=\cos(x)-x\sin(x)

So, our entire equation is:

=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}=\cos(x)-x\sin(x)

To find our derivative, we need to solve for dy/dx. So, let's factor out a dy/dx from the left. This yields:

\frac{dy}{dx}(\sin(y)+y\cos(y))=\cos(x)-x\sin(x)

Finally, divide everything by the expression inside the parentheses to obtain our derivative:

\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}

And we're done!

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2 years ago
Write whether the scenario represents a linear function or an exponential function? Explain why.
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The scenario represents a linear function. The rate is at a constant increase therefore it is linear.

Linear because it’s a constant rate

Since it’s doubled, and doesn’t go at a constant rate, it is a exponential function

Exponential since it increases by a multiplicative rate. It’s not constant
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2 years ago
Y = x^2+ 7x - 5 can be written in the form y = (x + a)^2+b
BARSIC [14]

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = (x - h)² + k (h, k) are the coordinates of the vertex

Given y = x² + 7x - 5

To express in vertex form use the method of completing the square

add/subtract ( half the coefficient of the x- term )²

y = x² + 2( \frac{7}{2} )x +\frac{49}{4} - \frac{49}{4} - 5

y = (x + \frac{7}{2} )² - \frac{49}{4} - \frac{20}{4}

y = (x + \frac{7}{2} )² - \frac{69}{4}

Hence

a = \frac{7}{2} and b = - \frac{69}{4}

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3 years ago
The equation x^3+x^2+ax-4=0 has one root equal to -2. Find the value of a.​
Vedmedyk [2.9K]

Answer:

a = - 4

Step-by-step explanation:

Given x = - 2 is a root then f(- 2) = 0

f(x) = x³ + x² + ax - 4, thus

f(- 2) = (- 2)³ + (- 2)² - 2a - 4 = 0, that is

f(- 2) = - 8 + 4 - 2a - 4 = 0, thus

- 8 - 2a = 0 ( add 8 to both sides )

- 2a = 8 ( divide both sides by - 2 )

a = - 4

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